541.82/241.23 MAYBE 541.82/241.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 541.82/241.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 541.82/241.25 541.82/241.25 541.82/241.25 Outermost Termination of the given OTRS could not be shown: 541.82/241.25 541.82/241.25 (0) OTRS 541.82/241.25 (1) Thiemann-SpecialC-Transformation [EQUIVALENT, 0 ms] 541.82/241.25 (2) QTRS 541.82/241.25 (3) QTRSRRRProof [EQUIVALENT, 101 ms] 541.82/241.25 (4) QTRS 541.82/241.25 (5) DependencyPairsProof [EQUIVALENT, 0 ms] 541.82/241.25 (6) QDP 541.82/241.25 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (8) AND 541.82/241.25 (9) QDP 541.82/241.25 (10) UsableRulesProof [EQUIVALENT, 0 ms] 541.82/241.25 (11) QDP 541.82/241.25 (12) QReductionProof [EQUIVALENT, 0 ms] 541.82/241.25 (13) QDP 541.82/241.25 (14) UsableRulesReductionPairsProof [EQUIVALENT, 29 ms] 541.82/241.25 (15) QDP 541.82/241.25 (16) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (17) TRUE 541.82/241.25 (18) QDP 541.82/241.25 (19) UsableRulesProof [EQUIVALENT, 0 ms] 541.82/241.25 (20) QDP 541.82/241.25 (21) QReductionProof [EQUIVALENT, 0 ms] 541.82/241.25 (22) QDP 541.82/241.25 (23) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (24) QDP 541.82/241.25 (25) QDPOrderProof [EQUIVALENT, 11 ms] 541.82/241.25 (26) QDP 541.82/241.25 (27) UsableRulesProof [EQUIVALENT, 0 ms] 541.82/241.25 (28) QDP 541.82/241.25 (29) QReductionProof [EQUIVALENT, 0 ms] 541.82/241.25 (30) QDP 541.82/241.25 (31) Trivial-Transformation [SOUND, 0 ms] 541.82/241.25 (32) QTRS 541.82/241.25 (33) QTRSRRRProof [EQUIVALENT, 85 ms] 541.82/241.25 (34) QTRS 541.82/241.25 (35) DependencyPairsProof [EQUIVALENT, 0 ms] 541.82/241.25 (36) QDP 541.82/241.25 (37) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (38) AND 541.82/241.25 (39) QDP 541.82/241.25 (40) UsableRulesProof [EQUIVALENT, 0 ms] 541.82/241.25 (41) QDP 541.82/241.25 (42) NonTerminationLoopProof [COMPLETE, 0 ms] 541.82/241.25 (43) NO 541.82/241.25 (44) QDP 541.82/241.25 (45) UsableRulesProof [EQUIVALENT, 0 ms] 541.82/241.25 (46) QDP 541.82/241.25 (47) NonTerminationLoopProof [COMPLETE, 0 ms] 541.82/241.25 (48) NO 541.82/241.25 (49) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] 541.82/241.25 (50) QTRS 541.82/241.25 (51) QTRSRRRProof [EQUIVALENT, 1116 ms] 541.82/241.25 (52) QTRS 541.82/241.25 (53) AAECC Innermost [EQUIVALENT, 831 ms] 541.82/241.25 (54) QTRS 541.82/241.25 (55) DependencyPairsProof [EQUIVALENT, 296 ms] 541.82/241.25 (56) QDP 541.82/241.25 (57) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (58) AND 541.82/241.25 (59) QDP 541.82/241.25 (60) UsableRulesProof [EQUIVALENT, 0 ms] 541.82/241.25 (61) QDP 541.82/241.25 (62) QReductionProof [EQUIVALENT, 0 ms] 541.82/241.25 (63) QDP 541.82/241.25 (64) QDPSizeChangeProof [EQUIVALENT, 0 ms] 541.82/241.25 (65) YES 541.82/241.25 (66) QDP 541.82/241.25 (67) UsableRulesProof [EQUIVALENT, 0 ms] 541.82/241.25 (68) QDP 541.82/241.25 (69) QReductionProof [EQUIVALENT, 97 ms] 541.82/241.25 (70) QDP 541.82/241.25 (71) TransformationProof [EQUIVALENT, 296 ms] 541.82/241.25 (72) QDP 541.82/241.25 (73) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (74) QDP 541.82/241.25 (75) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (76) QDP 541.82/241.25 (77) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (78) QDP 541.82/241.25 (79) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (80) QDP 541.82/241.25 (81) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (82) QDP 541.82/241.25 (83) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (84) QDP 541.82/241.25 (85) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (86) QDP 541.82/241.25 (87) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (88) QDP 541.82/241.25 (89) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (90) QDP 541.82/241.25 (91) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (92) QDP 541.82/241.25 (93) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (94) QDP 541.82/241.25 (95) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (96) QDP 541.82/241.25 (97) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (98) QDP 541.82/241.25 (99) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (100) QDP 541.82/241.25 (101) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (102) QDP 541.82/241.25 (103) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (104) QDP 541.82/241.25 (105) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (106) QDP 541.82/241.25 (107) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (108) QDP 541.82/241.25 (109) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (110) QDP 541.82/241.25 (111) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (112) QDP 541.82/241.25 (113) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (114) QDP 541.82/241.25 (115) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (116) QDP 541.82/241.25 (117) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (118) QDP 541.82/241.25 (119) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (120) QDP 541.82/241.25 (121) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (122) QDP 541.82/241.25 (123) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (124) QDP 541.82/241.25 (125) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (126) QDP 541.82/241.25 (127) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (128) QDP 541.82/241.25 (129) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (130) QDP 541.82/241.25 (131) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (132) QDP 541.82/241.25 (133) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (134) QDP 541.82/241.25 (135) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (136) QDP 541.82/241.25 (137) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (138) QDP 541.82/241.25 (139) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (140) QDP 541.82/241.25 (141) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (142) QDP 541.82/241.25 (143) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (144) QDP 541.82/241.25 (145) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (146) QDP 541.82/241.25 (147) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (148) QDP 541.82/241.25 (149) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (150) QDP 541.82/241.25 (151) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (152) QDP 541.82/241.25 (153) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (154) QDP 541.82/241.25 (155) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (156) QDP 541.82/241.25 (157) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (158) QDP 541.82/241.25 (159) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (160) QDP 541.82/241.25 (161) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (162) QDP 541.82/241.25 (163) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (164) QDP 541.82/241.25 (165) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (166) QDP 541.82/241.25 (167) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (168) QDP 541.82/241.25 (169) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (170) QDP 541.82/241.25 (171) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (172) QDP 541.82/241.25 (173) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (174) QDP 541.82/241.25 (175) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (176) QDP 541.82/241.25 (177) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (178) QDP 541.82/241.25 (179) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (180) QDP 541.82/241.25 (181) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (182) QDP 541.82/241.25 (183) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (184) QDP 541.82/241.25 (185) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (186) QDP 541.82/241.25 (187) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (188) QDP 541.82/241.25 (189) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (190) QDP 541.82/241.25 (191) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (192) QDP 541.82/241.25 (193) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (194) QDP 541.82/241.25 (195) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (196) QDP 541.82/241.25 (197) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (198) QDP 541.82/241.25 (199) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (200) QDP 541.82/241.25 (201) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (202) QDP 541.82/241.25 (203) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (204) QDP 541.82/241.25 (205) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (206) QDP 541.82/241.25 (207) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (208) QDP 541.82/241.25 (209) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (210) QDP 541.82/241.25 (211) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (212) QDP 541.82/241.25 (213) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (214) QDP 541.82/241.25 (215) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (216) QDP 541.82/241.25 (217) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (218) QDP 541.82/241.25 (219) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (220) QDP 541.82/241.25 (221) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (222) QDP 541.82/241.25 (223) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (224) QDP 541.82/241.25 (225) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (226) QDP 541.82/241.25 (227) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (228) QDP 541.82/241.25 (229) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (230) QDP 541.82/241.25 (231) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (232) QDP 541.82/241.25 (233) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (234) QDP 541.82/241.25 (235) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (236) QDP 541.82/241.25 (237) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (238) QDP 541.82/241.25 (239) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (240) QDP 541.82/241.25 (241) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (242) QDP 541.82/241.25 (243) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (244) QDP 541.82/241.25 (245) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (246) QDP 541.82/241.25 (247) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (248) QDP 541.82/241.25 (249) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (250) QDP 541.82/241.25 (251) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (252) QDP 541.82/241.25 (253) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (254) QDP 541.82/241.25 (255) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (256) QDP 541.82/241.25 (257) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (258) QDP 541.82/241.25 (259) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (260) QDP 541.82/241.25 (261) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (262) QDP 541.82/241.25 (263) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (264) QDP 541.82/241.25 (265) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (266) QDP 541.82/241.25 (267) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (268) QDP 541.82/241.25 (269) TransformationProof [EQUIVALENT, 3 ms] 541.82/241.25 (270) QDP 541.82/241.25 (271) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (272) QDP 541.82/241.25 (273) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (274) QDP 541.82/241.25 (275) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (276) QDP 541.82/241.25 (277) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (278) QDP 541.82/241.25 (279) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (280) QDP 541.82/241.25 (281) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (282) QDP 541.82/241.25 (283) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (284) QDP 541.82/241.25 (285) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (286) QDP 541.82/241.25 (287) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (288) QDP 541.82/241.25 (289) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (290) QDP 541.82/241.25 (291) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (292) QDP 541.82/241.25 (293) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (294) QDP 541.82/241.25 (295) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (296) QDP 541.82/241.25 (297) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (298) QDP 541.82/241.25 (299) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (300) QDP 541.82/241.25 (301) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (302) QDP 541.82/241.25 (303) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (304) QDP 541.82/241.25 (305) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (306) QDP 541.82/241.25 (307) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (308) QDP 541.82/241.25 (309) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (310) QDP 541.82/241.25 (311) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (312) QDP 541.82/241.25 (313) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (314) QDP 541.82/241.25 (315) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (316) QDP 541.82/241.25 (317) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (318) QDP 541.82/241.25 (319) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (320) QDP 541.82/241.25 (321) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (322) QDP 541.82/241.25 (323) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (324) QDP 541.82/241.25 (325) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (326) QDP 541.82/241.25 (327) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (328) QDP 541.82/241.25 (329) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (330) QDP 541.82/241.25 (331) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (332) QDP 541.82/241.25 (333) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (334) QDP 541.82/241.25 (335) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (336) QDP 541.82/241.25 (337) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (338) QDP 541.82/241.25 (339) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (340) QDP 541.82/241.25 (341) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (342) QDP 541.82/241.25 (343) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (344) QDP 541.82/241.25 (345) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (346) QDP 541.82/241.25 (347) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (348) QDP 541.82/241.25 (349) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (350) QDP 541.82/241.25 (351) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (352) QDP 541.82/241.25 (353) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (354) QDP 541.82/241.25 (355) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (356) QDP 541.82/241.25 (357) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (358) QDP 541.82/241.25 (359) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (360) QDP 541.82/241.25 (361) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (362) QDP 541.82/241.25 (363) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (364) QDP 541.82/241.25 (365) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (366) QDP 541.82/241.25 (367) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (368) QDP 541.82/241.25 (369) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (370) QDP 541.82/241.25 (371) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (372) QDP 541.82/241.25 (373) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (374) QDP 541.82/241.25 (375) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (376) QDP 541.82/241.25 (377) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (378) QDP 541.82/241.25 (379) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (380) QDP 541.82/241.25 (381) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (382) QDP 541.82/241.25 (383) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (384) QDP 541.82/241.25 (385) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (386) QDP 541.82/241.25 (387) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (388) QDP 541.82/241.25 (389) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (390) QDP 541.82/241.25 (391) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (392) QDP 541.82/241.25 (393) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (394) QDP 541.82/241.25 (395) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (396) QDP 541.82/241.25 (397) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (398) QDP 541.82/241.25 (399) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (400) QDP 541.82/241.25 (401) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (402) QDP 541.82/241.25 (403) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (404) QDP 541.82/241.25 (405) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (406) QDP 541.82/241.25 (407) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (408) QDP 541.82/241.25 (409) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (410) QDP 541.82/241.25 (411) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (412) QDP 541.82/241.25 (413) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (414) QDP 541.82/241.25 (415) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (416) QDP 541.82/241.25 (417) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (418) QDP 541.82/241.25 (419) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (420) QDP 541.82/241.25 (421) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (422) QDP 541.82/241.25 (423) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (424) QDP 541.82/241.25 (425) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (426) QDP 541.82/241.25 (427) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (428) QDP 541.82/241.25 (429) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (430) QDP 541.82/241.25 (431) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (432) QDP 541.82/241.25 (433) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (434) QDP 541.82/241.25 (435) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (436) QDP 541.82/241.25 (437) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (438) QDP 541.82/241.25 (439) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (440) QDP 541.82/241.25 (441) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (442) QDP 541.82/241.25 (443) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (444) QDP 541.82/241.25 (445) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (446) QDP 541.82/241.25 (447) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (448) QDP 541.82/241.25 (449) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (450) QDP 541.82/241.25 (451) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (452) QDP 541.82/241.25 (453) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (454) QDP 541.82/241.25 (455) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (456) QDP 541.82/241.25 (457) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (458) QDP 541.82/241.25 (459) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (460) QDP 541.82/241.25 (461) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (462) QDP 541.82/241.25 (463) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (464) QDP 541.82/241.25 (465) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (466) QDP 541.82/241.25 (467) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (468) QDP 541.82/241.25 (469) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (470) QDP 541.82/241.25 (471) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (472) QDP 541.82/241.25 (473) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (474) QDP 541.82/241.25 (475) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (476) QDP 541.82/241.25 (477) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (478) QDP 541.82/241.25 (479) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (480) QDP 541.82/241.25 (481) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (482) QDP 541.82/241.25 (483) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (484) QDP 541.82/241.25 (485) TransformationProof [EQUIVALENT, 3 ms] 541.82/241.25 (486) QDP 541.82/241.25 (487) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (488) QDP 541.82/241.25 (489) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (490) QDP 541.82/241.25 (491) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (492) QDP 541.82/241.25 (493) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (494) QDP 541.82/241.25 (495) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (496) QDP 541.82/241.25 (497) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (498) QDP 541.82/241.25 (499) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (500) QDP 541.82/241.25 (501) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (502) QDP 541.82/241.25 (503) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (504) QDP 541.82/241.25 (505) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (506) QDP 541.82/241.25 (507) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (508) QDP 541.82/241.25 (509) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (510) QDP 541.82/241.25 (511) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (512) QDP 541.82/241.25 (513) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (514) QDP 541.82/241.25 (515) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (516) QDP 541.82/241.25 (517) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (518) QDP 541.82/241.25 (519) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (520) QDP 541.82/241.25 (521) TransformationProof [EQUIVALENT, 3 ms] 541.82/241.25 (522) QDP 541.82/241.25 (523) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (524) QDP 541.82/241.25 (525) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (526) QDP 541.82/241.25 (527) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (528) QDP 541.82/241.25 (529) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (530) QDP 541.82/241.25 (531) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (532) QDP 541.82/241.25 (533) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (534) QDP 541.82/241.25 (535) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (536) QDP 541.82/241.25 (537) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (538) QDP 541.82/241.25 (539) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (540) QDP 541.82/241.25 (541) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (542) QDP 541.82/241.25 (543) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (544) QDP 541.82/241.25 (545) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (546) QDP 541.82/241.25 (547) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (548) QDP 541.82/241.25 (549) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (550) QDP 541.82/241.25 (551) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (552) QDP 541.82/241.25 (553) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (554) QDP 541.82/241.25 (555) TransformationProof [EQUIVALENT, 4 ms] 541.82/241.25 (556) QDP 541.82/241.25 (557) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (558) QDP 541.82/241.25 (559) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (560) QDP 541.82/241.25 (561) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (562) QDP 541.82/241.25 (563) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (564) QDP 541.82/241.25 (565) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (566) QDP 541.82/241.25 (567) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (568) QDP 541.82/241.25 (569) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (570) QDP 541.82/241.25 (571) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (572) QDP 541.82/241.25 (573) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (574) QDP 541.82/241.25 (575) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (576) QDP 541.82/241.25 (577) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (578) QDP 541.82/241.25 (579) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (580) QDP 541.82/241.25 (581) TransformationProof [EQUIVALENT, 4 ms] 541.82/241.25 (582) QDP 541.82/241.25 (583) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (584) QDP 541.82/241.25 (585) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (586) QDP 541.82/241.25 (587) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (588) QDP 541.82/241.25 (589) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (590) QDP 541.82/241.25 (591) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (592) QDP 541.82/241.25 (593) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (594) QDP 541.82/241.25 (595) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (596) QDP 541.82/241.25 (597) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (598) QDP 541.82/241.25 (599) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (600) QDP 541.82/241.25 (601) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (602) QDP 541.82/241.25 (603) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (604) QDP 541.82/241.25 (605) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (606) QDP 541.82/241.25 (607) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (608) QDP 541.82/241.25 (609) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (610) QDP 541.82/241.25 (611) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (612) QDP 541.82/241.25 (613) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (614) QDP 541.82/241.25 (615) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (616) QDP 541.82/241.25 (617) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (618) QDP 541.82/241.25 (619) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (620) QDP 541.82/241.25 (621) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (622) QDP 541.82/241.25 (623) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (624) QDP 541.82/241.25 (625) TransformationProof [EQUIVALENT, 2 ms] 541.82/241.25 (626) QDP 541.82/241.25 (627) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (628) QDP 541.82/241.25 (629) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (630) QDP 541.82/241.25 (631) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (632) QDP 541.82/241.25 (633) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (634) QDP 541.82/241.25 (635) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (636) QDP 541.82/241.25 (637) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (638) QDP 541.82/241.25 (639) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (640) QDP 541.82/241.25 (641) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (642) QDP 541.82/241.25 (643) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (644) QDP 541.82/241.25 (645) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (646) QDP 541.82/241.25 (647) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (648) QDP 541.82/241.25 (649) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (650) QDP 541.82/241.25 (651) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (652) QDP 541.82/241.25 (653) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (654) QDP 541.82/241.25 (655) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (656) QDP 541.82/241.25 (657) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (658) QDP 541.82/241.25 (659) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (660) QDP 541.82/241.25 (661) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (662) QDP 541.82/241.25 (663) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (664) QDP 541.82/241.25 (665) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (666) QDP 541.82/241.25 (667) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (668) QDP 541.82/241.25 (669) TransformationProof [EQUIVALENT, 4 ms] 541.82/241.25 (670) QDP 541.82/241.25 (671) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (672) QDP 541.82/241.25 (673) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (674) QDP 541.82/241.25 (675) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (676) QDP 541.82/241.25 (677) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (678) QDP 541.82/241.25 (679) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (680) QDP 541.82/241.25 (681) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (682) QDP 541.82/241.25 (683) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (684) QDP 541.82/241.25 (685) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (686) QDP 541.82/241.25 (687) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (688) QDP 541.82/241.25 (689) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (690) QDP 541.82/241.25 (691) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (692) QDP 541.82/241.25 (693) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (694) QDP 541.82/241.25 (695) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (696) QDP 541.82/241.25 (697) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (698) QDP 541.82/241.25 (699) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (700) QDP 541.82/241.25 (701) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (702) QDP 541.82/241.25 (703) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (704) QDP 541.82/241.25 (705) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (706) QDP 541.82/241.25 (707) TransformationProof [EQUIVALENT, 1 ms] 541.82/241.25 (708) QDP 541.82/241.25 (709) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (710) QDP 541.82/241.25 (711) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (712) QDP 541.82/241.25 (713) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (714) QDP 541.82/241.25 (715) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (716) QDP 541.82/241.25 (717) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (718) QDP 541.82/241.25 (719) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (720) QDP 541.82/241.25 (721) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (722) QDP 541.82/241.25 (723) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (724) QDP 541.82/241.25 (725) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (726) QDP 541.82/241.25 (727) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (728) QDP 541.82/241.25 (729) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (730) QDP 541.82/241.25 (731) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (732) QDP 541.82/241.25 (733) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (734) QDP 541.82/241.25 (735) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (736) QDP 541.82/241.25 (737) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (738) QDP 541.82/241.25 (739) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (740) QDP 541.82/241.25 (741) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (742) QDP 541.82/241.25 (743) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (744) QDP 541.82/241.25 (745) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (746) QDP 541.82/241.25 (747) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (748) QDP 541.82/241.25 (749) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (750) QDP 541.82/241.25 (751) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (752) QDP 541.82/241.25 (753) TransformationProof [EQUIVALENT, 1 ms] 541.82/241.25 (754) QDP 541.82/241.25 (755) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (756) QDP 541.82/241.25 (757) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (758) QDP 541.82/241.25 (759) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (760) QDP 541.82/241.25 (761) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (762) QDP 541.82/241.25 (763) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (764) QDP 541.82/241.25 (765) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (766) QDP 541.82/241.25 (767) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (768) QDP 541.82/241.25 (769) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (770) QDP 541.82/241.25 (771) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (772) QDP 541.82/241.25 (773) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (774) QDP 541.82/241.25 (775) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (776) QDP 541.82/241.25 (777) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (778) QDP 541.82/241.25 (779) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (780) QDP 541.82/241.25 (781) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (782) QDP 541.82/241.25 (783) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (784) QDP 541.82/241.25 (785) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (786) QDP 541.82/241.25 (787) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (788) QDP 541.82/241.25 (789) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (790) QDP 541.82/241.25 (791) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (792) QDP 541.82/241.25 (793) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (794) QDP 541.82/241.25 (795) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (796) QDP 541.82/241.25 (797) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (798) QDP 541.82/241.25 (799) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (800) QDP 541.82/241.25 (801) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (802) QDP 541.82/241.25 (803) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (804) QDP 541.82/241.25 (805) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (806) QDP 541.82/241.25 (807) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (808) QDP 541.82/241.25 (809) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (810) QDP 541.82/241.25 (811) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (812) QDP 541.82/241.25 (813) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (814) QDP 541.82/241.25 (815) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (816) QDP 541.82/241.25 (817) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (818) QDP 541.82/241.25 (819) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (820) QDP 541.82/241.25 (821) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (822) QDP 541.82/241.25 (823) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (824) QDP 541.82/241.25 (825) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (826) QDP 541.82/241.25 (827) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (828) QDP 541.82/241.25 (829) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (830) QDP 541.82/241.25 (831) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (832) QDP 541.82/241.25 (833) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (834) QDP 541.82/241.25 (835) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (836) QDP 541.82/241.25 (837) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (838) QDP 541.82/241.25 (839) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (840) QDP 541.82/241.25 (841) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (842) QDP 541.82/241.25 (843) TransformationProof [EQUIVALENT, 1 ms] 541.82/241.25 (844) QDP 541.82/241.25 (845) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (846) QDP 541.82/241.25 (847) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (848) QDP 541.82/241.25 (849) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (850) QDP 541.82/241.25 (851) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (852) QDP 541.82/241.25 (853) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (854) QDP 541.82/241.25 (855) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (856) QDP 541.82/241.25 (857) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (858) QDP 541.82/241.25 (859) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (860) QDP 541.82/241.25 (861) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (862) QDP 541.82/241.25 (863) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (864) QDP 541.82/241.25 (865) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (866) QDP 541.82/241.25 (867) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (868) QDP 541.82/241.25 (869) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (870) QDP 541.82/241.25 (871) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (872) QDP 541.82/241.25 (873) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (874) QDP 541.82/241.25 (875) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (876) QDP 541.82/241.25 (877) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (878) QDP 541.82/241.25 (879) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (880) QDP 541.82/241.25 (881) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (882) QDP 541.82/241.25 (883) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (884) QDP 541.82/241.25 (885) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (886) QDP 541.82/241.25 (887) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (888) QDP 541.82/241.25 (889) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (890) QDP 541.82/241.25 (891) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (892) QDP 541.82/241.25 (893) TransformationProof [EQUIVALENT, 1 ms] 541.82/241.25 (894) QDP 541.82/241.25 (895) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (896) QDP 541.82/241.25 (897) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (898) QDP 541.82/241.25 (899) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (900) QDP 541.82/241.25 (901) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (902) QDP 541.82/241.25 (903) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (904) QDP 541.82/241.25 (905) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (906) QDP 541.82/241.25 (907) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (908) QDP 541.82/241.25 (909) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (910) QDP 541.82/241.25 (911) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (912) QDP 541.82/241.25 (913) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (914) QDP 541.82/241.25 (915) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (916) QDP 541.82/241.25 (917) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (918) QDP 541.82/241.25 (919) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (920) QDP 541.82/241.25 (921) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (922) QDP 541.82/241.25 (923) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (924) QDP 541.82/241.25 (925) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (926) QDP 541.82/241.25 (927) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (928) QDP 541.82/241.25 (929) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (930) QDP 541.82/241.25 (931) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (932) QDP 541.82/241.25 (933) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (934) QDP 541.82/241.25 (935) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (936) QDP 541.82/241.25 (937) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (938) QDP 541.82/241.25 (939) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (940) QDP 541.82/241.25 (941) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (942) QDP 541.82/241.25 (943) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (944) QDP 541.82/241.25 (945) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (946) QDP 541.82/241.25 (947) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (948) QDP 541.82/241.25 (949) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (950) QDP 541.82/241.25 (951) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (952) QDP 541.82/241.25 (953) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (954) QDP 541.82/241.25 (955) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (956) QDP 541.82/241.25 (957) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (958) QDP 541.82/241.25 (959) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (960) QDP 541.82/241.25 (961) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (962) QDP 541.82/241.25 (963) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (964) QDP 541.82/241.25 (965) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (966) QDP 541.82/241.25 (967) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (968) QDP 541.82/241.25 (969) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (970) QDP 541.82/241.25 (971) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (972) QDP 541.82/241.25 (973) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (974) QDP 541.82/241.25 (975) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (976) QDP 541.82/241.25 (977) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (978) QDP 541.82/241.25 (979) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (980) QDP 541.82/241.25 (981) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (982) QDP 541.82/241.25 (983) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (984) QDP 541.82/241.25 (985) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (986) QDP 541.82/241.25 (987) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (988) QDP 541.82/241.25 (989) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (990) QDP 541.82/241.25 (991) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (992) QDP 541.82/241.25 (993) TransformationProof [EQUIVALENT, 3 ms] 541.82/241.25 (994) QDP 541.82/241.25 (995) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (996) QDP 541.82/241.25 (997) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (998) QDP 541.82/241.25 (999) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1000) QDP 541.82/241.25 (1001) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1002) QDP 541.82/241.25 (1003) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1004) QDP 541.82/241.25 (1005) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1006) QDP 541.82/241.25 (1007) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1008) QDP 541.82/241.25 (1009) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1010) QDP 541.82/241.25 (1011) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1012) QDP 541.82/241.25 (1013) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1014) QDP 541.82/241.25 (1015) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1016) QDP 541.82/241.25 (1017) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1018) QDP 541.82/241.25 (1019) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1020) QDP 541.82/241.25 (1021) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1022) QDP 541.82/241.25 (1023) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1024) QDP 541.82/241.25 (1025) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1026) QDP 541.82/241.25 (1027) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1028) QDP 541.82/241.25 (1029) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1030) QDP 541.82/241.25 (1031) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1032) QDP 541.82/241.25 (1033) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1034) QDP 541.82/241.25 (1035) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1036) QDP 541.82/241.25 (1037) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1038) QDP 541.82/241.25 (1039) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1040) QDP 541.82/241.25 (1041) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1042) QDP 541.82/241.25 (1043) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1044) QDP 541.82/241.25 (1045) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1046) QDP 541.82/241.25 (1047) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1048) QDP 541.82/241.25 (1049) TransformationProof [EQUIVALENT, 1 ms] 541.82/241.25 (1050) QDP 541.82/241.25 (1051) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1052) QDP 541.82/241.25 (1053) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1054) QDP 541.82/241.25 (1055) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1056) QDP 541.82/241.25 (1057) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1058) QDP 541.82/241.25 (1059) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1060) QDP 541.82/241.25 (1061) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1062) QDP 541.82/241.25 (1063) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1064) QDP 541.82/241.25 (1065) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1066) QDP 541.82/241.25 (1067) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1068) QDP 541.82/241.25 (1069) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1070) QDP 541.82/241.25 (1071) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1072) QDP 541.82/241.25 (1073) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1074) QDP 541.82/241.25 (1075) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1076) QDP 541.82/241.25 (1077) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1078) QDP 541.82/241.25 (1079) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1080) QDP 541.82/241.25 (1081) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1082) QDP 541.82/241.25 (1083) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1084) QDP 541.82/241.25 (1085) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1086) QDP 541.82/241.25 (1087) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1088) QDP 541.82/241.25 (1089) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1090) QDP 541.82/241.25 (1091) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1092) QDP 541.82/241.25 (1093) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1094) QDP 541.82/241.25 (1095) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1096) QDP 541.82/241.25 (1097) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1098) QDP 541.82/241.25 (1099) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1100) QDP 541.82/241.25 (1101) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1102) QDP 541.82/241.25 (1103) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1104) QDP 541.82/241.25 (1105) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1106) QDP 541.82/241.25 (1107) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1108) QDP 541.82/241.25 (1109) TransformationProof [EQUIVALENT, 1 ms] 541.82/241.25 (1110) QDP 541.82/241.25 (1111) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1112) QDP 541.82/241.25 (1113) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1114) QDP 541.82/241.25 (1115) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1116) QDP 541.82/241.25 (1117) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1118) QDP 541.82/241.25 (1119) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1120) QDP 541.82/241.25 (1121) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1122) QDP 541.82/241.25 (1123) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1124) QDP 541.82/241.25 (1125) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1126) QDP 541.82/241.25 (1127) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1128) QDP 541.82/241.25 (1129) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1130) QDP 541.82/241.25 (1131) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1132) QDP 541.82/241.25 (1133) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1134) QDP 541.82/241.25 (1135) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1136) QDP 541.82/241.25 (1137) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1138) QDP 541.82/241.25 (1139) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1140) QDP 541.82/241.25 (1141) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1142) QDP 541.82/241.25 (1143) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1144) QDP 541.82/241.25 (1145) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1146) QDP 541.82/241.25 (1147) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1148) QDP 541.82/241.25 (1149) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1150) QDP 541.82/241.25 (1151) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1152) QDP 541.82/241.25 (1153) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1154) QDP 541.82/241.25 (1155) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1156) QDP 541.82/241.25 (1157) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1158) QDP 541.82/241.25 (1159) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1160) QDP 541.82/241.25 (1161) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1162) QDP 541.82/241.25 (1163) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1164) QDP 541.82/241.25 (1165) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1166) QDP 541.82/241.25 (1167) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1168) QDP 541.82/241.25 (1169) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1170) QDP 541.82/241.25 (1171) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1172) QDP 541.82/241.25 (1173) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1174) QDP 541.82/241.25 (1175) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1176) QDP 541.82/241.25 (1177) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1178) QDP 541.82/241.25 (1179) TransformationProof [EQUIVALENT, 1 ms] 541.82/241.25 (1180) QDP 541.82/241.25 (1181) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1182) QDP 541.82/241.25 (1183) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1184) QDP 541.82/241.25 (1185) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1186) QDP 541.82/241.25 (1187) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1188) QDP 541.82/241.25 (1189) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1190) QDP 541.82/241.25 (1191) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1192) QDP 541.82/241.25 (1193) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1194) QDP 541.82/241.25 (1195) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1196) QDP 541.82/241.25 (1197) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1198) QDP 541.82/241.25 (1199) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1200) QDP 541.82/241.25 (1201) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1202) QDP 541.82/241.25 (1203) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1204) QDP 541.82/241.25 (1205) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1206) QDP 541.82/241.25 (1207) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1208) QDP 541.82/241.25 (1209) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1210) QDP 541.82/241.25 (1211) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1212) QDP 541.82/241.25 (1213) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1214) QDP 541.82/241.25 (1215) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1216) QDP 541.82/241.25 (1217) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1218) QDP 541.82/241.25 (1219) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1220) QDP 541.82/241.25 (1221) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1222) QDP 541.82/241.25 (1223) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1224) QDP 541.82/241.25 (1225) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1226) QDP 541.82/241.25 (1227) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1228) QDP 541.82/241.25 (1229) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1230) QDP 541.82/241.25 (1231) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1232) QDP 541.82/241.25 (1233) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1234) QDP 541.82/241.25 (1235) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1236) QDP 541.82/241.25 (1237) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1238) QDP 541.82/241.25 (1239) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1240) QDP 541.82/241.25 (1241) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1242) QDP 541.82/241.25 (1243) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1244) QDP 541.82/241.25 (1245) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1246) QDP 541.82/241.25 (1247) TransformationProof [EQUIVALENT, 2 ms] 541.82/241.25 (1248) QDP 541.82/241.25 (1249) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1250) QDP 541.82/241.25 (1251) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1252) QDP 541.82/241.25 (1253) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1254) QDP 541.82/241.25 (1255) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1256) QDP 541.82/241.25 (1257) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1258) QDP 541.82/241.25 (1259) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1260) QDP 541.82/241.25 (1261) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1262) QDP 541.82/241.25 (1263) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1264) QDP 541.82/241.25 (1265) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1266) QDP 541.82/241.25 (1267) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1268) QDP 541.82/241.25 (1269) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1270) QDP 541.82/241.25 (1271) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1272) QDP 541.82/241.25 (1273) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1274) QDP 541.82/241.25 (1275) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1276) QDP 541.82/241.25 (1277) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1278) QDP 541.82/241.25 (1279) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1280) QDP 541.82/241.25 (1281) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1282) QDP 541.82/241.25 (1283) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1284) QDP 541.82/241.25 (1285) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1286) QDP 541.82/241.25 (1287) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1288) QDP 541.82/241.25 (1289) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1290) QDP 541.82/241.25 (1291) TransformationProof [EQUIVALENT, 0 ms] 541.82/241.25 (1292) QDP 541.82/241.25 (1293) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1294) QDP 541.82/241.25 (1295) QDPOrderProof [EQUIVALENT, 76 ms] 541.82/241.25 (1296) QDP 541.82/241.25 (1297) QDPOrderProof [EQUIVALENT, 58 ms] 541.82/241.25 (1298) QDP 541.82/241.25 (1299) MNOCProof [EQUIVALENT, 0 ms] 541.82/241.25 (1300) QDP 541.82/241.25 (1301) SplitQDPProof [EQUIVALENT, 0 ms] 541.82/241.25 (1302) AND 541.82/241.25 (1303) QDP 541.82/241.25 (1304) SemLabProof [SOUND, 0 ms] 541.82/241.25 (1305) QDP 541.82/241.25 (1306) UsableRulesReductionPairsProof [EQUIVALENT, 129 ms] 541.82/241.25 (1307) QDP 541.82/241.25 (1308) MRRProof [EQUIVALENT, 147 ms] 541.82/241.25 (1309) QDP 541.82/241.25 (1310) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1311) QDP 541.82/241.25 (1312) PisEmptyProof [SOUND, 0 ms] 541.82/241.25 (1313) TRUE 541.82/241.25 (1314) QDP 541.82/241.25 (1315) SplitQDPProof [EQUIVALENT, 0 ms] 541.82/241.25 (1316) AND 541.82/241.25 (1317) QDP 541.82/241.25 (1318) SemLabProof [SOUND, 0 ms] 541.82/241.25 (1319) QDP 541.82/241.25 (1320) UsableRulesReductionPairsProof [EQUIVALENT, 157 ms] 541.82/241.25 (1321) QDP 541.82/241.25 (1322) MRRProof [EQUIVALENT, 74 ms] 541.82/241.25 (1323) QDP 541.82/241.25 (1324) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1325) QDP 541.82/241.25 (1326) QDPOrderProof [EQUIVALENT, 62 ms] 541.82/241.25 (1327) QDP 541.82/241.25 (1328) PisEmptyProof [SOUND, 0 ms] 541.82/241.25 (1329) TRUE 541.82/241.25 (1330) QDP 541.82/241.25 (1331) SplitQDPProof [EQUIVALENT, 0 ms] 541.82/241.25 (1332) AND 541.82/241.25 (1333) QDP 541.82/241.25 (1334) SemLabProof [SOUND, 0 ms] 541.82/241.25 (1335) QDP 541.82/241.25 (1336) UsableRulesReductionPairsProof [EQUIVALENT, 147 ms] 541.82/241.25 (1337) QDP 541.82/241.25 (1338) MRRProof [EQUIVALENT, 150 ms] 541.82/241.25 (1339) QDP 541.82/241.25 (1340) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1341) QDP 541.82/241.25 (1342) QDPOrderProof [EQUIVALENT, 48 ms] 541.82/241.25 (1343) QDP 541.82/241.25 (1344) PisEmptyProof [SOUND, 0 ms] 541.82/241.25 (1345) TRUE 541.82/241.25 (1346) QDP 541.82/241.25 (1347) SplitQDPProof [EQUIVALENT, 0 ms] 541.82/241.25 (1348) AND 541.82/241.25 (1349) QDP 541.82/241.25 (1350) SemLabProof [SOUND, 0 ms] 541.82/241.25 (1351) QDP 541.82/241.25 (1352) MRRProof [EQUIVALENT, 96 ms] 541.82/241.25 (1353) QDP 541.82/241.25 (1354) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1355) QDP 541.82/241.25 (1356) PisEmptyProof [SOUND, 0 ms] 541.82/241.25 (1357) TRUE 541.82/241.25 (1358) QDP 541.82/241.25 (1359) SplitQDPProof [EQUIVALENT, 0 ms] 541.82/241.25 (1360) AND 541.82/241.25 (1361) QDP 541.82/241.25 (1362) SemLabProof [SOUND, 0 ms] 541.82/241.25 (1363) QDP 541.82/241.25 (1364) MRRProof [EQUIVALENT, 121 ms] 541.82/241.25 (1365) QDP 541.82/241.25 (1366) DependencyGraphProof [EQUIVALENT, 0 ms] 541.82/241.25 (1367) QDP 541.82/241.25 (1368) UsableRulesReductionPairsProof [EQUIVALENT, 78 ms] 541.82/241.25 (1369) QDP 541.82/241.25 (1370) MRRProof [EQUIVALENT, 48 ms] 541.82/241.25 (1371) QDP 541.82/241.25 (1372) PisEmptyProof [SOUND, 0 ms] 541.82/241.25 (1373) TRUE 541.82/241.25 (1374) QDP 541.82/241.25 541.82/241.25 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (0) 541.82/241.25 Obligation: 541.82/241.25 Term rewrite system R: 541.82/241.25 The TRS R consists of the following rules: 541.82/241.25 541.82/241.25 a -> f(a) 541.82/241.25 b -> g(b) 541.82/241.25 a -> b 541.82/241.25 f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c 541.82/241.25 g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c 541.82/241.25 541.82/241.25 541.82/241.25 541.82/241.25 Outermost Strategy. 541.82/241.25 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (1) Thiemann-SpecialC-Transformation (EQUIVALENT) 541.82/241.25 We applied the Thiemann-SpecialC transformation to transform the outermost TRS to an innermost TRS. 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (2) 541.82/241.25 Obligation: 541.82/241.25 Q restricted rewrite system: 541.82/241.25 The TRS R consists of the following rules: 541.82/241.25 541.82/241.25 top(go_up(x)) -> top(reduce(x)) 541.82/241.25 reduce(f(x_1)) -> check_f(redex_f(x_1)) 541.82/241.25 reduce(g(x_1)) -> check_g(redex_g(x_1)) 541.82/241.25 reduce(a) -> go_up(f(a)) 541.82/241.25 reduce(b) -> go_up(g(b)) 541.82/241.25 reduce(a) -> go_up(b) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 541.82/241.25 check_f(result_f(x)) -> go_up(x) 541.82/241.25 check_g(result_g(x)) -> go_up(x) 541.82/241.25 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 541.82/241.25 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 541.82/241.25 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 541.82/241.25 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 541.82/241.25 541.82/241.25 The set Q consists of the following terms: 541.82/241.25 541.82/241.25 top(go_up(x0)) 541.82/241.25 reduce(f(x0)) 541.82/241.25 reduce(g(x0)) 541.82/241.25 reduce(a) 541.82/241.25 reduce(b) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 541.82/241.25 check_f(result_f(x0)) 541.82/241.25 check_g(result_g(x0)) 541.82/241.25 check_f(redex_f(x0)) 541.82/241.25 check_g(redex_g(x0)) 541.82/241.25 in_f_1(go_up(x0)) 541.82/241.25 in_g_1(go_up(x0)) 541.82/241.25 541.82/241.25 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (3) QTRSRRRProof (EQUIVALENT) 541.82/241.25 Used ordering: 541.82/241.25 Polynomial interpretation [POLO]: 541.82/241.25 541.82/241.25 POL(a) = 2 541.82/241.25 POL(b) = 1 541.82/241.25 POL(c) = 0 541.82/241.25 POL(check_f(x_1)) = 2*x_1 541.82/241.25 POL(check_g(x_1)) = 2*x_1 541.82/241.25 POL(f(x_1)) = x_1 541.82/241.25 POL(g(x_1)) = x_1 541.82/241.25 POL(go_up(x_1)) = 2*x_1 541.82/241.25 POL(in_f_1(x_1)) = x_1 541.82/241.25 POL(in_g_1(x_1)) = x_1 541.82/241.25 POL(redex_f(x_1)) = x_1 541.82/241.25 POL(redex_g(x_1)) = x_1 541.82/241.25 POL(reduce(x_1)) = 2*x_1 541.82/241.25 POL(result_f(x_1)) = 2*x_1 541.82/241.25 POL(result_g(x_1)) = x_1 541.82/241.25 POL(top(x_1)) = 2*x_1 541.82/241.25 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 541.82/241.25 541.82/241.25 reduce(a) -> go_up(b) 541.82/241.25 541.82/241.25 541.82/241.25 541.82/241.25 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (4) 541.82/241.25 Obligation: 541.82/241.25 Q restricted rewrite system: 541.82/241.25 The TRS R consists of the following rules: 541.82/241.25 541.82/241.25 top(go_up(x)) -> top(reduce(x)) 541.82/241.25 reduce(f(x_1)) -> check_f(redex_f(x_1)) 541.82/241.25 reduce(g(x_1)) -> check_g(redex_g(x_1)) 541.82/241.25 reduce(a) -> go_up(f(a)) 541.82/241.25 reduce(b) -> go_up(g(b)) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 541.82/241.25 check_f(result_f(x)) -> go_up(x) 541.82/241.25 check_g(result_g(x)) -> go_up(x) 541.82/241.25 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 541.82/241.25 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 541.82/241.25 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 541.82/241.25 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 541.82/241.25 541.82/241.25 The set Q consists of the following terms: 541.82/241.25 541.82/241.25 top(go_up(x0)) 541.82/241.25 reduce(f(x0)) 541.82/241.25 reduce(g(x0)) 541.82/241.25 reduce(a) 541.82/241.25 reduce(b) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 541.82/241.25 check_f(result_f(x0)) 541.82/241.25 check_g(result_g(x0)) 541.82/241.25 check_f(redex_f(x0)) 541.82/241.25 check_g(redex_g(x0)) 541.82/241.25 in_f_1(go_up(x0)) 541.82/241.25 in_g_1(go_up(x0)) 541.82/241.25 541.82/241.25 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (5) DependencyPairsProof (EQUIVALENT) 541.82/241.25 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (6) 541.82/241.25 Obligation: 541.82/241.25 Q DP problem: 541.82/241.25 The TRS P consists of the following rules: 541.82/241.25 541.82/241.25 TOP(go_up(x)) -> TOP(reduce(x)) 541.82/241.25 TOP(go_up(x)) -> REDUCE(x) 541.82/241.25 REDUCE(f(x_1)) -> CHECK_F(redex_f(x_1)) 541.82/241.25 REDUCE(f(x_1)) -> REDEX_F(x_1) 541.82/241.25 REDUCE(g(x_1)) -> CHECK_G(redex_g(x_1)) 541.82/241.25 REDUCE(g(x_1)) -> REDEX_G(x_1) 541.82/241.25 CHECK_F(redex_f(x_1)) -> IN_F_1(reduce(x_1)) 541.82/241.25 CHECK_F(redex_f(x_1)) -> REDUCE(x_1) 541.82/241.25 CHECK_G(redex_g(x_1)) -> IN_G_1(reduce(x_1)) 541.82/241.25 CHECK_G(redex_g(x_1)) -> REDUCE(x_1) 541.82/241.25 541.82/241.25 The TRS R consists of the following rules: 541.82/241.25 541.82/241.25 top(go_up(x)) -> top(reduce(x)) 541.82/241.25 reduce(f(x_1)) -> check_f(redex_f(x_1)) 541.82/241.25 reduce(g(x_1)) -> check_g(redex_g(x_1)) 541.82/241.25 reduce(a) -> go_up(f(a)) 541.82/241.25 reduce(b) -> go_up(g(b)) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 541.82/241.25 check_f(result_f(x)) -> go_up(x) 541.82/241.25 check_g(result_g(x)) -> go_up(x) 541.82/241.25 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 541.82/241.25 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 541.82/241.25 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 541.82/241.25 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 541.82/241.25 541.82/241.25 The set Q consists of the following terms: 541.82/241.25 541.82/241.25 top(go_up(x0)) 541.82/241.25 reduce(f(x0)) 541.82/241.25 reduce(g(x0)) 541.82/241.25 reduce(a) 541.82/241.25 reduce(b) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 541.82/241.25 check_f(result_f(x0)) 541.82/241.25 check_g(result_g(x0)) 541.82/241.25 check_f(redex_f(x0)) 541.82/241.25 check_g(redex_g(x0)) 541.82/241.25 in_f_1(go_up(x0)) 541.82/241.25 in_g_1(go_up(x0)) 541.82/241.25 541.82/241.25 We have to consider all minimal (P,Q,R)-chains. 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (7) DependencyGraphProof (EQUIVALENT) 541.82/241.25 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 5 less nodes. 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (8) 541.82/241.25 Complex Obligation (AND) 541.82/241.25 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (9) 541.82/241.25 Obligation: 541.82/241.25 Q DP problem: 541.82/241.25 The TRS P consists of the following rules: 541.82/241.25 541.82/241.25 CHECK_F(redex_f(x_1)) -> REDUCE(x_1) 541.82/241.25 REDUCE(f(x_1)) -> CHECK_F(redex_f(x_1)) 541.82/241.25 REDUCE(g(x_1)) -> CHECK_G(redex_g(x_1)) 541.82/241.25 CHECK_G(redex_g(x_1)) -> REDUCE(x_1) 541.82/241.25 541.82/241.25 The TRS R consists of the following rules: 541.82/241.25 541.82/241.25 top(go_up(x)) -> top(reduce(x)) 541.82/241.25 reduce(f(x_1)) -> check_f(redex_f(x_1)) 541.82/241.25 reduce(g(x_1)) -> check_g(redex_g(x_1)) 541.82/241.25 reduce(a) -> go_up(f(a)) 541.82/241.25 reduce(b) -> go_up(g(b)) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 541.82/241.25 check_f(result_f(x)) -> go_up(x) 541.82/241.25 check_g(result_g(x)) -> go_up(x) 541.82/241.25 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 541.82/241.25 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 541.82/241.25 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 541.82/241.25 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 541.82/241.25 541.82/241.25 The set Q consists of the following terms: 541.82/241.25 541.82/241.25 top(go_up(x0)) 541.82/241.25 reduce(f(x0)) 541.82/241.25 reduce(g(x0)) 541.82/241.25 reduce(a) 541.82/241.25 reduce(b) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 541.82/241.25 check_f(result_f(x0)) 541.82/241.25 check_g(result_g(x0)) 541.82/241.25 check_f(redex_f(x0)) 541.82/241.25 check_g(redex_g(x0)) 541.82/241.25 in_f_1(go_up(x0)) 541.82/241.25 in_g_1(go_up(x0)) 541.82/241.25 541.82/241.25 We have to consider all minimal (P,Q,R)-chains. 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (10) UsableRulesProof (EQUIVALENT) 541.82/241.25 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. 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (11) 541.82/241.25 Obligation: 541.82/241.25 Q DP problem: 541.82/241.25 The TRS P consists of the following rules: 541.82/241.25 541.82/241.25 CHECK_F(redex_f(x_1)) -> REDUCE(x_1) 541.82/241.25 REDUCE(f(x_1)) -> CHECK_F(redex_f(x_1)) 541.82/241.25 REDUCE(g(x_1)) -> CHECK_G(redex_g(x_1)) 541.82/241.25 CHECK_G(redex_g(x_1)) -> REDUCE(x_1) 541.82/241.25 541.82/241.25 The TRS R consists of the following rules: 541.82/241.25 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 541.82/241.25 541.82/241.25 The set Q consists of the following terms: 541.82/241.25 541.82/241.25 top(go_up(x0)) 541.82/241.25 reduce(f(x0)) 541.82/241.25 reduce(g(x0)) 541.82/241.25 reduce(a) 541.82/241.25 reduce(b) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 541.82/241.25 check_f(result_f(x0)) 541.82/241.25 check_g(result_g(x0)) 541.82/241.25 check_f(redex_f(x0)) 541.82/241.25 check_g(redex_g(x0)) 541.82/241.25 in_f_1(go_up(x0)) 541.82/241.25 in_g_1(go_up(x0)) 541.82/241.25 541.82/241.25 We have to consider all minimal (P,Q,R)-chains. 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (12) QReductionProof (EQUIVALENT) 541.82/241.25 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 541.82/241.25 541.82/241.25 top(go_up(x0)) 541.82/241.25 reduce(f(x0)) 541.82/241.25 reduce(g(x0)) 541.82/241.25 reduce(a) 541.82/241.25 reduce(b) 541.82/241.25 check_f(result_f(x0)) 541.82/241.25 check_g(result_g(x0)) 541.82/241.25 check_f(redex_f(x0)) 541.82/241.25 check_g(redex_g(x0)) 541.82/241.25 in_f_1(go_up(x0)) 541.82/241.25 in_g_1(go_up(x0)) 541.82/241.25 541.82/241.25 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (13) 541.82/241.25 Obligation: 541.82/241.25 Q DP problem: 541.82/241.25 The TRS P consists of the following rules: 541.82/241.25 541.82/241.25 CHECK_F(redex_f(x_1)) -> REDUCE(x_1) 541.82/241.25 REDUCE(f(x_1)) -> CHECK_F(redex_f(x_1)) 541.82/241.25 REDUCE(g(x_1)) -> CHECK_G(redex_g(x_1)) 541.82/241.25 CHECK_G(redex_g(x_1)) -> REDUCE(x_1) 541.82/241.25 541.82/241.25 The TRS R consists of the following rules: 541.82/241.25 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 541.82/241.25 541.82/241.25 The set Q consists of the following terms: 541.82/241.25 541.82/241.25 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 541.82/241.25 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 541.82/241.25 541.82/241.25 We have to consider all minimal (P,Q,R)-chains. 541.82/241.25 ---------------------------------------- 541.82/241.25 541.82/241.25 (14) UsableRulesReductionPairsProof (EQUIVALENT) 541.82/241.25 By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well. 541.82/241.26 541.82/241.26 The following dependency pairs can be deleted: 541.82/241.26 541.82/241.26 REDUCE(f(x_1)) -> CHECK_F(redex_f(x_1)) 541.82/241.26 REDUCE(g(x_1)) -> CHECK_G(redex_g(x_1)) 541.82/241.26 The following rules are removed from R: 541.82/241.26 541.82/241.26 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 541.82/241.26 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 541.82/241.26 Used ordering: POLO with Polynomial interpretation [POLO]: 541.82/241.26 541.82/241.26 POL(CHECK_F(x_1)) = x_1 541.82/241.26 POL(CHECK_G(x_1)) = x_1 541.82/241.26 POL(REDUCE(x_1)) = 2*x_1 541.82/241.26 POL(c) = 0 541.82/241.26 POL(f(x_1)) = 2*x_1 541.82/241.26 POL(g(x_1)) = 2*x_1 541.82/241.26 POL(redex_f(x_1)) = 2*x_1 541.82/241.26 POL(redex_g(x_1)) = 2*x_1 541.82/241.26 POL(result_f(x_1)) = x_1 541.82/241.26 POL(result_g(x_1)) = x_1 541.82/241.26 541.82/241.26 541.82/241.26 ---------------------------------------- 541.82/241.26 541.82/241.26 (15) 541.82/241.26 Obligation: 541.82/241.26 Q DP problem: 541.82/241.26 The TRS P consists of the following rules: 541.82/241.26 541.82/241.26 CHECK_F(redex_f(x_1)) -> REDUCE(x_1) 541.82/241.26 CHECK_G(redex_g(x_1)) -> REDUCE(x_1) 541.82/241.26 541.82/241.26 R is empty. 541.82/241.26 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 542.07/241.28 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (16) DependencyGraphProof (EQUIVALENT) 542.07/241.28 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (17) 542.07/241.28 TRUE 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (18) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 TOP(go_up(x)) -> TOP(reduce(x)) 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 top(go_up(x)) -> top(reduce(x)) 542.07/241.28 reduce(f(x_1)) -> check_f(redex_f(x_1)) 542.07/241.28 reduce(g(x_1)) -> check_g(redex_g(x_1)) 542.07/241.28 reduce(a) -> go_up(f(a)) 542.07/241.28 reduce(b) -> go_up(g(b)) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 542.07/241.28 check_f(result_f(x)) -> go_up(x) 542.07/241.28 check_g(result_g(x)) -> go_up(x) 542.07/241.28 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 542.07/241.28 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 542.07/241.28 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 542.07/241.28 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 542.07/241.28 542.07/241.28 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 top(go_up(x0)) 542.07/241.28 reduce(f(x0)) 542.07/241.28 reduce(g(x0)) 542.07/241.28 reduce(a) 542.07/241.28 reduce(b) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 542.07/241.28 check_f(result_f(x0)) 542.07/241.28 check_g(result_g(x0)) 542.07/241.28 check_f(redex_f(x0)) 542.07/241.28 check_g(redex_g(x0)) 542.07/241.28 in_f_1(go_up(x0)) 542.07/241.28 in_g_1(go_up(x0)) 542.07/241.28 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (19) UsableRulesProof (EQUIVALENT) 542.07/241.28 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. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (20) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 TOP(go_up(x)) -> TOP(reduce(x)) 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 reduce(f(x_1)) -> check_f(redex_f(x_1)) 542.07/241.28 reduce(g(x_1)) -> check_g(redex_g(x_1)) 542.07/241.28 reduce(a) -> go_up(f(a)) 542.07/241.28 reduce(b) -> go_up(g(b)) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 542.07/241.28 check_g(result_g(x)) -> go_up(x) 542.07/241.28 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 542.07/241.28 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 542.07/241.28 check_f(result_f(x)) -> go_up(x) 542.07/241.28 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 542.07/241.28 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 542.07/241.28 542.07/241.28 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 top(go_up(x0)) 542.07/241.28 reduce(f(x0)) 542.07/241.28 reduce(g(x0)) 542.07/241.28 reduce(a) 542.07/241.28 reduce(b) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 542.07/241.28 check_f(result_f(x0)) 542.07/241.28 check_g(result_g(x0)) 542.07/241.28 check_f(redex_f(x0)) 542.07/241.28 check_g(redex_g(x0)) 542.07/241.28 in_f_1(go_up(x0)) 542.07/241.28 in_g_1(go_up(x0)) 542.07/241.28 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (21) QReductionProof (EQUIVALENT) 542.07/241.28 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 542.07/241.28 542.07/241.28 top(go_up(x0)) 542.07/241.28 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (22) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 TOP(go_up(x)) -> TOP(reduce(x)) 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 reduce(f(x_1)) -> check_f(redex_f(x_1)) 542.07/241.28 reduce(g(x_1)) -> check_g(redex_g(x_1)) 542.07/241.28 reduce(a) -> go_up(f(a)) 542.07/241.28 reduce(b) -> go_up(g(b)) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 542.07/241.28 check_g(result_g(x)) -> go_up(x) 542.07/241.28 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 542.07/241.28 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 542.07/241.28 check_f(result_f(x)) -> go_up(x) 542.07/241.28 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 542.07/241.28 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 542.07/241.28 542.07/241.28 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 reduce(f(x0)) 542.07/241.28 reduce(g(x0)) 542.07/241.28 reduce(a) 542.07/241.28 reduce(b) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 542.07/241.28 check_f(result_f(x0)) 542.07/241.28 check_g(result_g(x0)) 542.07/241.28 check_f(redex_f(x0)) 542.07/241.28 check_g(redex_g(x0)) 542.07/241.28 in_f_1(go_up(x0)) 542.07/241.28 in_g_1(go_up(x0)) 542.07/241.28 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (23) TransformationProof (EQUIVALENT) 542.07/241.28 By narrowing [LPAR04] the rule TOP(go_up(x)) -> TOP(reduce(x)) at position [0] we obtained the following new rules [LPAR04]: 542.07/241.28 542.07/241.28 (TOP(go_up(f(x0))) -> TOP(check_f(redex_f(x0))),TOP(go_up(f(x0))) -> TOP(check_f(redex_f(x0)))) 542.07/241.28 (TOP(go_up(g(x0))) -> TOP(check_g(redex_g(x0))),TOP(go_up(g(x0))) -> TOP(check_g(redex_g(x0)))) 542.07/241.28 (TOP(go_up(a)) -> TOP(go_up(f(a))),TOP(go_up(a)) -> TOP(go_up(f(a)))) 542.07/241.28 (TOP(go_up(b)) -> TOP(go_up(g(b))),TOP(go_up(b)) -> TOP(go_up(g(b)))) 542.07/241.28 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (24) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 TOP(go_up(f(x0))) -> TOP(check_f(redex_f(x0))) 542.07/241.28 TOP(go_up(g(x0))) -> TOP(check_g(redex_g(x0))) 542.07/241.28 TOP(go_up(a)) -> TOP(go_up(f(a))) 542.07/241.28 TOP(go_up(b)) -> TOP(go_up(g(b))) 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 reduce(f(x_1)) -> check_f(redex_f(x_1)) 542.07/241.28 reduce(g(x_1)) -> check_g(redex_g(x_1)) 542.07/241.28 reduce(a) -> go_up(f(a)) 542.07/241.28 reduce(b) -> go_up(g(b)) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 542.07/241.28 check_g(result_g(x)) -> go_up(x) 542.07/241.28 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 542.07/241.28 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 542.07/241.28 check_f(result_f(x)) -> go_up(x) 542.07/241.28 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 542.07/241.28 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 542.07/241.28 542.07/241.28 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 reduce(f(x0)) 542.07/241.28 reduce(g(x0)) 542.07/241.28 reduce(a) 542.07/241.28 reduce(b) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 542.07/241.28 check_f(result_f(x0)) 542.07/241.28 check_g(result_g(x0)) 542.07/241.28 check_f(redex_f(x0)) 542.07/241.28 check_g(redex_g(x0)) 542.07/241.28 in_f_1(go_up(x0)) 542.07/241.28 in_g_1(go_up(x0)) 542.07/241.28 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (25) QDPOrderProof (EQUIVALENT) 542.07/241.28 We use the reduction pair processor [LPAR04,JAR06]. 542.07/241.28 542.07/241.28 542.07/241.28 The following pairs can be oriented strictly and are deleted. 542.07/241.28 542.07/241.28 TOP(go_up(a)) -> TOP(go_up(f(a))) 542.07/241.28 TOP(go_up(b)) -> TOP(go_up(g(b))) 542.07/241.28 The remaining pairs can at least be oriented weakly. 542.07/241.28 Used ordering: Polynomial interpretation [POLO]: 542.07/241.28 542.07/241.28 POL(TOP(x_1)) = x_1 542.07/241.28 POL(a) = 1 542.07/241.28 POL(b) = 1 542.07/241.28 POL(c) = 0 542.07/241.28 POL(check_f(x_1)) = x_1 542.07/241.28 POL(check_g(x_1)) = x_1 542.07/241.28 POL(f(x_1)) = 0 542.07/241.28 POL(g(x_1)) = 0 542.07/241.28 POL(go_up(x_1)) = x_1 542.07/241.28 POL(in_f_1(x_1)) = 0 542.07/241.28 POL(in_g_1(x_1)) = 0 542.07/241.28 POL(redex_f(x_1)) = 0 542.07/241.28 POL(redex_g(x_1)) = 0 542.07/241.28 POL(reduce(x_1)) = 0 542.07/241.28 POL(result_f(x_1)) = x_1 542.07/241.28 POL(result_g(x_1)) = x_1 542.07/241.28 542.07/241.28 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 542.07/241.28 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 542.07/241.28 check_f(result_f(x)) -> go_up(x) 542.07/241.28 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 542.07/241.28 check_g(result_g(x)) -> go_up(x) 542.07/241.28 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 542.07/241.28 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 542.07/241.28 reduce(f(x_1)) -> check_f(redex_f(x_1)) 542.07/241.28 reduce(g(x_1)) -> check_g(redex_g(x_1)) 542.07/241.28 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 542.07/241.28 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (26) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 TOP(go_up(f(x0))) -> TOP(check_f(redex_f(x0))) 542.07/241.28 TOP(go_up(g(x0))) -> TOP(check_g(redex_g(x0))) 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 reduce(f(x_1)) -> check_f(redex_f(x_1)) 542.07/241.28 reduce(g(x_1)) -> check_g(redex_g(x_1)) 542.07/241.28 reduce(a) -> go_up(f(a)) 542.07/241.28 reduce(b) -> go_up(g(b)) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 542.07/241.28 check_g(result_g(x)) -> go_up(x) 542.07/241.28 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 542.07/241.28 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 542.07/241.28 check_f(result_f(x)) -> go_up(x) 542.07/241.28 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 542.07/241.28 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 542.07/241.28 542.07/241.28 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 reduce(f(x0)) 542.07/241.28 reduce(g(x0)) 542.07/241.28 reduce(a) 542.07/241.28 reduce(b) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 542.07/241.28 check_f(result_f(x0)) 542.07/241.28 check_g(result_g(x0)) 542.07/241.28 check_f(redex_f(x0)) 542.07/241.28 check_g(redex_g(x0)) 542.07/241.28 in_f_1(go_up(x0)) 542.07/241.28 in_g_1(go_up(x0)) 542.07/241.28 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (27) UsableRulesProof (EQUIVALENT) 542.07/241.28 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. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (28) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 TOP(go_up(x)) -> TOP(reduce(x)) 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 reduce(f(x_1)) -> check_f(redex_f(x_1)) 542.07/241.28 reduce(g(x_1)) -> check_g(redex_g(x_1)) 542.07/241.28 reduce(a) -> go_up(f(a)) 542.07/241.28 reduce(b) -> go_up(g(b)) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 542.07/241.28 check_g(result_g(x)) -> go_up(x) 542.07/241.28 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 542.07/241.28 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 542.07/241.28 check_f(result_f(x)) -> go_up(x) 542.07/241.28 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 542.07/241.28 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 542.07/241.28 542.07/241.28 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 top(go_up(x0)) 542.07/241.28 reduce(f(x0)) 542.07/241.28 reduce(g(x0)) 542.07/241.28 reduce(a) 542.07/241.28 reduce(b) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 542.07/241.28 check_f(result_f(x0)) 542.07/241.28 check_g(result_g(x0)) 542.07/241.28 check_f(redex_f(x0)) 542.07/241.28 check_g(redex_g(x0)) 542.07/241.28 in_f_1(go_up(x0)) 542.07/241.28 in_g_1(go_up(x0)) 542.07/241.28 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (29) QReductionProof (EQUIVALENT) 542.07/241.28 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 542.07/241.28 542.07/241.28 top(go_up(x0)) 542.07/241.28 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (30) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 TOP(go_up(x)) -> TOP(reduce(x)) 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 reduce(f(x_1)) -> check_f(redex_f(x_1)) 542.07/241.28 reduce(g(x_1)) -> check_g(redex_g(x_1)) 542.07/241.28 reduce(a) -> go_up(f(a)) 542.07/241.28 reduce(b) -> go_up(g(b)) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x)))))))))) -> result_g(c) 542.07/241.28 check_g(result_g(x)) -> go_up(x) 542.07/241.28 check_g(redex_g(x_1)) -> in_g_1(reduce(x_1)) 542.07/241.28 in_g_1(go_up(x_1)) -> go_up(g(x_1)) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x)))))))))) -> result_f(c) 542.07/241.28 check_f(result_f(x)) -> go_up(x) 542.07/241.28 check_f(redex_f(x_1)) -> in_f_1(reduce(x_1)) 542.07/241.28 in_f_1(go_up(x_1)) -> go_up(f(x_1)) 542.07/241.28 542.07/241.28 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 reduce(f(x0)) 542.07/241.28 reduce(g(x0)) 542.07/241.28 reduce(a) 542.07/241.28 reduce(b) 542.07/241.28 redex_f(f(f(f(f(f(f(f(f(f(x0)))))))))) 542.07/241.28 redex_g(g(g(g(g(g(g(g(g(g(x0)))))))))) 542.07/241.28 check_f(result_f(x0)) 542.07/241.28 check_g(result_g(x0)) 542.07/241.28 check_f(redex_f(x0)) 542.07/241.28 check_g(redex_g(x0)) 542.07/241.28 in_f_1(go_up(x0)) 542.07/241.28 in_g_1(go_up(x0)) 542.07/241.28 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (31) Trivial-Transformation (SOUND) 542.07/241.28 We applied the Trivial transformation to transform the outermost TRS to a standard TRS. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (32) 542.07/241.28 Obligation: 542.07/241.28 Q restricted rewrite system: 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 a -> f(a) 542.07/241.28 b -> g(b) 542.07/241.28 a -> b 542.07/241.28 f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c 542.07/241.28 g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c 542.07/241.28 542.07/241.28 Q is empty. 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (33) QTRSRRRProof (EQUIVALENT) 542.07/241.28 Used ordering: 542.07/241.28 Polynomial interpretation [POLO]: 542.07/241.28 542.07/241.28 POL(a) = 1 542.07/241.28 POL(b) = 0 542.07/241.28 POL(c) = 0 542.07/241.28 POL(f(x_1)) = x_1 542.07/241.28 POL(g(x_1)) = 2*x_1 542.07/241.28 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 542.07/241.28 542.07/241.28 a -> b 542.07/241.28 542.07/241.28 542.07/241.28 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (34) 542.07/241.28 Obligation: 542.07/241.28 Q restricted rewrite system: 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 a -> f(a) 542.07/241.28 b -> g(b) 542.07/241.28 f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c 542.07/241.28 g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c 542.07/241.28 542.07/241.28 Q is empty. 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (35) DependencyPairsProof (EQUIVALENT) 542.07/241.28 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (36) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 A -> F(a) 542.07/241.28 A -> A 542.07/241.28 B -> G(b) 542.07/241.28 B -> B 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 a -> f(a) 542.07/241.28 b -> g(b) 542.07/241.28 f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c 542.07/241.28 g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c 542.07/241.28 542.07/241.28 Q is empty. 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (37) DependencyGraphProof (EQUIVALENT) 542.07/241.28 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 2 less nodes. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (38) 542.07/241.28 Complex Obligation (AND) 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (39) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 B -> B 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 a -> f(a) 542.07/241.28 b -> g(b) 542.07/241.28 f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c 542.07/241.28 g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c 542.07/241.28 542.07/241.28 Q is empty. 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (40) UsableRulesProof (EQUIVALENT) 542.07/241.28 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (41) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 B -> B 542.07/241.28 542.07/241.28 R is empty. 542.07/241.28 Q is empty. 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (42) NonTerminationLoopProof (COMPLETE) 542.07/241.28 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 542.07/241.28 Found a loop by semiunifying a rule from P directly. 542.07/241.28 542.07/241.28 s = B evaluates to t =B 542.07/241.28 542.07/241.28 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 542.07/241.28 * Matcher: [ ] 542.07/241.28 * Semiunifier: [ ] 542.07/241.28 542.07/241.28 -------------------------------------------------------------------------------- 542.07/241.28 Rewriting sequence 542.07/241.28 542.07/241.28 The DP semiunifies directly so there is only one rewrite step from B to B. 542.07/241.28 542.07/241.28 542.07/241.28 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (43) 542.07/241.28 NO 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (44) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 A -> A 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 a -> f(a) 542.07/241.28 b -> g(b) 542.07/241.28 f(f(f(f(f(f(f(f(f(f(x)))))))))) -> c 542.07/241.28 g(g(g(g(g(g(g(g(g(g(x)))))))))) -> c 542.07/241.28 542.07/241.28 Q is empty. 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (45) UsableRulesProof (EQUIVALENT) 542.07/241.28 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (46) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 A -> A 542.07/241.28 542.07/241.28 R is empty. 542.07/241.28 Q is empty. 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (47) NonTerminationLoopProof (COMPLETE) 542.07/241.28 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 542.07/241.28 Found a loop by semiunifying a rule from P directly. 542.07/241.28 542.07/241.28 s = A evaluates to t =A 542.07/241.28 542.07/241.28 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 542.07/241.28 * Matcher: [ ] 542.07/241.28 * Semiunifier: [ ] 542.07/241.28 542.07/241.28 -------------------------------------------------------------------------------- 542.07/241.28 Rewriting sequence 542.07/241.28 542.07/241.28 The DP semiunifies directly so there is only one rewrite step from A to A. 542.07/241.28 542.07/241.28 542.07/241.28 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (48) 542.07/241.28 NO 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (49) Raffelsieper-Zantema-Transformation (SOUND) 542.07/241.28 We applied the Raffelsieper-Zantema transformation to transform the outermost TRS to a standard TRS. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (50) 542.07/241.28 Obligation: 542.07/241.28 Q restricted rewrite system: 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 down(a) -> up(f(a)) 542.07/241.28 down(b) -> up(g(b)) 542.07/241.28 down(a) -> up(b) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.28 top(up(x)) -> top(down(x)) 542.07/241.28 down(f(a)) -> f_flat(down(a)) 542.07/241.28 down(f(b)) -> f_flat(down(b)) 542.07/241.28 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.28 down(f(c)) -> f_flat(down(c)) 542.07/241.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.28 down(g(a)) -> g_flat(down(a)) 542.07/241.28 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.28 down(g(b)) -> g_flat(down(b)) 542.07/241.28 down(g(c)) -> g_flat(down(c)) 542.07/241.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.28 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.28 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.28 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.28 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.28 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.28 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.28 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.28 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.28 542.07/241.28 Q is empty. 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (51) QTRSRRRProof (EQUIVALENT) 542.07/241.28 Used ordering: 542.07/241.28 Polynomial interpretation [POLO]: 542.07/241.28 542.07/241.28 POL(a) = 1 542.07/241.28 POL(b) = 0 542.07/241.28 POL(c) = 0 542.07/241.28 POL(down(x_1)) = 2*x_1 542.07/241.28 POL(f(x_1)) = x_1 542.07/241.28 POL(f_flat(x_1)) = x_1 542.07/241.28 POL(fresh_constant) = 0 542.07/241.28 POL(g(x_1)) = x_1 542.07/241.28 POL(g_flat(x_1)) = x_1 542.07/241.28 POL(top(x_1)) = 2*x_1 542.07/241.28 POL(up(x_1)) = 2*x_1 542.07/241.28 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 542.07/241.28 542.07/241.28 down(a) -> up(b) 542.07/241.28 542.07/241.28 542.07/241.28 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (52) 542.07/241.28 Obligation: 542.07/241.28 Q restricted rewrite system: 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 down(a) -> up(f(a)) 542.07/241.28 down(b) -> up(g(b)) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.28 top(up(x)) -> top(down(x)) 542.07/241.28 down(f(a)) -> f_flat(down(a)) 542.07/241.28 down(f(b)) -> f_flat(down(b)) 542.07/241.28 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.28 down(f(c)) -> f_flat(down(c)) 542.07/241.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.28 down(g(a)) -> g_flat(down(a)) 542.07/241.28 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.28 down(g(b)) -> g_flat(down(b)) 542.07/241.28 down(g(c)) -> g_flat(down(c)) 542.07/241.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.28 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.28 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.28 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.28 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.28 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.28 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.28 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.28 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.28 542.07/241.28 Q is empty. 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (53) AAECC Innermost (EQUIVALENT) 542.07/241.28 We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 542.07/241.28 down(f(a)) -> f_flat(down(a)) 542.07/241.28 down(f(b)) -> f_flat(down(b)) 542.07/241.28 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.28 down(f(c)) -> f_flat(down(c)) 542.07/241.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.28 down(g(a)) -> g_flat(down(a)) 542.07/241.28 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.28 down(g(b)) -> g_flat(down(b)) 542.07/241.28 down(g(c)) -> g_flat(down(c)) 542.07/241.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.28 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.28 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.28 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.28 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.28 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.28 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.28 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.28 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.28 down(a) -> up(f(a)) 542.07/241.28 down(b) -> up(g(b)) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.28 542.07/241.28 The TRS R 2 is 542.07/241.28 top(up(x)) -> top(down(x)) 542.07/241.28 542.07/241.28 The signature Sigma is {top_1} 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (54) 542.07/241.28 Obligation: 542.07/241.28 Q restricted rewrite system: 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 down(a) -> up(f(a)) 542.07/241.28 down(b) -> up(g(b)) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.28 top(up(x)) -> top(down(x)) 542.07/241.28 down(f(a)) -> f_flat(down(a)) 542.07/241.28 down(f(b)) -> f_flat(down(b)) 542.07/241.28 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.28 down(f(c)) -> f_flat(down(c)) 542.07/241.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.28 down(g(a)) -> g_flat(down(a)) 542.07/241.28 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.28 down(g(b)) -> g_flat(down(b)) 542.07/241.28 down(g(c)) -> g_flat(down(c)) 542.07/241.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.28 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.28 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.28 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.28 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.28 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.28 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.28 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.28 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.28 542.07/241.28 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 down(a) 542.07/241.28 down(b) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.28 top(up(x0)) 542.07/241.28 down(f(a)) 542.07/241.28 down(f(b)) 542.07/241.28 down(f(g(x0))) 542.07/241.28 down(f(c)) 542.07/241.28 down(f(fresh_constant)) 542.07/241.28 down(g(a)) 542.07/241.28 down(g(f(x0))) 542.07/241.28 down(g(b)) 542.07/241.28 down(g(c)) 542.07/241.28 down(g(fresh_constant)) 542.07/241.28 down(f(f(a))) 542.07/241.28 down(f(f(b))) 542.07/241.28 down(f(f(g(x0)))) 542.07/241.28 down(f(f(c))) 542.07/241.28 down(f(f(fresh_constant))) 542.07/241.28 down(g(g(a))) 542.07/241.28 down(g(g(f(x0)))) 542.07/241.28 down(g(g(b))) 542.07/241.28 down(g(g(c))) 542.07/241.28 down(g(g(fresh_constant))) 542.07/241.28 down(f(f(f(a)))) 542.07/241.28 down(f(f(f(b)))) 542.07/241.28 down(f(f(f(g(x0))))) 542.07/241.28 down(f(f(f(c)))) 542.07/241.28 down(f(f(f(fresh_constant)))) 542.07/241.28 down(g(g(g(a)))) 542.07/241.28 down(g(g(g(f(x0))))) 542.07/241.28 down(g(g(g(b)))) 542.07/241.28 down(g(g(g(c)))) 542.07/241.28 down(g(g(g(fresh_constant)))) 542.07/241.28 down(f(f(f(f(a))))) 542.07/241.28 down(f(f(f(f(b))))) 542.07/241.28 down(f(f(f(f(g(x0)))))) 542.07/241.28 down(f(f(f(f(c))))) 542.07/241.28 down(f(f(f(f(fresh_constant))))) 542.07/241.28 down(g(g(g(g(a))))) 542.07/241.28 down(g(g(g(g(f(x0)))))) 542.07/241.28 down(g(g(g(g(b))))) 542.07/241.28 down(g(g(g(g(c))))) 542.07/241.28 down(g(g(g(g(fresh_constant))))) 542.07/241.28 down(f(f(f(f(f(a)))))) 542.07/241.28 down(f(f(f(f(f(b)))))) 542.07/241.28 down(f(f(f(f(f(g(x0))))))) 542.07/241.28 down(f(f(f(f(f(c)))))) 542.07/241.28 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.28 down(g(g(g(g(g(a)))))) 542.07/241.28 down(g(g(g(g(g(f(x0))))))) 542.07/241.28 down(g(g(g(g(g(b)))))) 542.07/241.28 down(g(g(g(g(g(c)))))) 542.07/241.28 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.28 down(f(f(f(f(f(f(a))))))) 542.07/241.28 down(f(f(f(f(f(f(b))))))) 542.07/241.28 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.28 down(f(f(f(f(f(f(c))))))) 542.07/241.28 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.28 down(g(g(g(g(g(g(a))))))) 542.07/241.28 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.28 down(g(g(g(g(g(g(b))))))) 542.07/241.28 down(g(g(g(g(g(g(c))))))) 542.07/241.28 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.28 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.28 f_flat(up(x0)) 542.07/241.28 g_flat(up(x0)) 542.07/241.28 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (55) DependencyPairsProof (EQUIVALENT) 542.07/241.28 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (56) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 TOP(up(x)) -> TOP(down(x)) 542.07/241.28 TOP(up(x)) -> DOWN(x) 542.07/241.28 DOWN(f(a)) -> F_FLAT(down(a)) 542.07/241.28 DOWN(f(a)) -> DOWN(a) 542.07/241.28 DOWN(f(b)) -> F_FLAT(down(b)) 542.07/241.28 DOWN(f(b)) -> DOWN(b) 542.07/241.28 DOWN(f(g(y4))) -> F_FLAT(down(g(y4))) 542.07/241.28 DOWN(f(g(y4))) -> DOWN(g(y4)) 542.07/241.28 DOWN(f(c)) -> F_FLAT(down(c)) 542.07/241.28 DOWN(f(c)) -> DOWN(c) 542.07/241.28 DOWN(f(fresh_constant)) -> F_FLAT(down(fresh_constant)) 542.07/241.28 DOWN(f(fresh_constant)) -> DOWN(fresh_constant) 542.07/241.28 DOWN(g(a)) -> G_FLAT(down(a)) 542.07/241.28 DOWN(g(a)) -> DOWN(a) 542.07/241.28 DOWN(g(f(y6))) -> G_FLAT(down(f(y6))) 542.07/241.28 DOWN(g(f(y6))) -> DOWN(f(y6)) 542.07/241.28 DOWN(g(b)) -> G_FLAT(down(b)) 542.07/241.28 DOWN(g(b)) -> DOWN(b) 542.07/241.28 DOWN(g(c)) -> G_FLAT(down(c)) 542.07/241.28 DOWN(g(c)) -> DOWN(c) 542.07/241.28 DOWN(g(fresh_constant)) -> G_FLAT(down(fresh_constant)) 542.07/241.28 DOWN(g(fresh_constant)) -> DOWN(fresh_constant) 542.07/241.28 DOWN(f(f(a))) -> F_FLAT(down(f(a))) 542.07/241.28 DOWN(f(f(a))) -> DOWN(f(a)) 542.07/241.28 DOWN(f(f(b))) -> F_FLAT(down(f(b))) 542.07/241.28 DOWN(f(f(b))) -> DOWN(f(b)) 542.07/241.28 DOWN(f(f(g(y10)))) -> F_FLAT(down(f(g(y10)))) 542.07/241.28 DOWN(f(f(g(y10)))) -> DOWN(f(g(y10))) 542.07/241.28 DOWN(f(f(c))) -> F_FLAT(down(f(c))) 542.07/241.28 DOWN(f(f(c))) -> DOWN(f(c)) 542.07/241.28 DOWN(f(f(fresh_constant))) -> F_FLAT(down(f(fresh_constant))) 542.07/241.28 DOWN(f(f(fresh_constant))) -> DOWN(f(fresh_constant)) 542.07/241.28 DOWN(g(g(a))) -> G_FLAT(down(g(a))) 542.07/241.28 DOWN(g(g(a))) -> DOWN(g(a)) 542.07/241.28 DOWN(g(g(f(y12)))) -> G_FLAT(down(g(f(y12)))) 542.07/241.28 DOWN(g(g(f(y12)))) -> DOWN(g(f(y12))) 542.07/241.28 DOWN(g(g(b))) -> G_FLAT(down(g(b))) 542.07/241.28 DOWN(g(g(b))) -> DOWN(g(b)) 542.07/241.28 DOWN(g(g(c))) -> G_FLAT(down(g(c))) 542.07/241.28 DOWN(g(g(c))) -> DOWN(g(c)) 542.07/241.28 DOWN(g(g(fresh_constant))) -> G_FLAT(down(g(fresh_constant))) 542.07/241.28 DOWN(g(g(fresh_constant))) -> DOWN(g(fresh_constant)) 542.07/241.28 DOWN(f(f(f(a)))) -> F_FLAT(down(f(f(a)))) 542.07/241.28 DOWN(f(f(f(a)))) -> DOWN(f(f(a))) 542.07/241.28 DOWN(f(f(f(b)))) -> F_FLAT(down(f(f(b)))) 542.07/241.28 DOWN(f(f(f(b)))) -> DOWN(f(f(b))) 542.07/241.28 DOWN(f(f(f(g(y16))))) -> F_FLAT(down(f(f(g(y16))))) 542.07/241.28 DOWN(f(f(f(g(y16))))) -> DOWN(f(f(g(y16)))) 542.07/241.28 DOWN(f(f(f(c)))) -> F_FLAT(down(f(f(c)))) 542.07/241.28 DOWN(f(f(f(c)))) -> DOWN(f(f(c))) 542.07/241.28 DOWN(f(f(f(fresh_constant)))) -> F_FLAT(down(f(f(fresh_constant)))) 542.07/241.28 DOWN(f(f(f(fresh_constant)))) -> DOWN(f(f(fresh_constant))) 542.07/241.28 DOWN(g(g(g(a)))) -> G_FLAT(down(g(g(a)))) 542.07/241.28 DOWN(g(g(g(a)))) -> DOWN(g(g(a))) 542.07/241.28 DOWN(g(g(g(f(y18))))) -> G_FLAT(down(g(g(f(y18))))) 542.07/241.28 DOWN(g(g(g(f(y18))))) -> DOWN(g(g(f(y18)))) 542.07/241.28 DOWN(g(g(g(b)))) -> G_FLAT(down(g(g(b)))) 542.07/241.28 DOWN(g(g(g(b)))) -> DOWN(g(g(b))) 542.07/241.28 DOWN(g(g(g(c)))) -> G_FLAT(down(g(g(c)))) 542.07/241.28 DOWN(g(g(g(c)))) -> DOWN(g(g(c))) 542.07/241.28 DOWN(g(g(g(fresh_constant)))) -> G_FLAT(down(g(g(fresh_constant)))) 542.07/241.28 DOWN(g(g(g(fresh_constant)))) -> DOWN(g(g(fresh_constant))) 542.07/241.28 DOWN(f(f(f(f(a))))) -> F_FLAT(down(f(f(f(a))))) 542.07/241.28 DOWN(f(f(f(f(a))))) -> DOWN(f(f(f(a)))) 542.07/241.28 DOWN(f(f(f(f(b))))) -> F_FLAT(down(f(f(f(b))))) 542.07/241.28 DOWN(f(f(f(f(b))))) -> DOWN(f(f(f(b)))) 542.07/241.28 DOWN(f(f(f(f(g(y22)))))) -> F_FLAT(down(f(f(f(g(y22)))))) 542.07/241.28 DOWN(f(f(f(f(g(y22)))))) -> DOWN(f(f(f(g(y22))))) 542.07/241.28 DOWN(f(f(f(f(c))))) -> F_FLAT(down(f(f(f(c))))) 542.07/241.28 DOWN(f(f(f(f(c))))) -> DOWN(f(f(f(c)))) 542.07/241.28 DOWN(f(f(f(f(fresh_constant))))) -> F_FLAT(down(f(f(f(fresh_constant))))) 542.07/241.28 DOWN(f(f(f(f(fresh_constant))))) -> DOWN(f(f(f(fresh_constant)))) 542.07/241.28 DOWN(g(g(g(g(a))))) -> G_FLAT(down(g(g(g(a))))) 542.07/241.28 DOWN(g(g(g(g(a))))) -> DOWN(g(g(g(a)))) 542.07/241.28 DOWN(g(g(g(g(f(y24)))))) -> G_FLAT(down(g(g(g(f(y24)))))) 542.07/241.28 DOWN(g(g(g(g(f(y24)))))) -> DOWN(g(g(g(f(y24))))) 542.07/241.28 DOWN(g(g(g(g(b))))) -> G_FLAT(down(g(g(g(b))))) 542.07/241.28 DOWN(g(g(g(g(b))))) -> DOWN(g(g(g(b)))) 542.07/241.28 DOWN(g(g(g(g(c))))) -> G_FLAT(down(g(g(g(c))))) 542.07/241.28 DOWN(g(g(g(g(c))))) -> DOWN(g(g(g(c)))) 542.07/241.28 DOWN(g(g(g(g(fresh_constant))))) -> G_FLAT(down(g(g(g(fresh_constant))))) 542.07/241.28 DOWN(g(g(g(g(fresh_constant))))) -> DOWN(g(g(g(fresh_constant)))) 542.07/241.28 DOWN(f(f(f(f(f(a)))))) -> F_FLAT(down(f(f(f(f(a)))))) 542.07/241.28 DOWN(f(f(f(f(f(a)))))) -> DOWN(f(f(f(f(a))))) 542.07/241.28 DOWN(f(f(f(f(f(b)))))) -> F_FLAT(down(f(f(f(f(b)))))) 542.07/241.28 DOWN(f(f(f(f(f(b)))))) -> DOWN(f(f(f(f(b))))) 542.07/241.28 DOWN(f(f(f(f(f(g(y28))))))) -> F_FLAT(down(f(f(f(f(g(y28))))))) 542.07/241.28 DOWN(f(f(f(f(f(g(y28))))))) -> DOWN(f(f(f(f(g(y28)))))) 542.07/241.28 DOWN(f(f(f(f(f(c)))))) -> F_FLAT(down(f(f(f(f(c)))))) 542.07/241.28 DOWN(f(f(f(f(f(c)))))) -> DOWN(f(f(f(f(c))))) 542.07/241.28 DOWN(f(f(f(f(f(fresh_constant)))))) -> F_FLAT(down(f(f(f(f(fresh_constant)))))) 542.07/241.28 DOWN(f(f(f(f(f(fresh_constant)))))) -> DOWN(f(f(f(f(fresh_constant))))) 542.07/241.28 DOWN(g(g(g(g(g(a)))))) -> G_FLAT(down(g(g(g(g(a)))))) 542.07/241.28 DOWN(g(g(g(g(g(a)))))) -> DOWN(g(g(g(g(a))))) 542.07/241.28 DOWN(g(g(g(g(g(f(y30))))))) -> G_FLAT(down(g(g(g(g(f(y30))))))) 542.07/241.28 DOWN(g(g(g(g(g(f(y30))))))) -> DOWN(g(g(g(g(f(y30)))))) 542.07/241.28 DOWN(g(g(g(g(g(b)))))) -> G_FLAT(down(g(g(g(g(b)))))) 542.07/241.28 DOWN(g(g(g(g(g(b)))))) -> DOWN(g(g(g(g(b))))) 542.07/241.28 DOWN(g(g(g(g(g(c)))))) -> G_FLAT(down(g(g(g(g(c)))))) 542.07/241.28 DOWN(g(g(g(g(g(c)))))) -> DOWN(g(g(g(g(c))))) 542.07/241.28 DOWN(g(g(g(g(g(fresh_constant)))))) -> G_FLAT(down(g(g(g(g(fresh_constant)))))) 542.07/241.28 DOWN(g(g(g(g(g(fresh_constant)))))) -> DOWN(g(g(g(g(fresh_constant))))) 542.07/241.28 DOWN(f(f(f(f(f(f(a))))))) -> F_FLAT(down(f(f(f(f(f(a))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(a))))))) -> DOWN(f(f(f(f(f(a)))))) 542.07/241.28 DOWN(f(f(f(f(f(f(b))))))) -> F_FLAT(down(f(f(f(f(f(b))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(b))))))) -> DOWN(f(f(f(f(f(b)))))) 542.07/241.28 DOWN(f(f(f(f(f(f(g(y34)))))))) -> F_FLAT(down(f(f(f(f(f(g(y34)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(g(y34)))))))) -> DOWN(f(f(f(f(f(g(y34))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(c))))))) -> F_FLAT(down(f(f(f(f(f(c))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(c))))))) -> DOWN(f(f(f(f(f(c)))))) 542.07/241.28 DOWN(f(f(f(f(f(f(fresh_constant))))))) -> F_FLAT(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(fresh_constant))))))) -> DOWN(f(f(f(f(f(fresh_constant)))))) 542.07/241.28 DOWN(g(g(g(g(g(g(a))))))) -> G_FLAT(down(g(g(g(g(g(a))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(a))))))) -> DOWN(g(g(g(g(g(a)))))) 542.07/241.28 DOWN(g(g(g(g(g(g(f(y36)))))))) -> G_FLAT(down(g(g(g(g(g(f(y36)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(f(y36)))))))) -> DOWN(g(g(g(g(g(f(y36))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(b))))))) -> G_FLAT(down(g(g(g(g(g(b))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(b))))))) -> DOWN(g(g(g(g(g(b)))))) 542.07/241.28 DOWN(g(g(g(g(g(g(c))))))) -> G_FLAT(down(g(g(g(g(g(c))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(c))))))) -> DOWN(g(g(g(g(g(c)))))) 542.07/241.28 DOWN(g(g(g(g(g(g(fresh_constant))))))) -> G_FLAT(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(fresh_constant))))))) -> DOWN(g(g(g(g(g(fresh_constant)))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(a)))))))) -> F_FLAT(down(f(f(f(f(f(f(a)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(a)))))))) -> DOWN(f(f(f(f(f(f(a))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(b)))))))) -> F_FLAT(down(f(f(f(f(f(f(b)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(b)))))))) -> DOWN(f(f(f(f(f(f(b))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(g(y40))))))))) -> F_FLAT(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(g(y40))))))))) -> DOWN(f(f(f(f(f(f(g(y40)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(c)))))))) -> F_FLAT(down(f(f(f(f(f(f(c)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(c)))))))) -> DOWN(f(f(f(f(f(f(c))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(fresh_constant)))))))) -> F_FLAT(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(fresh_constant)))))))) -> DOWN(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(a)))))))) -> G_FLAT(down(g(g(g(g(g(g(a)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(a)))))))) -> DOWN(g(g(g(g(g(g(a))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(f(y42))))))))) -> G_FLAT(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(f(y42))))))))) -> DOWN(g(g(g(g(g(g(f(y42)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(b)))))))) -> G_FLAT(down(g(g(g(g(g(g(b)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(b)))))))) -> DOWN(g(g(g(g(g(g(b))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(c)))))))) -> G_FLAT(down(g(g(g(g(g(g(c)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(c)))))))) -> DOWN(g(g(g(g(g(g(c))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(fresh_constant)))))))) -> G_FLAT(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(fresh_constant)))))))) -> DOWN(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(a))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(a))))))))) -> DOWN(f(f(f(f(f(f(f(a)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(b))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(b))))))))) -> DOWN(f(f(f(f(f(f(f(b)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(g(y46)))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(g(y46)))))))))) -> DOWN(f(f(f(f(f(f(f(g(y46))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(c))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(c))))))))) -> DOWN(f(f(f(f(f(f(f(c)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> DOWN(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(a))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(a))))))))) -> DOWN(g(g(g(g(g(g(g(a)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(f(y48)))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(f(y48)))))))))) -> DOWN(g(g(g(g(g(g(g(f(y48))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(b))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(b))))))))) -> DOWN(g(g(g(g(g(g(g(b)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(c))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(c))))))))) -> DOWN(g(g(g(g(g(g(g(c)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> DOWN(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(a)))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(a)))))))))) -> DOWN(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(b)))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(b)))))))))) -> DOWN(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> DOWN(f(f(f(f(f(f(f(f(g(y52)))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(c)))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(c)))))))))) -> DOWN(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> F_FLAT(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> DOWN(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(a)))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(a)))))))))) -> DOWN(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> DOWN(g(g(g(g(g(g(g(g(f(y54)))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(b)))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(b)))))))))) -> DOWN(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(c)))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(c)))))))))) -> DOWN(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> G_FLAT(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> DOWN(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.28 542.07/241.28 The TRS R consists of the following rules: 542.07/241.28 542.07/241.28 down(a) -> up(f(a)) 542.07/241.28 down(b) -> up(g(b)) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.28 top(up(x)) -> top(down(x)) 542.07/241.28 down(f(a)) -> f_flat(down(a)) 542.07/241.28 down(f(b)) -> f_flat(down(b)) 542.07/241.28 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.28 down(f(c)) -> f_flat(down(c)) 542.07/241.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.28 down(g(a)) -> g_flat(down(a)) 542.07/241.28 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.28 down(g(b)) -> g_flat(down(b)) 542.07/241.28 down(g(c)) -> g_flat(down(c)) 542.07/241.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.28 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.28 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.28 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.28 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.28 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.28 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.28 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.28 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.28 542.07/241.28 The set Q consists of the following terms: 542.07/241.28 542.07/241.28 down(a) 542.07/241.28 down(b) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.28 top(up(x0)) 542.07/241.28 down(f(a)) 542.07/241.28 down(f(b)) 542.07/241.28 down(f(g(x0))) 542.07/241.28 down(f(c)) 542.07/241.28 down(f(fresh_constant)) 542.07/241.28 down(g(a)) 542.07/241.28 down(g(f(x0))) 542.07/241.28 down(g(b)) 542.07/241.28 down(g(c)) 542.07/241.28 down(g(fresh_constant)) 542.07/241.28 down(f(f(a))) 542.07/241.28 down(f(f(b))) 542.07/241.28 down(f(f(g(x0)))) 542.07/241.28 down(f(f(c))) 542.07/241.28 down(f(f(fresh_constant))) 542.07/241.28 down(g(g(a))) 542.07/241.28 down(g(g(f(x0)))) 542.07/241.28 down(g(g(b))) 542.07/241.28 down(g(g(c))) 542.07/241.28 down(g(g(fresh_constant))) 542.07/241.28 down(f(f(f(a)))) 542.07/241.28 down(f(f(f(b)))) 542.07/241.28 down(f(f(f(g(x0))))) 542.07/241.28 down(f(f(f(c)))) 542.07/241.28 down(f(f(f(fresh_constant)))) 542.07/241.28 down(g(g(g(a)))) 542.07/241.28 down(g(g(g(f(x0))))) 542.07/241.28 down(g(g(g(b)))) 542.07/241.28 down(g(g(g(c)))) 542.07/241.28 down(g(g(g(fresh_constant)))) 542.07/241.28 down(f(f(f(f(a))))) 542.07/241.28 down(f(f(f(f(b))))) 542.07/241.28 down(f(f(f(f(g(x0)))))) 542.07/241.28 down(f(f(f(f(c))))) 542.07/241.28 down(f(f(f(f(fresh_constant))))) 542.07/241.28 down(g(g(g(g(a))))) 542.07/241.28 down(g(g(g(g(f(x0)))))) 542.07/241.28 down(g(g(g(g(b))))) 542.07/241.28 down(g(g(g(g(c))))) 542.07/241.28 down(g(g(g(g(fresh_constant))))) 542.07/241.28 down(f(f(f(f(f(a)))))) 542.07/241.28 down(f(f(f(f(f(b)))))) 542.07/241.28 down(f(f(f(f(f(g(x0))))))) 542.07/241.28 down(f(f(f(f(f(c)))))) 542.07/241.28 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.28 down(g(g(g(g(g(a)))))) 542.07/241.28 down(g(g(g(g(g(f(x0))))))) 542.07/241.28 down(g(g(g(g(g(b)))))) 542.07/241.28 down(g(g(g(g(g(c)))))) 542.07/241.28 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.28 down(f(f(f(f(f(f(a))))))) 542.07/241.28 down(f(f(f(f(f(f(b))))))) 542.07/241.28 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.28 down(f(f(f(f(f(f(c))))))) 542.07/241.28 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.28 down(g(g(g(g(g(g(a))))))) 542.07/241.28 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.28 down(g(g(g(g(g(g(b))))))) 542.07/241.28 down(g(g(g(g(g(g(c))))))) 542.07/241.28 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.28 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.28 f_flat(up(x0)) 542.07/241.28 g_flat(up(x0)) 542.07/241.28 542.07/241.28 We have to consider all minimal (P,Q,R)-chains. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (57) DependencyGraphProof (EQUIVALENT) 542.07/241.28 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 163 less nodes. 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (58) 542.07/241.28 Complex Obligation (AND) 542.07/241.28 542.07/241.28 ---------------------------------------- 542.07/241.28 542.07/241.28 (59) 542.07/241.28 Obligation: 542.07/241.28 Q DP problem: 542.07/241.28 The TRS P consists of the following rules: 542.07/241.28 542.07/241.28 DOWN(f(g(y4))) -> DOWN(g(y4)) 542.07/241.28 DOWN(g(f(y6))) -> DOWN(f(y6)) 542.07/241.28 DOWN(f(f(g(y10)))) -> DOWN(f(g(y10))) 542.07/241.28 DOWN(f(f(f(g(y16))))) -> DOWN(f(f(g(y16)))) 542.07/241.28 DOWN(f(f(f(f(g(y22)))))) -> DOWN(f(f(f(g(y22))))) 542.07/241.28 DOWN(f(f(f(f(f(g(y28))))))) -> DOWN(f(f(f(f(g(y28)))))) 542.07/241.28 DOWN(f(f(f(f(f(f(g(y34)))))))) -> DOWN(f(f(f(f(f(g(y34))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(g(y40))))))))) -> DOWN(f(f(f(f(f(f(g(y40)))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(g(y46)))))))))) -> DOWN(f(f(f(f(f(f(f(g(y46))))))))) 542.07/241.28 DOWN(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> DOWN(f(f(f(f(f(f(f(f(g(y52)))))))))) 542.07/241.28 DOWN(g(g(f(y12)))) -> DOWN(g(f(y12))) 542.07/241.28 DOWN(g(g(g(f(y18))))) -> DOWN(g(g(f(y18)))) 542.07/241.28 DOWN(g(g(g(g(f(y24)))))) -> DOWN(g(g(g(f(y24))))) 542.07/241.28 DOWN(g(g(g(g(g(f(y30))))))) -> DOWN(g(g(g(g(f(y30)))))) 542.07/241.28 DOWN(g(g(g(g(g(g(f(y36)))))))) -> DOWN(g(g(g(g(g(f(y36))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(f(y42))))))))) -> DOWN(g(g(g(g(g(g(f(y42)))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(f(y48)))))))))) -> DOWN(g(g(g(g(g(g(g(f(y48))))))))) 542.07/241.28 DOWN(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> DOWN(g(g(g(g(g(g(g(g(f(y54)))))))))) 542.07/241.29 542.07/241.29 The TRS R consists of the following rules: 542.07/241.29 542.07/241.29 down(a) -> up(f(a)) 542.07/241.29 down(b) -> up(g(b)) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.29 top(up(x)) -> top(down(x)) 542.07/241.29 down(f(a)) -> f_flat(down(a)) 542.07/241.29 down(f(b)) -> f_flat(down(b)) 542.07/241.29 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.29 down(f(c)) -> f_flat(down(c)) 542.07/241.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.29 down(g(a)) -> g_flat(down(a)) 542.07/241.29 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.29 down(g(b)) -> g_flat(down(b)) 542.07/241.29 down(g(c)) -> g_flat(down(c)) 542.07/241.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.29 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.29 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.29 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.29 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.29 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.29 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.29 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.29 542.07/241.29 The set Q consists of the following terms: 542.07/241.29 542.07/241.29 down(a) 542.07/241.29 down(b) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.29 top(up(x0)) 542.07/241.29 down(f(a)) 542.07/241.29 down(f(b)) 542.07/241.29 down(f(g(x0))) 542.07/241.29 down(f(c)) 542.07/241.29 down(f(fresh_constant)) 542.07/241.29 down(g(a)) 542.07/241.29 down(g(f(x0))) 542.07/241.29 down(g(b)) 542.07/241.29 down(g(c)) 542.07/241.29 down(g(fresh_constant)) 542.07/241.29 down(f(f(a))) 542.07/241.29 down(f(f(b))) 542.07/241.29 down(f(f(g(x0)))) 542.07/241.29 down(f(f(c))) 542.07/241.29 down(f(f(fresh_constant))) 542.07/241.29 down(g(g(a))) 542.07/241.29 down(g(g(f(x0)))) 542.07/241.29 down(g(g(b))) 542.07/241.29 down(g(g(c))) 542.07/241.29 down(g(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) 542.07/241.29 down(f(f(f(g(x0))))) 542.07/241.29 down(f(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) 542.07/241.29 down(g(g(g(f(x0))))) 542.07/241.29 down(g(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(x0)))))) 542.07/241.29 down(f(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(x0)))))) 542.07/241.29 down(g(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(x0))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(x0))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 f_flat(up(x0)) 542.07/241.29 g_flat(up(x0)) 542.07/241.29 542.07/241.29 We have to consider all minimal (P,Q,R)-chains. 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (60) UsableRulesProof (EQUIVALENT) 542.07/241.29 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. 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (61) 542.07/241.29 Obligation: 542.07/241.29 Q DP problem: 542.07/241.29 The TRS P consists of the following rules: 542.07/241.29 542.07/241.29 DOWN(f(g(y4))) -> DOWN(g(y4)) 542.07/241.29 DOWN(g(f(y6))) -> DOWN(f(y6)) 542.07/241.29 DOWN(f(f(g(y10)))) -> DOWN(f(g(y10))) 542.07/241.29 DOWN(f(f(f(g(y16))))) -> DOWN(f(f(g(y16)))) 542.07/241.29 DOWN(f(f(f(f(g(y22)))))) -> DOWN(f(f(f(g(y22))))) 542.07/241.29 DOWN(f(f(f(f(f(g(y28))))))) -> DOWN(f(f(f(f(g(y28)))))) 542.07/241.29 DOWN(f(f(f(f(f(f(g(y34)))))))) -> DOWN(f(f(f(f(f(g(y34))))))) 542.07/241.29 DOWN(f(f(f(f(f(f(f(g(y40))))))))) -> DOWN(f(f(f(f(f(f(g(y40)))))))) 542.07/241.29 DOWN(f(f(f(f(f(f(f(f(g(y46)))))))))) -> DOWN(f(f(f(f(f(f(f(g(y46))))))))) 542.07/241.29 DOWN(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> DOWN(f(f(f(f(f(f(f(f(g(y52)))))))))) 542.07/241.29 DOWN(g(g(f(y12)))) -> DOWN(g(f(y12))) 542.07/241.29 DOWN(g(g(g(f(y18))))) -> DOWN(g(g(f(y18)))) 542.07/241.29 DOWN(g(g(g(g(f(y24)))))) -> DOWN(g(g(g(f(y24))))) 542.07/241.29 DOWN(g(g(g(g(g(f(y30))))))) -> DOWN(g(g(g(g(f(y30)))))) 542.07/241.29 DOWN(g(g(g(g(g(g(f(y36)))))))) -> DOWN(g(g(g(g(g(f(y36))))))) 542.07/241.29 DOWN(g(g(g(g(g(g(g(f(y42))))))))) -> DOWN(g(g(g(g(g(g(f(y42)))))))) 542.07/241.29 DOWN(g(g(g(g(g(g(g(g(f(y48)))))))))) -> DOWN(g(g(g(g(g(g(g(f(y48))))))))) 542.07/241.29 DOWN(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> DOWN(g(g(g(g(g(g(g(g(f(y54)))))))))) 542.07/241.29 542.07/241.29 R is empty. 542.07/241.29 The set Q consists of the following terms: 542.07/241.29 542.07/241.29 down(a) 542.07/241.29 down(b) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.29 top(up(x0)) 542.07/241.29 down(f(a)) 542.07/241.29 down(f(b)) 542.07/241.29 down(f(g(x0))) 542.07/241.29 down(f(c)) 542.07/241.29 down(f(fresh_constant)) 542.07/241.29 down(g(a)) 542.07/241.29 down(g(f(x0))) 542.07/241.29 down(g(b)) 542.07/241.29 down(g(c)) 542.07/241.29 down(g(fresh_constant)) 542.07/241.29 down(f(f(a))) 542.07/241.29 down(f(f(b))) 542.07/241.29 down(f(f(g(x0)))) 542.07/241.29 down(f(f(c))) 542.07/241.29 down(f(f(fresh_constant))) 542.07/241.29 down(g(g(a))) 542.07/241.29 down(g(g(f(x0)))) 542.07/241.29 down(g(g(b))) 542.07/241.29 down(g(g(c))) 542.07/241.29 down(g(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) 542.07/241.29 down(f(f(f(g(x0))))) 542.07/241.29 down(f(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) 542.07/241.29 down(g(g(g(f(x0))))) 542.07/241.29 down(g(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(x0)))))) 542.07/241.29 down(f(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(x0)))))) 542.07/241.29 down(g(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(x0))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(x0))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 f_flat(up(x0)) 542.07/241.29 g_flat(up(x0)) 542.07/241.29 542.07/241.29 We have to consider all minimal (P,Q,R)-chains. 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (62) QReductionProof (EQUIVALENT) 542.07/241.29 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 542.07/241.29 542.07/241.29 down(a) 542.07/241.29 down(b) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.29 top(up(x0)) 542.07/241.29 down(f(a)) 542.07/241.29 down(f(b)) 542.07/241.29 down(f(g(x0))) 542.07/241.29 down(f(c)) 542.07/241.29 down(f(fresh_constant)) 542.07/241.29 down(g(a)) 542.07/241.29 down(g(f(x0))) 542.07/241.29 down(g(b)) 542.07/241.29 down(g(c)) 542.07/241.29 down(g(fresh_constant)) 542.07/241.29 down(f(f(a))) 542.07/241.29 down(f(f(b))) 542.07/241.29 down(f(f(g(x0)))) 542.07/241.29 down(f(f(c))) 542.07/241.29 down(f(f(fresh_constant))) 542.07/241.29 down(g(g(a))) 542.07/241.29 down(g(g(f(x0)))) 542.07/241.29 down(g(g(b))) 542.07/241.29 down(g(g(c))) 542.07/241.29 down(g(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) 542.07/241.29 down(f(f(f(g(x0))))) 542.07/241.29 down(f(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) 542.07/241.29 down(g(g(g(f(x0))))) 542.07/241.29 down(g(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(x0)))))) 542.07/241.29 down(f(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(x0)))))) 542.07/241.29 down(g(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(x0))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(x0))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 f_flat(up(x0)) 542.07/241.29 g_flat(up(x0)) 542.07/241.29 542.07/241.29 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (63) 542.07/241.29 Obligation: 542.07/241.29 Q DP problem: 542.07/241.29 The TRS P consists of the following rules: 542.07/241.29 542.07/241.29 DOWN(f(g(y4))) -> DOWN(g(y4)) 542.07/241.29 DOWN(g(f(y6))) -> DOWN(f(y6)) 542.07/241.29 DOWN(f(f(g(y10)))) -> DOWN(f(g(y10))) 542.07/241.29 DOWN(f(f(f(g(y16))))) -> DOWN(f(f(g(y16)))) 542.07/241.29 DOWN(f(f(f(f(g(y22)))))) -> DOWN(f(f(f(g(y22))))) 542.07/241.29 DOWN(f(f(f(f(f(g(y28))))))) -> DOWN(f(f(f(f(g(y28)))))) 542.07/241.29 DOWN(f(f(f(f(f(f(g(y34)))))))) -> DOWN(f(f(f(f(f(g(y34))))))) 542.07/241.29 DOWN(f(f(f(f(f(f(f(g(y40))))))))) -> DOWN(f(f(f(f(f(f(g(y40)))))))) 542.07/241.29 DOWN(f(f(f(f(f(f(f(f(g(y46)))))))))) -> DOWN(f(f(f(f(f(f(f(g(y46))))))))) 542.07/241.29 DOWN(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> DOWN(f(f(f(f(f(f(f(f(g(y52)))))))))) 542.07/241.29 DOWN(g(g(f(y12)))) -> DOWN(g(f(y12))) 542.07/241.29 DOWN(g(g(g(f(y18))))) -> DOWN(g(g(f(y18)))) 542.07/241.29 DOWN(g(g(g(g(f(y24)))))) -> DOWN(g(g(g(f(y24))))) 542.07/241.29 DOWN(g(g(g(g(g(f(y30))))))) -> DOWN(g(g(g(g(f(y30)))))) 542.07/241.29 DOWN(g(g(g(g(g(g(f(y36)))))))) -> DOWN(g(g(g(g(g(f(y36))))))) 542.07/241.29 DOWN(g(g(g(g(g(g(g(f(y42))))))))) -> DOWN(g(g(g(g(g(g(f(y42)))))))) 542.07/241.29 DOWN(g(g(g(g(g(g(g(g(f(y48)))))))))) -> DOWN(g(g(g(g(g(g(g(f(y48))))))))) 542.07/241.29 DOWN(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> DOWN(g(g(g(g(g(g(g(g(f(y54)))))))))) 542.07/241.29 542.07/241.29 R is empty. 542.07/241.29 Q is empty. 542.07/241.29 We have to consider all minimal (P,Q,R)-chains. 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (64) QDPSizeChangeProof (EQUIVALENT) 542.07/241.29 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. 542.07/241.29 542.07/241.29 From the DPs we obtained the following set of size-change graphs: 542.07/241.29 *DOWN(g(f(y6))) -> DOWN(f(y6)) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(f(f(g(y10)))) -> DOWN(f(g(y10))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(g(g(f(y12)))) -> DOWN(g(f(y12))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(f(g(y4))) -> DOWN(g(y4)) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(f(f(f(g(y16))))) -> DOWN(f(f(g(y16)))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(f(f(f(f(g(y22)))))) -> DOWN(f(f(f(g(y22))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(f(f(f(f(f(g(y28))))))) -> DOWN(f(f(f(f(g(y28)))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(f(f(f(f(f(f(g(y34)))))))) -> DOWN(f(f(f(f(f(g(y34))))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(f(f(f(f(f(f(f(g(y40))))))))) -> DOWN(f(f(f(f(f(f(g(y40)))))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(f(f(f(f(f(f(f(f(g(y46)))))))))) -> DOWN(f(f(f(f(f(f(f(g(y46))))))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> DOWN(f(f(f(f(f(f(f(f(g(y52)))))))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(g(g(g(f(y18))))) -> DOWN(g(g(f(y18)))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(g(g(g(g(f(y24)))))) -> DOWN(g(g(g(f(y24))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(g(g(g(g(g(f(y30))))))) -> DOWN(g(g(g(g(f(y30)))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(g(g(g(g(g(g(f(y36)))))))) -> DOWN(g(g(g(g(g(f(y36))))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(g(g(g(g(g(g(g(f(y42))))))))) -> DOWN(g(g(g(g(g(g(f(y42)))))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(g(g(g(g(g(g(g(g(f(y48)))))))))) -> DOWN(g(g(g(g(g(g(g(f(y48))))))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 *DOWN(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> DOWN(g(g(g(g(g(g(g(g(f(y54)))))))))) 542.07/241.29 The graph contains the following edges 1 > 1 542.07/241.29 542.07/241.29 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (65) 542.07/241.29 YES 542.07/241.29 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (66) 542.07/241.29 Obligation: 542.07/241.29 Q DP problem: 542.07/241.29 The TRS P consists of the following rules: 542.07/241.29 542.07/241.29 TOP(up(x)) -> TOP(down(x)) 542.07/241.29 542.07/241.29 The TRS R consists of the following rules: 542.07/241.29 542.07/241.29 down(a) -> up(f(a)) 542.07/241.29 down(b) -> up(g(b)) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.29 top(up(x)) -> top(down(x)) 542.07/241.29 down(f(a)) -> f_flat(down(a)) 542.07/241.29 down(f(b)) -> f_flat(down(b)) 542.07/241.29 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.29 down(f(c)) -> f_flat(down(c)) 542.07/241.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.29 down(g(a)) -> g_flat(down(a)) 542.07/241.29 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.29 down(g(b)) -> g_flat(down(b)) 542.07/241.29 down(g(c)) -> g_flat(down(c)) 542.07/241.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.29 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.29 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.29 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.29 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.29 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.29 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.29 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.29 542.07/241.29 The set Q consists of the following terms: 542.07/241.29 542.07/241.29 down(a) 542.07/241.29 down(b) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.29 top(up(x0)) 542.07/241.29 down(f(a)) 542.07/241.29 down(f(b)) 542.07/241.29 down(f(g(x0))) 542.07/241.29 down(f(c)) 542.07/241.29 down(f(fresh_constant)) 542.07/241.29 down(g(a)) 542.07/241.29 down(g(f(x0))) 542.07/241.29 down(g(b)) 542.07/241.29 down(g(c)) 542.07/241.29 down(g(fresh_constant)) 542.07/241.29 down(f(f(a))) 542.07/241.29 down(f(f(b))) 542.07/241.29 down(f(f(g(x0)))) 542.07/241.29 down(f(f(c))) 542.07/241.29 down(f(f(fresh_constant))) 542.07/241.29 down(g(g(a))) 542.07/241.29 down(g(g(f(x0)))) 542.07/241.29 down(g(g(b))) 542.07/241.29 down(g(g(c))) 542.07/241.29 down(g(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) 542.07/241.29 down(f(f(f(g(x0))))) 542.07/241.29 down(f(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) 542.07/241.29 down(g(g(g(f(x0))))) 542.07/241.29 down(g(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(x0)))))) 542.07/241.29 down(f(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(x0)))))) 542.07/241.29 down(g(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(x0))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(x0))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 f_flat(up(x0)) 542.07/241.29 g_flat(up(x0)) 542.07/241.29 542.07/241.29 We have to consider all minimal (P,Q,R)-chains. 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (67) UsableRulesProof (EQUIVALENT) 542.07/241.29 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. 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (68) 542.07/241.29 Obligation: 542.07/241.29 Q DP problem: 542.07/241.29 The TRS P consists of the following rules: 542.07/241.29 542.07/241.29 TOP(up(x)) -> TOP(down(x)) 542.07/241.29 542.07/241.29 The TRS R consists of the following rules: 542.07/241.29 542.07/241.29 down(a) -> up(f(a)) 542.07/241.29 down(b) -> up(g(b)) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.29 down(f(a)) -> f_flat(down(a)) 542.07/241.29 down(f(b)) -> f_flat(down(b)) 542.07/241.29 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.29 down(f(c)) -> f_flat(down(c)) 542.07/241.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.29 down(g(a)) -> g_flat(down(a)) 542.07/241.29 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.29 down(g(b)) -> g_flat(down(b)) 542.07/241.29 down(g(c)) -> g_flat(down(c)) 542.07/241.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.29 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.29 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.29 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.29 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.29 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.29 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.29 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.29 542.07/241.29 The set Q consists of the following terms: 542.07/241.29 542.07/241.29 down(a) 542.07/241.29 down(b) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.29 top(up(x0)) 542.07/241.29 down(f(a)) 542.07/241.29 down(f(b)) 542.07/241.29 down(f(g(x0))) 542.07/241.29 down(f(c)) 542.07/241.29 down(f(fresh_constant)) 542.07/241.29 down(g(a)) 542.07/241.29 down(g(f(x0))) 542.07/241.29 down(g(b)) 542.07/241.29 down(g(c)) 542.07/241.29 down(g(fresh_constant)) 542.07/241.29 down(f(f(a))) 542.07/241.29 down(f(f(b))) 542.07/241.29 down(f(f(g(x0)))) 542.07/241.29 down(f(f(c))) 542.07/241.29 down(f(f(fresh_constant))) 542.07/241.29 down(g(g(a))) 542.07/241.29 down(g(g(f(x0)))) 542.07/241.29 down(g(g(b))) 542.07/241.29 down(g(g(c))) 542.07/241.29 down(g(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) 542.07/241.29 down(f(f(f(g(x0))))) 542.07/241.29 down(f(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) 542.07/241.29 down(g(g(g(f(x0))))) 542.07/241.29 down(g(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(x0)))))) 542.07/241.29 down(f(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(x0)))))) 542.07/241.29 down(g(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(x0))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(x0))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 f_flat(up(x0)) 542.07/241.29 g_flat(up(x0)) 542.07/241.29 542.07/241.29 We have to consider all minimal (P,Q,R)-chains. 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (69) QReductionProof (EQUIVALENT) 542.07/241.29 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 542.07/241.29 542.07/241.29 top(up(x0)) 542.07/241.29 542.07/241.29 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (70) 542.07/241.29 Obligation: 542.07/241.29 Q DP problem: 542.07/241.29 The TRS P consists of the following rules: 542.07/241.29 542.07/241.29 TOP(up(x)) -> TOP(down(x)) 542.07/241.29 542.07/241.29 The TRS R consists of the following rules: 542.07/241.29 542.07/241.29 down(a) -> up(f(a)) 542.07/241.29 down(b) -> up(g(b)) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.29 down(f(a)) -> f_flat(down(a)) 542.07/241.29 down(f(b)) -> f_flat(down(b)) 542.07/241.29 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.29 down(f(c)) -> f_flat(down(c)) 542.07/241.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.29 down(g(a)) -> g_flat(down(a)) 542.07/241.29 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.29 down(g(b)) -> g_flat(down(b)) 542.07/241.29 down(g(c)) -> g_flat(down(c)) 542.07/241.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.29 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.29 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.29 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.29 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.29 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.29 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.29 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.29 542.07/241.29 The set Q consists of the following terms: 542.07/241.29 542.07/241.29 down(a) 542.07/241.29 down(b) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.29 down(f(a)) 542.07/241.29 down(f(b)) 542.07/241.29 down(f(g(x0))) 542.07/241.29 down(f(c)) 542.07/241.29 down(f(fresh_constant)) 542.07/241.29 down(g(a)) 542.07/241.29 down(g(f(x0))) 542.07/241.29 down(g(b)) 542.07/241.29 down(g(c)) 542.07/241.29 down(g(fresh_constant)) 542.07/241.29 down(f(f(a))) 542.07/241.29 down(f(f(b))) 542.07/241.29 down(f(f(g(x0)))) 542.07/241.29 down(f(f(c))) 542.07/241.29 down(f(f(fresh_constant))) 542.07/241.29 down(g(g(a))) 542.07/241.29 down(g(g(f(x0)))) 542.07/241.29 down(g(g(b))) 542.07/241.29 down(g(g(c))) 542.07/241.29 down(g(g(fresh_constant))) 542.07/241.29 down(f(f(f(a)))) 542.07/241.29 down(f(f(f(b)))) 542.07/241.29 down(f(f(f(g(x0))))) 542.07/241.29 down(f(f(f(c)))) 542.07/241.29 down(f(f(f(fresh_constant)))) 542.07/241.29 down(g(g(g(a)))) 542.07/241.29 down(g(g(g(f(x0))))) 542.07/241.29 down(g(g(g(b)))) 542.07/241.29 down(g(g(g(c)))) 542.07/241.29 down(g(g(g(fresh_constant)))) 542.07/241.29 down(f(f(f(f(a))))) 542.07/241.29 down(f(f(f(f(b))))) 542.07/241.29 down(f(f(f(f(g(x0)))))) 542.07/241.29 down(f(f(f(f(c))))) 542.07/241.29 down(f(f(f(f(fresh_constant))))) 542.07/241.29 down(g(g(g(g(a))))) 542.07/241.29 down(g(g(g(g(f(x0)))))) 542.07/241.29 down(g(g(g(g(b))))) 542.07/241.29 down(g(g(g(g(c))))) 542.07/241.29 down(g(g(g(g(fresh_constant))))) 542.07/241.29 down(f(f(f(f(f(a)))))) 542.07/241.29 down(f(f(f(f(f(b)))))) 542.07/241.29 down(f(f(f(f(f(g(x0))))))) 542.07/241.29 down(f(f(f(f(f(c)))))) 542.07/241.29 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.29 down(g(g(g(g(g(a)))))) 542.07/241.29 down(g(g(g(g(g(f(x0))))))) 542.07/241.29 down(g(g(g(g(g(b)))))) 542.07/241.29 down(g(g(g(g(g(c)))))) 542.07/241.29 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.29 down(f(f(f(f(f(f(a))))))) 542.07/241.29 down(f(f(f(f(f(f(b))))))) 542.07/241.29 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.29 down(f(f(f(f(f(f(c))))))) 542.07/241.29 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.29 down(g(g(g(g(g(g(a))))))) 542.07/241.29 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.29 down(g(g(g(g(g(g(b))))))) 542.07/241.29 down(g(g(g(g(g(g(c))))))) 542.07/241.29 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.29 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 f_flat(up(x0)) 542.07/241.29 g_flat(up(x0)) 542.07/241.29 542.07/241.29 We have to consider all minimal (P,Q,R)-chains. 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (71) TransformationProof (EQUIVALENT) 542.07/241.29 By narrowing [LPAR04] the rule TOP(up(x)) -> TOP(down(x)) at position [0] we obtained the following new rules [LPAR04]: 542.07/241.29 542.07/241.29 (TOP(up(a)) -> TOP(up(f(a))),TOP(up(a)) -> TOP(up(f(a)))) 542.07/241.29 (TOP(up(b)) -> TOP(up(g(b))),TOP(up(b)) -> TOP(up(g(b)))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(f(f(x0)))))))))))) -> TOP(up(c)),TOP(up(f(f(f(f(f(f(f(f(f(f(x0)))))))))))) -> TOP(up(c))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(g(g(x0)))))))))))) -> TOP(up(c)),TOP(up(g(g(g(g(g(g(g(g(g(g(x0)))))))))))) -> TOP(up(c))) 542.07/241.29 (TOP(up(f(a))) -> TOP(f_flat(down(a))),TOP(up(f(a))) -> TOP(f_flat(down(a)))) 542.07/241.29 (TOP(up(f(b))) -> TOP(f_flat(down(b))),TOP(up(f(b))) -> TOP(f_flat(down(b)))) 542.07/241.29 (TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))),TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0))))) 542.07/241.29 (TOP(up(f(c))) -> TOP(f_flat(down(c))),TOP(up(f(c))) -> TOP(f_flat(down(c)))) 542.07/241.29 (TOP(up(f(fresh_constant))) -> TOP(f_flat(down(fresh_constant))),TOP(up(f(fresh_constant))) -> TOP(f_flat(down(fresh_constant)))) 542.07/241.29 (TOP(up(g(a))) -> TOP(g_flat(down(a))),TOP(up(g(a))) -> TOP(g_flat(down(a)))) 542.07/241.29 (TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))),TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0))))) 542.07/241.29 (TOP(up(g(b))) -> TOP(g_flat(down(b))),TOP(up(g(b))) -> TOP(g_flat(down(b)))) 542.07/241.29 (TOP(up(g(c))) -> TOP(g_flat(down(c))),TOP(up(g(c))) -> TOP(g_flat(down(c)))) 542.07/241.29 (TOP(up(g(fresh_constant))) -> TOP(g_flat(down(fresh_constant))),TOP(up(g(fresh_constant))) -> TOP(g_flat(down(fresh_constant)))) 542.07/241.29 (TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))),TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a))))) 542.07/241.29 (TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))),TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b))))) 542.07/241.29 (TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))),TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0)))))) 542.07/241.29 (TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))),TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c))))) 542.07/241.29 (TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))),TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant))))) 542.07/241.29 (TOP(up(g(g(a)))) -> TOP(g_flat(down(g(a)))),TOP(up(g(g(a)))) -> TOP(g_flat(down(g(a))))) 542.07/241.29 (TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0))))),TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0)))))) 542.07/241.29 (TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))),TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b))))) 542.07/241.29 (TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))),TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c))))) 542.07/241.29 (TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))),TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant))))) 542.07/241.29 (TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))),TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a)))))) 542.07/241.29 (TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))),TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b)))))) 542.07/241.29 (TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))),TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0))))))) 542.07/241.29 (TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))),TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c)))))) 542.07/241.29 (TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))),TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant)))))) 542.07/241.29 (TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))),TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a)))))) 542.07/241.29 (TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))),TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0))))))) 542.07/241.29 (TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))),TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b)))))) 542.07/241.29 (TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))),TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c)))))) 542.07/241.29 (TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))),TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant)))))) 542.07/241.29 (TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))),TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a))))))) 542.07/241.29 (TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))),TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b))))))) 542.07/241.29 (TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))),TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0)))))))) 542.07/241.29 (TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))),TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c))))))) 542.07/241.29 (TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))),TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant))))))) 542.07/241.29 (TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))),TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a))))))) 542.07/241.29 (TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))),TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0)))))))) 542.07/241.29 (TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))),TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b))))))) 542.07/241.29 (TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))),TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c))))))) 542.07/241.29 (TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))),TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a)))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b)))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))),TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))),TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c)))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))),TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a)))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))),TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b)))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))),TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c)))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))),TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))),TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))),TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))),TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))),TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))),TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))),TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))),TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))),TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))),TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))),TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))),TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))),TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))),TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))),TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))),TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))),TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))),TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))),TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a)))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b)))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0))))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c)))))))))))) 542.07/241.29 (TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a)))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0))))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b)))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c)))))))))))) 542.07/241.29 (TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))))) 542.07/241.29 542.07/241.29 542.07/241.29 ---------------------------------------- 542.07/241.29 542.07/241.29 (72) 542.07/241.29 Obligation: 542.07/241.29 Q DP problem: 542.07/241.29 The TRS P consists of the following rules: 542.07/241.29 542.07/241.29 TOP(up(a)) -> TOP(up(f(a))) 542.07/241.29 TOP(up(b)) -> TOP(up(g(b))) 542.07/241.29 TOP(up(f(f(f(f(f(f(f(f(f(f(x0)))))))))))) -> TOP(up(c)) 542.07/241.29 TOP(up(g(g(g(g(g(g(g(g(g(g(x0)))))))))))) -> TOP(up(c)) 542.07/241.29 TOP(up(f(a))) -> TOP(f_flat(down(a))) 542.07/241.29 TOP(up(f(b))) -> TOP(f_flat(down(b))) 542.07/241.29 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.29 TOP(up(f(c))) -> TOP(f_flat(down(c))) 542.07/241.29 TOP(up(f(fresh_constant))) -> TOP(f_flat(down(fresh_constant))) 542.07/241.29 TOP(up(g(a))) -> TOP(g_flat(down(a))) 542.07/241.29 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.29 TOP(up(g(b))) -> TOP(g_flat(down(b))) 542.07/241.29 TOP(up(g(c))) -> TOP(g_flat(down(c))) 542.07/241.29 TOP(up(g(fresh_constant))) -> TOP(g_flat(down(fresh_constant))) 542.07/241.29 TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))) 542.07/241.29 TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) 542.07/241.29 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.29 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.29 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.29 TOP(up(g(g(a)))) -> TOP(g_flat(down(g(a)))) 542.07/241.29 TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0))))) 542.07/241.29 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.29 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.29 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.29 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.29 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.29 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.29 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.29 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.29 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.29 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.29 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.29 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.29 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.29 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.29 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.29 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.29 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.29 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.29 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.29 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.29 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.29 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.29 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.29 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.29 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.29 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.29 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.29 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.29 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.29 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.29 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.29 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.29 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.29 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.29 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.29 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.29 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.29 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.29 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.29 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.29 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.30 542.07/241.30 The TRS R consists of the following rules: 542.07/241.30 542.07/241.30 down(a) -> up(f(a)) 542.07/241.30 down(b) -> up(g(b)) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.30 down(f(a)) -> f_flat(down(a)) 542.07/241.30 down(f(b)) -> f_flat(down(b)) 542.07/241.30 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.30 down(f(c)) -> f_flat(down(c)) 542.07/241.30 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.30 down(g(a)) -> g_flat(down(a)) 542.07/241.30 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.30 down(g(b)) -> g_flat(down(b)) 542.07/241.30 down(g(c)) -> g_flat(down(c)) 542.07/241.30 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.30 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.30 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.30 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.30 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.30 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.30 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.30 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.30 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.30 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.30 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.30 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.30 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.30 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.30 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.30 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.30 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.30 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.30 542.07/241.30 The set Q consists of the following terms: 542.07/241.30 542.07/241.30 down(a) 542.07/241.30 down(b) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.30 down(f(a)) 542.07/241.30 down(f(b)) 542.07/241.30 down(f(g(x0))) 542.07/241.30 down(f(c)) 542.07/241.30 down(f(fresh_constant)) 542.07/241.30 down(g(a)) 542.07/241.30 down(g(f(x0))) 542.07/241.30 down(g(b)) 542.07/241.30 down(g(c)) 542.07/241.30 down(g(fresh_constant)) 542.07/241.30 down(f(f(a))) 542.07/241.30 down(f(f(b))) 542.07/241.30 down(f(f(g(x0)))) 542.07/241.30 down(f(f(c))) 542.07/241.30 down(f(f(fresh_constant))) 542.07/241.30 down(g(g(a))) 542.07/241.30 down(g(g(f(x0)))) 542.07/241.30 down(g(g(b))) 542.07/241.30 down(g(g(c))) 542.07/241.30 down(g(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) 542.07/241.30 down(f(f(f(g(x0))))) 542.07/241.30 down(f(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) 542.07/241.30 down(g(g(g(f(x0))))) 542.07/241.30 down(g(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(x0)))))) 542.07/241.30 down(f(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(x0)))))) 542.07/241.30 down(g(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(x0))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(x0))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 f_flat(up(x0)) 542.07/241.30 g_flat(up(x0)) 542.07/241.30 542.07/241.30 We have to consider all minimal (P,Q,R)-chains. 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (73) DependencyGraphProof (EQUIVALENT) 542.07/241.30 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 8 less nodes. 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (74) 542.07/241.30 Obligation: 542.07/241.30 Q DP problem: 542.07/241.30 The TRS P consists of the following rules: 542.07/241.30 542.07/241.30 TOP(up(f(a))) -> TOP(f_flat(down(a))) 542.07/241.30 TOP(up(f(b))) -> TOP(f_flat(down(b))) 542.07/241.30 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.30 TOP(up(g(a))) -> TOP(g_flat(down(a))) 542.07/241.30 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.30 TOP(up(g(b))) -> TOP(g_flat(down(b))) 542.07/241.30 TOP(up(g(g(a)))) -> TOP(g_flat(down(g(a)))) 542.07/241.30 TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0))))) 542.07/241.30 TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))) 542.07/241.30 TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) 542.07/241.30 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.30 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.30 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.30 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.30 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.30 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.30 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.30 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.30 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.30 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.30 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.30 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.30 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.30 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.30 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.30 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.30 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.30 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.30 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.30 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.30 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.30 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.30 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.30 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.30 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.30 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.30 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.30 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.30 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.30 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.30 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.30 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.30 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.30 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.30 542.07/241.30 The TRS R consists of the following rules: 542.07/241.30 542.07/241.30 down(a) -> up(f(a)) 542.07/241.30 down(b) -> up(g(b)) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.30 down(f(a)) -> f_flat(down(a)) 542.07/241.30 down(f(b)) -> f_flat(down(b)) 542.07/241.30 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.30 down(f(c)) -> f_flat(down(c)) 542.07/241.30 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.30 down(g(a)) -> g_flat(down(a)) 542.07/241.30 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.30 down(g(b)) -> g_flat(down(b)) 542.07/241.30 down(g(c)) -> g_flat(down(c)) 542.07/241.30 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.30 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.30 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.30 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.30 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.30 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.30 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.30 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.30 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.30 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.30 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.30 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.30 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.30 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.30 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.30 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.30 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.30 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.30 542.07/241.30 The set Q consists of the following terms: 542.07/241.30 542.07/241.30 down(a) 542.07/241.30 down(b) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.30 down(f(a)) 542.07/241.30 down(f(b)) 542.07/241.30 down(f(g(x0))) 542.07/241.30 down(f(c)) 542.07/241.30 down(f(fresh_constant)) 542.07/241.30 down(g(a)) 542.07/241.30 down(g(f(x0))) 542.07/241.30 down(g(b)) 542.07/241.30 down(g(c)) 542.07/241.30 down(g(fresh_constant)) 542.07/241.30 down(f(f(a))) 542.07/241.30 down(f(f(b))) 542.07/241.30 down(f(f(g(x0)))) 542.07/241.30 down(f(f(c))) 542.07/241.30 down(f(f(fresh_constant))) 542.07/241.30 down(g(g(a))) 542.07/241.30 down(g(g(f(x0)))) 542.07/241.30 down(g(g(b))) 542.07/241.30 down(g(g(c))) 542.07/241.30 down(g(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) 542.07/241.30 down(f(f(f(g(x0))))) 542.07/241.30 down(f(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) 542.07/241.30 down(g(g(g(f(x0))))) 542.07/241.30 down(g(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(x0)))))) 542.07/241.30 down(f(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(x0)))))) 542.07/241.30 down(g(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(x0))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(x0))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 f_flat(up(x0)) 542.07/241.30 g_flat(up(x0)) 542.07/241.30 542.07/241.30 We have to consider all minimal (P,Q,R)-chains. 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (75) TransformationProof (EQUIVALENT) 542.07/241.30 By rewriting [LPAR04] the rule TOP(up(f(a))) -> TOP(f_flat(down(a))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.30 542.07/241.30 (TOP(up(f(a))) -> TOP(f_flat(up(f(a)))),TOP(up(f(a))) -> TOP(f_flat(up(f(a))))) 542.07/241.30 542.07/241.30 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (76) 542.07/241.30 Obligation: 542.07/241.30 Q DP problem: 542.07/241.30 The TRS P consists of the following rules: 542.07/241.30 542.07/241.30 TOP(up(f(b))) -> TOP(f_flat(down(b))) 542.07/241.30 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.30 TOP(up(g(a))) -> TOP(g_flat(down(a))) 542.07/241.30 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.30 TOP(up(g(b))) -> TOP(g_flat(down(b))) 542.07/241.30 TOP(up(g(g(a)))) -> TOP(g_flat(down(g(a)))) 542.07/241.30 TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0))))) 542.07/241.30 TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))) 542.07/241.30 TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) 542.07/241.30 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.30 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.30 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.30 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.30 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.30 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.30 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.30 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.30 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.30 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.30 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.30 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.30 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.30 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.30 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.30 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.30 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.30 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.30 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.30 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.30 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.30 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.30 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.30 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.30 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.30 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.30 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.30 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.30 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.30 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.30 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.30 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.30 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.30 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.30 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.30 542.07/241.30 The TRS R consists of the following rules: 542.07/241.30 542.07/241.30 down(a) -> up(f(a)) 542.07/241.30 down(b) -> up(g(b)) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.30 down(f(a)) -> f_flat(down(a)) 542.07/241.30 down(f(b)) -> f_flat(down(b)) 542.07/241.30 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.30 down(f(c)) -> f_flat(down(c)) 542.07/241.30 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.30 down(g(a)) -> g_flat(down(a)) 542.07/241.30 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.30 down(g(b)) -> g_flat(down(b)) 542.07/241.30 down(g(c)) -> g_flat(down(c)) 542.07/241.30 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.30 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.30 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.30 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.30 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.30 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.30 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.30 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.30 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.30 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.30 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.30 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.30 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.30 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.30 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.30 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.30 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.30 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.30 542.07/241.30 The set Q consists of the following terms: 542.07/241.30 542.07/241.30 down(a) 542.07/241.30 down(b) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.30 down(f(a)) 542.07/241.30 down(f(b)) 542.07/241.30 down(f(g(x0))) 542.07/241.30 down(f(c)) 542.07/241.30 down(f(fresh_constant)) 542.07/241.30 down(g(a)) 542.07/241.30 down(g(f(x0))) 542.07/241.30 down(g(b)) 542.07/241.30 down(g(c)) 542.07/241.30 down(g(fresh_constant)) 542.07/241.30 down(f(f(a))) 542.07/241.30 down(f(f(b))) 542.07/241.30 down(f(f(g(x0)))) 542.07/241.30 down(f(f(c))) 542.07/241.30 down(f(f(fresh_constant))) 542.07/241.30 down(g(g(a))) 542.07/241.30 down(g(g(f(x0)))) 542.07/241.30 down(g(g(b))) 542.07/241.30 down(g(g(c))) 542.07/241.30 down(g(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) 542.07/241.30 down(f(f(f(g(x0))))) 542.07/241.30 down(f(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) 542.07/241.30 down(g(g(g(f(x0))))) 542.07/241.30 down(g(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(x0)))))) 542.07/241.30 down(f(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(x0)))))) 542.07/241.30 down(g(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(x0))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(x0))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 f_flat(up(x0)) 542.07/241.30 g_flat(up(x0)) 542.07/241.30 542.07/241.30 We have to consider all minimal (P,Q,R)-chains. 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (77) TransformationProof (EQUIVALENT) 542.07/241.30 By rewriting [LPAR04] the rule TOP(up(f(b))) -> TOP(f_flat(down(b))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.30 542.07/241.30 (TOP(up(f(b))) -> TOP(f_flat(up(g(b)))),TOP(up(f(b))) -> TOP(f_flat(up(g(b))))) 542.07/241.30 542.07/241.30 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (78) 542.07/241.30 Obligation: 542.07/241.30 Q DP problem: 542.07/241.30 The TRS P consists of the following rules: 542.07/241.30 542.07/241.30 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.30 TOP(up(g(a))) -> TOP(g_flat(down(a))) 542.07/241.30 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.30 TOP(up(g(b))) -> TOP(g_flat(down(b))) 542.07/241.30 TOP(up(g(g(a)))) -> TOP(g_flat(down(g(a)))) 542.07/241.30 TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0))))) 542.07/241.30 TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))) 542.07/241.30 TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) 542.07/241.30 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.30 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.30 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.30 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.30 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.30 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.30 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.30 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.30 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.30 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.30 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.30 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.30 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.30 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.30 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.30 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.30 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.30 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.30 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.30 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.30 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.30 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.30 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.30 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.30 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.30 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.30 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.30 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.30 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.30 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.30 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.30 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.30 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.30 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.30 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.30 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.30 542.07/241.30 The TRS R consists of the following rules: 542.07/241.30 542.07/241.30 down(a) -> up(f(a)) 542.07/241.30 down(b) -> up(g(b)) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.30 down(f(a)) -> f_flat(down(a)) 542.07/241.30 down(f(b)) -> f_flat(down(b)) 542.07/241.30 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.30 down(f(c)) -> f_flat(down(c)) 542.07/241.30 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.30 down(g(a)) -> g_flat(down(a)) 542.07/241.30 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.30 down(g(b)) -> g_flat(down(b)) 542.07/241.30 down(g(c)) -> g_flat(down(c)) 542.07/241.30 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.30 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.30 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.30 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.30 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.30 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.30 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.30 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.30 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.30 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.30 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.30 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.30 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.30 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.30 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.30 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.30 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.30 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.30 542.07/241.30 The set Q consists of the following terms: 542.07/241.30 542.07/241.30 down(a) 542.07/241.30 down(b) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.30 down(f(a)) 542.07/241.30 down(f(b)) 542.07/241.30 down(f(g(x0))) 542.07/241.30 down(f(c)) 542.07/241.30 down(f(fresh_constant)) 542.07/241.30 down(g(a)) 542.07/241.30 down(g(f(x0))) 542.07/241.30 down(g(b)) 542.07/241.30 down(g(c)) 542.07/241.30 down(g(fresh_constant)) 542.07/241.30 down(f(f(a))) 542.07/241.30 down(f(f(b))) 542.07/241.30 down(f(f(g(x0)))) 542.07/241.30 down(f(f(c))) 542.07/241.30 down(f(f(fresh_constant))) 542.07/241.30 down(g(g(a))) 542.07/241.30 down(g(g(f(x0)))) 542.07/241.30 down(g(g(b))) 542.07/241.30 down(g(g(c))) 542.07/241.30 down(g(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) 542.07/241.30 down(f(f(f(g(x0))))) 542.07/241.30 down(f(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) 542.07/241.30 down(g(g(g(f(x0))))) 542.07/241.30 down(g(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(x0)))))) 542.07/241.30 down(f(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(x0)))))) 542.07/241.30 down(g(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(x0))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(x0))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 f_flat(up(x0)) 542.07/241.30 g_flat(up(x0)) 542.07/241.30 542.07/241.30 We have to consider all minimal (P,Q,R)-chains. 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (79) TransformationProof (EQUIVALENT) 542.07/241.30 By rewriting [LPAR04] the rule TOP(up(g(a))) -> TOP(g_flat(down(a))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.30 542.07/241.30 (TOP(up(g(a))) -> TOP(g_flat(up(f(a)))),TOP(up(g(a))) -> TOP(g_flat(up(f(a))))) 542.07/241.30 542.07/241.30 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (80) 542.07/241.30 Obligation: 542.07/241.30 Q DP problem: 542.07/241.30 The TRS P consists of the following rules: 542.07/241.30 542.07/241.30 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.30 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.30 TOP(up(g(b))) -> TOP(g_flat(down(b))) 542.07/241.30 TOP(up(g(g(a)))) -> TOP(g_flat(down(g(a)))) 542.07/241.30 TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0))))) 542.07/241.30 TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))) 542.07/241.30 TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) 542.07/241.30 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.30 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.30 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.30 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.30 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.30 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.30 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.30 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.30 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.30 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.30 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.30 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.30 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.30 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.30 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.30 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.30 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.30 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.30 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.30 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.30 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.30 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.30 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.30 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.30 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.30 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.30 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.30 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.30 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.30 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.30 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.30 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.30 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.30 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.30 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.30 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.30 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.30 542.07/241.30 The TRS R consists of the following rules: 542.07/241.30 542.07/241.30 down(a) -> up(f(a)) 542.07/241.30 down(b) -> up(g(b)) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.30 down(f(a)) -> f_flat(down(a)) 542.07/241.30 down(f(b)) -> f_flat(down(b)) 542.07/241.30 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.30 down(f(c)) -> f_flat(down(c)) 542.07/241.30 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.30 down(g(a)) -> g_flat(down(a)) 542.07/241.30 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.30 down(g(b)) -> g_flat(down(b)) 542.07/241.30 down(g(c)) -> g_flat(down(c)) 542.07/241.30 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.30 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.30 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.30 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.30 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.30 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.30 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.30 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.30 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.30 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.30 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.30 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.30 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.30 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.30 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.30 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.30 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.30 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.30 542.07/241.30 The set Q consists of the following terms: 542.07/241.30 542.07/241.30 down(a) 542.07/241.30 down(b) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.30 down(f(a)) 542.07/241.30 down(f(b)) 542.07/241.30 down(f(g(x0))) 542.07/241.30 down(f(c)) 542.07/241.30 down(f(fresh_constant)) 542.07/241.30 down(g(a)) 542.07/241.30 down(g(f(x0))) 542.07/241.30 down(g(b)) 542.07/241.30 down(g(c)) 542.07/241.30 down(g(fresh_constant)) 542.07/241.30 down(f(f(a))) 542.07/241.30 down(f(f(b))) 542.07/241.30 down(f(f(g(x0)))) 542.07/241.30 down(f(f(c))) 542.07/241.30 down(f(f(fresh_constant))) 542.07/241.30 down(g(g(a))) 542.07/241.30 down(g(g(f(x0)))) 542.07/241.30 down(g(g(b))) 542.07/241.30 down(g(g(c))) 542.07/241.30 down(g(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) 542.07/241.30 down(f(f(f(g(x0))))) 542.07/241.30 down(f(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) 542.07/241.30 down(g(g(g(f(x0))))) 542.07/241.30 down(g(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(x0)))))) 542.07/241.30 down(f(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(x0)))))) 542.07/241.30 down(g(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(x0))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(x0))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 f_flat(up(x0)) 542.07/241.30 g_flat(up(x0)) 542.07/241.30 542.07/241.30 We have to consider all minimal (P,Q,R)-chains. 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (81) TransformationProof (EQUIVALENT) 542.07/241.30 By rewriting [LPAR04] the rule TOP(up(g(b))) -> TOP(g_flat(down(b))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.30 542.07/241.30 (TOP(up(g(b))) -> TOP(g_flat(up(g(b)))),TOP(up(g(b))) -> TOP(g_flat(up(g(b))))) 542.07/241.30 542.07/241.30 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (82) 542.07/241.30 Obligation: 542.07/241.30 Q DP problem: 542.07/241.30 The TRS P consists of the following rules: 542.07/241.30 542.07/241.30 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.30 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.30 TOP(up(g(g(a)))) -> TOP(g_flat(down(g(a)))) 542.07/241.30 TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0))))) 542.07/241.30 TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))) 542.07/241.30 TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) 542.07/241.30 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.30 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.30 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.30 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.30 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.30 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.30 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.30 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.30 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.30 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.30 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.30 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.30 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.30 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.30 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.30 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.30 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.30 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.30 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.30 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.30 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.30 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.30 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.30 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.30 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.30 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.30 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.30 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.30 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.30 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.30 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.30 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.30 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.30 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.30 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.30 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.30 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.30 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.30 542.07/241.30 The TRS R consists of the following rules: 542.07/241.30 542.07/241.30 down(a) -> up(f(a)) 542.07/241.30 down(b) -> up(g(b)) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.30 down(f(a)) -> f_flat(down(a)) 542.07/241.30 down(f(b)) -> f_flat(down(b)) 542.07/241.30 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.30 down(f(c)) -> f_flat(down(c)) 542.07/241.30 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.30 down(g(a)) -> g_flat(down(a)) 542.07/241.30 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.30 down(g(b)) -> g_flat(down(b)) 542.07/241.30 down(g(c)) -> g_flat(down(c)) 542.07/241.30 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.30 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.30 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.30 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.30 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.30 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.30 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.30 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.30 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.30 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.30 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.30 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.30 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.30 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.30 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.30 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.30 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.30 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.30 542.07/241.30 The set Q consists of the following terms: 542.07/241.30 542.07/241.30 down(a) 542.07/241.30 down(b) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.30 down(f(a)) 542.07/241.30 down(f(b)) 542.07/241.30 down(f(g(x0))) 542.07/241.30 down(f(c)) 542.07/241.30 down(f(fresh_constant)) 542.07/241.30 down(g(a)) 542.07/241.30 down(g(f(x0))) 542.07/241.30 down(g(b)) 542.07/241.30 down(g(c)) 542.07/241.30 down(g(fresh_constant)) 542.07/241.30 down(f(f(a))) 542.07/241.30 down(f(f(b))) 542.07/241.30 down(f(f(g(x0)))) 542.07/241.30 down(f(f(c))) 542.07/241.30 down(f(f(fresh_constant))) 542.07/241.30 down(g(g(a))) 542.07/241.30 down(g(g(f(x0)))) 542.07/241.30 down(g(g(b))) 542.07/241.30 down(g(g(c))) 542.07/241.30 down(g(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) 542.07/241.30 down(f(f(f(g(x0))))) 542.07/241.30 down(f(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) 542.07/241.30 down(g(g(g(f(x0))))) 542.07/241.30 down(g(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(x0)))))) 542.07/241.30 down(f(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(x0)))))) 542.07/241.30 down(g(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(x0))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(x0))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 f_flat(up(x0)) 542.07/241.30 g_flat(up(x0)) 542.07/241.30 542.07/241.30 We have to consider all minimal (P,Q,R)-chains. 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (83) TransformationProof (EQUIVALENT) 542.07/241.30 By rewriting [LPAR04] the rule TOP(up(g(g(a)))) -> TOP(g_flat(down(g(a)))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.30 542.07/241.30 (TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))),TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a))))) 542.07/241.30 542.07/241.30 542.07/241.30 ---------------------------------------- 542.07/241.30 542.07/241.30 (84) 542.07/241.30 Obligation: 542.07/241.30 Q DP problem: 542.07/241.30 The TRS P consists of the following rules: 542.07/241.30 542.07/241.30 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.30 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.30 TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0))))) 542.07/241.30 TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))) 542.07/241.30 TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) 542.07/241.30 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.30 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.30 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.30 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.30 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.30 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.30 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.30 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.30 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.30 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.30 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.30 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.30 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.30 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.30 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.30 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.30 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.30 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.30 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.30 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.30 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.30 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.30 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.30 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.30 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.30 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.30 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.30 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.30 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.30 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.30 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.30 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.30 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.30 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.30 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.30 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.30 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.30 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.30 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.30 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.30 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.07/241.30 542.07/241.30 The TRS R consists of the following rules: 542.07/241.30 542.07/241.30 down(a) -> up(f(a)) 542.07/241.30 down(b) -> up(g(b)) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.30 down(f(a)) -> f_flat(down(a)) 542.07/241.30 down(f(b)) -> f_flat(down(b)) 542.07/241.30 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.30 down(f(c)) -> f_flat(down(c)) 542.07/241.30 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.30 down(g(a)) -> g_flat(down(a)) 542.07/241.30 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.30 down(g(b)) -> g_flat(down(b)) 542.07/241.30 down(g(c)) -> g_flat(down(c)) 542.07/241.30 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.30 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.30 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.30 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.30 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.30 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.30 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.30 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.30 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.30 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.30 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.30 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.30 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.30 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.30 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.30 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.30 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.30 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.30 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.30 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.30 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.30 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.30 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.30 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.30 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.30 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.30 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.30 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.30 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.30 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.30 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.30 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.30 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.30 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.30 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.30 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.30 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.30 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.30 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.30 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.30 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.30 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.30 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.30 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.30 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.30 542.07/241.30 The set Q consists of the following terms: 542.07/241.30 542.07/241.30 down(a) 542.07/241.30 down(b) 542.07/241.30 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.30 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.30 down(f(a)) 542.07/241.30 down(f(b)) 542.07/241.30 down(f(g(x0))) 542.07/241.30 down(f(c)) 542.07/241.30 down(f(fresh_constant)) 542.07/241.30 down(g(a)) 542.07/241.30 down(g(f(x0))) 542.07/241.30 down(g(b)) 542.07/241.30 down(g(c)) 542.07/241.30 down(g(fresh_constant)) 542.07/241.30 down(f(f(a))) 542.07/241.30 down(f(f(b))) 542.07/241.30 down(f(f(g(x0)))) 542.07/241.30 down(f(f(c))) 542.07/241.30 down(f(f(fresh_constant))) 542.07/241.30 down(g(g(a))) 542.07/241.30 down(g(g(f(x0)))) 542.07/241.30 down(g(g(b))) 542.07/241.30 down(g(g(c))) 542.07/241.30 down(g(g(fresh_constant))) 542.07/241.30 down(f(f(f(a)))) 542.07/241.30 down(f(f(f(b)))) 542.07/241.30 down(f(f(f(g(x0))))) 542.07/241.30 down(f(f(f(c)))) 542.07/241.30 down(f(f(f(fresh_constant)))) 542.07/241.30 down(g(g(g(a)))) 542.07/241.30 down(g(g(g(f(x0))))) 542.07/241.30 down(g(g(g(b)))) 542.07/241.30 down(g(g(g(c)))) 542.07/241.30 down(g(g(g(fresh_constant)))) 542.07/241.30 down(f(f(f(f(a))))) 542.07/241.30 down(f(f(f(f(b))))) 542.07/241.30 down(f(f(f(f(g(x0)))))) 542.07/241.30 down(f(f(f(f(c))))) 542.07/241.31 down(f(f(f(f(fresh_constant))))) 542.07/241.31 down(g(g(g(g(a))))) 542.07/241.31 down(g(g(g(g(f(x0)))))) 542.07/241.31 down(g(g(g(g(b))))) 542.07/241.31 down(g(g(g(g(c))))) 542.07/241.31 down(g(g(g(g(fresh_constant))))) 542.07/241.31 down(f(f(f(f(f(a)))))) 542.07/241.31 down(f(f(f(f(f(b)))))) 542.07/241.31 down(f(f(f(f(f(g(x0))))))) 542.07/241.31 down(f(f(f(f(f(c)))))) 542.07/241.31 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.31 down(g(g(g(g(g(a)))))) 542.07/241.31 down(g(g(g(g(g(f(x0))))))) 542.07/241.31 down(g(g(g(g(g(b)))))) 542.07/241.31 down(g(g(g(g(g(c)))))) 542.07/241.31 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.31 down(f(f(f(f(f(f(a))))))) 542.07/241.31 down(f(f(f(f(f(f(b))))))) 542.07/241.31 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.31 down(f(f(f(f(f(f(c))))))) 542.07/241.31 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.31 down(g(g(g(g(g(g(a))))))) 542.07/241.31 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.31 down(g(g(g(g(g(g(b))))))) 542.07/241.31 down(g(g(g(g(g(g(c))))))) 542.07/241.31 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.31 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 f_flat(up(x0)) 542.07/241.31 g_flat(up(x0)) 542.07/241.31 542.07/241.31 We have to consider all minimal (P,Q,R)-chains. 542.07/241.31 ---------------------------------------- 542.07/241.31 542.07/241.31 (85) TransformationProof (EQUIVALENT) 542.07/241.31 By rewriting [LPAR04] the rule TOP(up(g(g(f(x0))))) -> TOP(g_flat(down(g(f(x0))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.31 542.07/241.31 (TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))),TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0)))))) 542.07/241.31 542.07/241.31 542.07/241.31 ---------------------------------------- 542.07/241.31 542.07/241.31 (86) 542.07/241.31 Obligation: 542.07/241.31 Q DP problem: 542.07/241.31 The TRS P consists of the following rules: 542.07/241.31 542.07/241.31 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.31 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.31 TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))) 542.07/241.31 TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) 542.07/241.31 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.31 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.31 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.31 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.31 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.31 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.31 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.31 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.31 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.31 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.31 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.31 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.31 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.31 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.31 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.31 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.31 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.31 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.31 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.31 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.31 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.31 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.31 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.31 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.31 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.31 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.31 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.31 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.31 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.31 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.31 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.31 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.31 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.31 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.31 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.31 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.31 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.31 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.31 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.07/241.31 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.07/241.31 542.07/241.31 The TRS R consists of the following rules: 542.07/241.31 542.07/241.31 down(a) -> up(f(a)) 542.07/241.31 down(b) -> up(g(b)) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.31 down(f(a)) -> f_flat(down(a)) 542.07/241.31 down(f(b)) -> f_flat(down(b)) 542.07/241.31 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.31 down(f(c)) -> f_flat(down(c)) 542.07/241.31 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.31 down(g(a)) -> g_flat(down(a)) 542.07/241.31 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.31 down(g(b)) -> g_flat(down(b)) 542.07/241.31 down(g(c)) -> g_flat(down(c)) 542.07/241.31 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.31 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.31 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.31 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.31 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.31 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.31 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.31 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.31 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.31 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.31 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.31 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.31 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.31 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.31 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.31 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.31 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.31 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.31 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.31 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.31 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.31 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.31 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.31 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.31 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.31 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.31 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.31 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.31 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.31 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.31 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.31 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.31 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.31 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.31 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.31 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.31 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.31 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.31 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.31 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.31 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.31 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.31 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.31 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.31 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.31 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.31 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.31 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.31 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.31 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.31 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.31 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.31 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.31 542.07/241.31 The set Q consists of the following terms: 542.07/241.31 542.07/241.31 down(a) 542.07/241.31 down(b) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.31 down(f(a)) 542.07/241.31 down(f(b)) 542.07/241.31 down(f(g(x0))) 542.07/241.31 down(f(c)) 542.07/241.31 down(f(fresh_constant)) 542.07/241.31 down(g(a)) 542.07/241.31 down(g(f(x0))) 542.07/241.31 down(g(b)) 542.07/241.31 down(g(c)) 542.07/241.31 down(g(fresh_constant)) 542.07/241.31 down(f(f(a))) 542.07/241.31 down(f(f(b))) 542.07/241.31 down(f(f(g(x0)))) 542.07/241.31 down(f(f(c))) 542.07/241.31 down(f(f(fresh_constant))) 542.07/241.31 down(g(g(a))) 542.07/241.31 down(g(g(f(x0)))) 542.07/241.31 down(g(g(b))) 542.07/241.31 down(g(g(c))) 542.07/241.31 down(g(g(fresh_constant))) 542.07/241.31 down(f(f(f(a)))) 542.07/241.31 down(f(f(f(b)))) 542.07/241.31 down(f(f(f(g(x0))))) 542.07/241.31 down(f(f(f(c)))) 542.07/241.31 down(f(f(f(fresh_constant)))) 542.07/241.31 down(g(g(g(a)))) 542.07/241.31 down(g(g(g(f(x0))))) 542.07/241.31 down(g(g(g(b)))) 542.07/241.31 down(g(g(g(c)))) 542.07/241.31 down(g(g(g(fresh_constant)))) 542.07/241.31 down(f(f(f(f(a))))) 542.07/241.31 down(f(f(f(f(b))))) 542.07/241.31 down(f(f(f(f(g(x0)))))) 542.07/241.31 down(f(f(f(f(c))))) 542.07/241.31 down(f(f(f(f(fresh_constant))))) 542.07/241.31 down(g(g(g(g(a))))) 542.07/241.31 down(g(g(g(g(f(x0)))))) 542.07/241.31 down(g(g(g(g(b))))) 542.07/241.31 down(g(g(g(g(c))))) 542.07/241.31 down(g(g(g(g(fresh_constant))))) 542.07/241.31 down(f(f(f(f(f(a)))))) 542.07/241.31 down(f(f(f(f(f(b)))))) 542.07/241.31 down(f(f(f(f(f(g(x0))))))) 542.07/241.31 down(f(f(f(f(f(c)))))) 542.07/241.31 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.31 down(g(g(g(g(g(a)))))) 542.07/241.31 down(g(g(g(g(g(f(x0))))))) 542.07/241.31 down(g(g(g(g(g(b)))))) 542.07/241.31 down(g(g(g(g(g(c)))))) 542.07/241.31 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.31 down(f(f(f(f(f(f(a))))))) 542.07/241.31 down(f(f(f(f(f(f(b))))))) 542.07/241.31 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.31 down(f(f(f(f(f(f(c))))))) 542.07/241.31 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.31 down(g(g(g(g(g(g(a))))))) 542.07/241.31 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.31 down(g(g(g(g(g(g(b))))))) 542.07/241.31 down(g(g(g(g(g(g(c))))))) 542.07/241.31 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.31 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 f_flat(up(x0)) 542.07/241.31 g_flat(up(x0)) 542.07/241.31 542.07/241.31 We have to consider all minimal (P,Q,R)-chains. 542.07/241.31 ---------------------------------------- 542.07/241.31 542.07/241.31 (87) TransformationProof (EQUIVALENT) 542.07/241.31 By rewriting [LPAR04] the rule TOP(up(f(f(a)))) -> TOP(f_flat(down(f(a)))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.31 542.07/241.31 (TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))),TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a))))) 542.07/241.31 542.07/241.31 542.07/241.31 ---------------------------------------- 542.07/241.31 542.07/241.31 (88) 542.07/241.31 Obligation: 542.07/241.31 Q DP problem: 542.07/241.31 The TRS P consists of the following rules: 542.07/241.31 542.07/241.31 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.31 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.31 TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) 542.07/241.31 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.31 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.31 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.31 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.31 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.31 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.31 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.31 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.31 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.31 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.31 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.31 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.31 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.31 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.31 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.31 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.31 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.31 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.31 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.31 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.31 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.31 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.31 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.31 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.31 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.31 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.31 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.31 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.31 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.31 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.31 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.31 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.31 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.31 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.31 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.31 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.31 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.31 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.31 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.07/241.31 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.07/241.31 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.07/241.31 542.07/241.31 The TRS R consists of the following rules: 542.07/241.31 542.07/241.31 down(a) -> up(f(a)) 542.07/241.31 down(b) -> up(g(b)) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.31 down(f(a)) -> f_flat(down(a)) 542.07/241.31 down(f(b)) -> f_flat(down(b)) 542.07/241.31 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.31 down(f(c)) -> f_flat(down(c)) 542.07/241.31 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.31 down(g(a)) -> g_flat(down(a)) 542.07/241.31 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.31 down(g(b)) -> g_flat(down(b)) 542.07/241.31 down(g(c)) -> g_flat(down(c)) 542.07/241.31 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.31 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.31 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.31 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.31 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.31 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.31 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.31 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.31 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.31 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.31 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.31 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.31 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.31 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.31 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.31 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.31 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.31 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.31 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.31 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.31 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.31 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.31 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.31 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.31 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.31 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.31 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.31 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.31 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.31 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.31 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.31 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.31 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.31 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.31 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.31 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.31 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.31 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.31 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.31 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.31 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.31 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.31 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.31 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.31 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.31 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.31 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.31 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.31 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.31 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.31 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.31 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.31 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.31 542.07/241.31 The set Q consists of the following terms: 542.07/241.31 542.07/241.31 down(a) 542.07/241.31 down(b) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.31 down(f(a)) 542.07/241.31 down(f(b)) 542.07/241.31 down(f(g(x0))) 542.07/241.31 down(f(c)) 542.07/241.31 down(f(fresh_constant)) 542.07/241.31 down(g(a)) 542.07/241.31 down(g(f(x0))) 542.07/241.31 down(g(b)) 542.07/241.31 down(g(c)) 542.07/241.31 down(g(fresh_constant)) 542.07/241.31 down(f(f(a))) 542.07/241.31 down(f(f(b))) 542.07/241.31 down(f(f(g(x0)))) 542.07/241.31 down(f(f(c))) 542.07/241.31 down(f(f(fresh_constant))) 542.07/241.31 down(g(g(a))) 542.07/241.31 down(g(g(f(x0)))) 542.07/241.31 down(g(g(b))) 542.07/241.31 down(g(g(c))) 542.07/241.31 down(g(g(fresh_constant))) 542.07/241.31 down(f(f(f(a)))) 542.07/241.31 down(f(f(f(b)))) 542.07/241.31 down(f(f(f(g(x0))))) 542.07/241.31 down(f(f(f(c)))) 542.07/241.31 down(f(f(f(fresh_constant)))) 542.07/241.31 down(g(g(g(a)))) 542.07/241.31 down(g(g(g(f(x0))))) 542.07/241.31 down(g(g(g(b)))) 542.07/241.31 down(g(g(g(c)))) 542.07/241.31 down(g(g(g(fresh_constant)))) 542.07/241.31 down(f(f(f(f(a))))) 542.07/241.31 down(f(f(f(f(b))))) 542.07/241.31 down(f(f(f(f(g(x0)))))) 542.07/241.31 down(f(f(f(f(c))))) 542.07/241.31 down(f(f(f(f(fresh_constant))))) 542.07/241.31 down(g(g(g(g(a))))) 542.07/241.31 down(g(g(g(g(f(x0)))))) 542.07/241.31 down(g(g(g(g(b))))) 542.07/241.31 down(g(g(g(g(c))))) 542.07/241.31 down(g(g(g(g(fresh_constant))))) 542.07/241.31 down(f(f(f(f(f(a)))))) 542.07/241.31 down(f(f(f(f(f(b)))))) 542.07/241.31 down(f(f(f(f(f(g(x0))))))) 542.07/241.31 down(f(f(f(f(f(c)))))) 542.07/241.31 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.31 down(g(g(g(g(g(a)))))) 542.07/241.31 down(g(g(g(g(g(f(x0))))))) 542.07/241.31 down(g(g(g(g(g(b)))))) 542.07/241.31 down(g(g(g(g(g(c)))))) 542.07/241.31 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.31 down(f(f(f(f(f(f(a))))))) 542.07/241.31 down(f(f(f(f(f(f(b))))))) 542.07/241.31 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.31 down(f(f(f(f(f(f(c))))))) 542.07/241.31 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.31 down(g(g(g(g(g(g(a))))))) 542.07/241.31 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.31 down(g(g(g(g(g(g(b))))))) 542.07/241.31 down(g(g(g(g(g(g(c))))))) 542.07/241.31 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.31 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 f_flat(up(x0)) 542.07/241.31 g_flat(up(x0)) 542.07/241.31 542.07/241.31 We have to consider all minimal (P,Q,R)-chains. 542.07/241.31 ---------------------------------------- 542.07/241.31 542.07/241.31 (89) TransformationProof (EQUIVALENT) 542.07/241.31 By rewriting [LPAR04] the rule TOP(up(f(f(b)))) -> TOP(f_flat(down(f(b)))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.31 542.07/241.31 (TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))),TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b))))) 542.07/241.31 542.07/241.31 542.07/241.31 ---------------------------------------- 542.07/241.31 542.07/241.31 (90) 542.07/241.31 Obligation: 542.07/241.31 Q DP problem: 542.07/241.31 The TRS P consists of the following rules: 542.07/241.31 542.07/241.31 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.31 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.31 TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) 542.07/241.31 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.31 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.31 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.31 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.31 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.31 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.31 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.31 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.31 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.31 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.31 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.31 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.31 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.31 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.31 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.31 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.31 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.31 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.31 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.31 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.31 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.31 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.31 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.31 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.31 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.31 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.31 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.31 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.31 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.31 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.31 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.31 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.31 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.31 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.31 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.31 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.31 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.31 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.07/241.31 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.07/241.31 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.07/241.31 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.07/241.31 542.07/241.31 The TRS R consists of the following rules: 542.07/241.31 542.07/241.31 down(a) -> up(f(a)) 542.07/241.31 down(b) -> up(g(b)) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.31 down(f(a)) -> f_flat(down(a)) 542.07/241.31 down(f(b)) -> f_flat(down(b)) 542.07/241.31 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.31 down(f(c)) -> f_flat(down(c)) 542.07/241.31 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.31 down(g(a)) -> g_flat(down(a)) 542.07/241.31 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.31 down(g(b)) -> g_flat(down(b)) 542.07/241.31 down(g(c)) -> g_flat(down(c)) 542.07/241.31 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.31 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.31 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.31 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.31 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.31 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.31 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.31 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.31 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.31 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.31 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.31 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.31 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.31 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.31 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.31 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.31 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.31 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.31 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.31 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.31 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.31 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.31 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.31 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.31 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.31 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.31 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.31 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.31 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.31 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.31 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.31 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.31 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.31 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.31 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.31 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.31 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.31 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.31 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.31 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.31 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.31 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.31 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.31 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.31 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.31 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.31 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.31 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.31 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.31 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.31 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.31 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.31 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.31 542.07/241.31 The set Q consists of the following terms: 542.07/241.31 542.07/241.31 down(a) 542.07/241.31 down(b) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.31 down(f(a)) 542.07/241.31 down(f(b)) 542.07/241.31 down(f(g(x0))) 542.07/241.31 down(f(c)) 542.07/241.31 down(f(fresh_constant)) 542.07/241.31 down(g(a)) 542.07/241.31 down(g(f(x0))) 542.07/241.31 down(g(b)) 542.07/241.31 down(g(c)) 542.07/241.31 down(g(fresh_constant)) 542.07/241.31 down(f(f(a))) 542.07/241.31 down(f(f(b))) 542.07/241.31 down(f(f(g(x0)))) 542.07/241.31 down(f(f(c))) 542.07/241.31 down(f(f(fresh_constant))) 542.07/241.31 down(g(g(a))) 542.07/241.31 down(g(g(f(x0)))) 542.07/241.31 down(g(g(b))) 542.07/241.31 down(g(g(c))) 542.07/241.31 down(g(g(fresh_constant))) 542.07/241.31 down(f(f(f(a)))) 542.07/241.31 down(f(f(f(b)))) 542.07/241.31 down(f(f(f(g(x0))))) 542.07/241.31 down(f(f(f(c)))) 542.07/241.31 down(f(f(f(fresh_constant)))) 542.07/241.31 down(g(g(g(a)))) 542.07/241.31 down(g(g(g(f(x0))))) 542.07/241.31 down(g(g(g(b)))) 542.07/241.31 down(g(g(g(c)))) 542.07/241.31 down(g(g(g(fresh_constant)))) 542.07/241.31 down(f(f(f(f(a))))) 542.07/241.31 down(f(f(f(f(b))))) 542.07/241.31 down(f(f(f(f(g(x0)))))) 542.07/241.31 down(f(f(f(f(c))))) 542.07/241.31 down(f(f(f(f(fresh_constant))))) 542.07/241.31 down(g(g(g(g(a))))) 542.07/241.31 down(g(g(g(g(f(x0)))))) 542.07/241.31 down(g(g(g(g(b))))) 542.07/241.31 down(g(g(g(g(c))))) 542.07/241.31 down(g(g(g(g(fresh_constant))))) 542.07/241.31 down(f(f(f(f(f(a)))))) 542.07/241.31 down(f(f(f(f(f(b)))))) 542.07/241.31 down(f(f(f(f(f(g(x0))))))) 542.07/241.31 down(f(f(f(f(f(c)))))) 542.07/241.31 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.31 down(g(g(g(g(g(a)))))) 542.07/241.31 down(g(g(g(g(g(f(x0))))))) 542.07/241.31 down(g(g(g(g(g(b)))))) 542.07/241.31 down(g(g(g(g(g(c)))))) 542.07/241.31 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.31 down(f(f(f(f(f(f(a))))))) 542.07/241.31 down(f(f(f(f(f(f(b))))))) 542.07/241.31 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.31 down(f(f(f(f(f(f(c))))))) 542.07/241.31 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.31 down(g(g(g(g(g(g(a))))))) 542.07/241.31 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.31 down(g(g(g(g(g(g(b))))))) 542.07/241.31 down(g(g(g(g(g(g(c))))))) 542.07/241.31 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.31 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 f_flat(up(x0)) 542.07/241.31 g_flat(up(x0)) 542.07/241.31 542.07/241.31 We have to consider all minimal (P,Q,R)-chains. 542.07/241.31 ---------------------------------------- 542.07/241.31 542.07/241.31 (91) TransformationProof (EQUIVALENT) 542.07/241.31 By rewriting [LPAR04] the rule TOP(up(f(f(g(x0))))) -> TOP(f_flat(down(f(g(x0))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.31 542.07/241.31 (TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))),TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0)))))) 542.07/241.31 542.07/241.31 542.07/241.31 ---------------------------------------- 542.07/241.31 542.07/241.31 (92) 542.07/241.31 Obligation: 542.07/241.31 Q DP problem: 542.07/241.31 The TRS P consists of the following rules: 542.07/241.31 542.07/241.31 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.31 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.31 TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) 542.07/241.31 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.31 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.31 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.31 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.31 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.31 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.31 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.31 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.31 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.31 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.31 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.31 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.31 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.31 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.31 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.31 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.31 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.31 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.31 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.31 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.31 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.31 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.31 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.31 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.31 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.31 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.31 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.31 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.31 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.31 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.31 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.31 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.31 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.31 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.31 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.31 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.31 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.31 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.31 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.07/241.31 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.07/241.31 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.07/241.31 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.07/241.31 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.07/241.31 542.07/241.31 The TRS R consists of the following rules: 542.07/241.31 542.07/241.31 down(a) -> up(f(a)) 542.07/241.31 down(b) -> up(g(b)) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.31 down(f(a)) -> f_flat(down(a)) 542.07/241.31 down(f(b)) -> f_flat(down(b)) 542.07/241.31 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.31 down(f(c)) -> f_flat(down(c)) 542.07/241.31 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.31 down(g(a)) -> g_flat(down(a)) 542.07/241.31 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.31 down(g(b)) -> g_flat(down(b)) 542.07/241.31 down(g(c)) -> g_flat(down(c)) 542.07/241.31 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.31 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.31 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.31 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.31 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.31 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.31 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.31 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.31 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.31 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.31 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.31 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.31 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.31 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.31 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.31 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.31 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.31 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.31 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.31 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.31 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.31 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.31 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.31 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.31 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.31 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.31 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.31 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.31 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.31 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.31 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.31 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.31 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.31 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.31 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.31 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.31 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.31 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.31 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.31 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.31 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.31 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.31 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.31 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.31 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.31 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.31 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.31 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.31 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.31 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.31 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.31 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.32 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.32 542.07/241.32 The set Q consists of the following terms: 542.07/241.32 542.07/241.32 down(a) 542.07/241.32 down(b) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.32 down(f(a)) 542.07/241.32 down(f(b)) 542.07/241.32 down(f(g(x0))) 542.07/241.32 down(f(c)) 542.07/241.32 down(f(fresh_constant)) 542.07/241.32 down(g(a)) 542.07/241.32 down(g(f(x0))) 542.07/241.32 down(g(b)) 542.07/241.32 down(g(c)) 542.07/241.32 down(g(fresh_constant)) 542.07/241.32 down(f(f(a))) 542.07/241.32 down(f(f(b))) 542.07/241.32 down(f(f(g(x0)))) 542.07/241.32 down(f(f(c))) 542.07/241.32 down(f(f(fresh_constant))) 542.07/241.32 down(g(g(a))) 542.07/241.32 down(g(g(f(x0)))) 542.07/241.32 down(g(g(b))) 542.07/241.32 down(g(g(c))) 542.07/241.32 down(g(g(fresh_constant))) 542.07/241.32 down(f(f(f(a)))) 542.07/241.32 down(f(f(f(b)))) 542.07/241.32 down(f(f(f(g(x0))))) 542.07/241.32 down(f(f(f(c)))) 542.07/241.32 down(f(f(f(fresh_constant)))) 542.07/241.32 down(g(g(g(a)))) 542.07/241.32 down(g(g(g(f(x0))))) 542.07/241.32 down(g(g(g(b)))) 542.07/241.32 down(g(g(g(c)))) 542.07/241.32 down(g(g(g(fresh_constant)))) 542.07/241.32 down(f(f(f(f(a))))) 542.07/241.32 down(f(f(f(f(b))))) 542.07/241.32 down(f(f(f(f(g(x0)))))) 542.07/241.32 down(f(f(f(f(c))))) 542.07/241.32 down(f(f(f(f(fresh_constant))))) 542.07/241.32 down(g(g(g(g(a))))) 542.07/241.32 down(g(g(g(g(f(x0)))))) 542.07/241.32 down(g(g(g(g(b))))) 542.07/241.32 down(g(g(g(g(c))))) 542.07/241.32 down(g(g(g(g(fresh_constant))))) 542.07/241.32 down(f(f(f(f(f(a)))))) 542.07/241.32 down(f(f(f(f(f(b)))))) 542.07/241.32 down(f(f(f(f(f(g(x0))))))) 542.07/241.32 down(f(f(f(f(f(c)))))) 542.07/241.32 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.32 down(g(g(g(g(g(a)))))) 542.07/241.32 down(g(g(g(g(g(f(x0))))))) 542.07/241.32 down(g(g(g(g(g(b)))))) 542.07/241.32 down(g(g(g(g(g(c)))))) 542.07/241.32 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.32 down(f(f(f(f(f(f(a))))))) 542.07/241.32 down(f(f(f(f(f(f(b))))))) 542.07/241.32 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.32 down(f(f(f(f(f(f(c))))))) 542.07/241.32 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.32 down(g(g(g(g(g(g(a))))))) 542.07/241.32 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.32 down(g(g(g(g(g(g(b))))))) 542.07/241.32 down(g(g(g(g(g(g(c))))))) 542.07/241.32 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.32 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 f_flat(up(x0)) 542.07/241.32 g_flat(up(x0)) 542.07/241.32 542.07/241.32 We have to consider all minimal (P,Q,R)-chains. 542.07/241.32 ---------------------------------------- 542.07/241.32 542.07/241.32 (93) TransformationProof (EQUIVALENT) 542.07/241.32 By rewriting [LPAR04] the rule TOP(up(f(f(c)))) -> TOP(f_flat(down(f(c)))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.32 542.07/241.32 (TOP(up(f(f(c)))) -> TOP(f_flat(f_flat(down(c)))),TOP(up(f(f(c)))) -> TOP(f_flat(f_flat(down(c))))) 542.07/241.32 542.07/241.32 542.07/241.32 ---------------------------------------- 542.07/241.32 542.07/241.32 (94) 542.07/241.32 Obligation: 542.07/241.32 Q DP problem: 542.07/241.32 The TRS P consists of the following rules: 542.07/241.32 542.07/241.32 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.32 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.32 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.32 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.32 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.32 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.32 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.32 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.32 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.32 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.32 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.32 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.32 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.32 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.32 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.32 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.32 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.32 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.32 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.32 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.32 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.32 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.32 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.32 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.32 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.32 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.32 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.32 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.32 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.32 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.32 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.32 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.32 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.32 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.32 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.32 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.32 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.32 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.32 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.07/241.32 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.07/241.32 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.07/241.32 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.07/241.32 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.07/241.32 TOP(up(f(f(c)))) -> TOP(f_flat(f_flat(down(c)))) 542.07/241.32 542.07/241.32 The TRS R consists of the following rules: 542.07/241.32 542.07/241.32 down(a) -> up(f(a)) 542.07/241.32 down(b) -> up(g(b)) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.32 down(f(a)) -> f_flat(down(a)) 542.07/241.32 down(f(b)) -> f_flat(down(b)) 542.07/241.32 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.32 down(f(c)) -> f_flat(down(c)) 542.07/241.32 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.32 down(g(a)) -> g_flat(down(a)) 542.07/241.32 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.32 down(g(b)) -> g_flat(down(b)) 542.07/241.32 down(g(c)) -> g_flat(down(c)) 542.07/241.32 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.32 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.32 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.32 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.32 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.32 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.32 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.32 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.32 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.32 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.32 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.32 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.32 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.32 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.32 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.32 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.32 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.32 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.32 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.32 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.32 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.32 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.32 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.32 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.32 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.32 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.32 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.32 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.32 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.32 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.32 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.32 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.32 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.32 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.32 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.32 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.32 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.32 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.32 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.32 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.32 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.32 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.32 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.32 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.32 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.32 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.32 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.32 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.32 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.32 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.32 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.32 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.32 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.32 542.07/241.32 The set Q consists of the following terms: 542.07/241.32 542.07/241.32 down(a) 542.07/241.32 down(b) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.32 down(f(a)) 542.07/241.32 down(f(b)) 542.07/241.32 down(f(g(x0))) 542.07/241.32 down(f(c)) 542.07/241.32 down(f(fresh_constant)) 542.07/241.32 down(g(a)) 542.07/241.32 down(g(f(x0))) 542.07/241.32 down(g(b)) 542.07/241.32 down(g(c)) 542.07/241.32 down(g(fresh_constant)) 542.07/241.32 down(f(f(a))) 542.07/241.32 down(f(f(b))) 542.07/241.32 down(f(f(g(x0)))) 542.07/241.32 down(f(f(c))) 542.07/241.32 down(f(f(fresh_constant))) 542.07/241.32 down(g(g(a))) 542.07/241.32 down(g(g(f(x0)))) 542.07/241.32 down(g(g(b))) 542.07/241.32 down(g(g(c))) 542.07/241.32 down(g(g(fresh_constant))) 542.07/241.32 down(f(f(f(a)))) 542.07/241.32 down(f(f(f(b)))) 542.07/241.32 down(f(f(f(g(x0))))) 542.07/241.32 down(f(f(f(c)))) 542.07/241.32 down(f(f(f(fresh_constant)))) 542.07/241.32 down(g(g(g(a)))) 542.07/241.32 down(g(g(g(f(x0))))) 542.07/241.32 down(g(g(g(b)))) 542.07/241.32 down(g(g(g(c)))) 542.07/241.32 down(g(g(g(fresh_constant)))) 542.07/241.32 down(f(f(f(f(a))))) 542.07/241.32 down(f(f(f(f(b))))) 542.07/241.32 down(f(f(f(f(g(x0)))))) 542.07/241.32 down(f(f(f(f(c))))) 542.07/241.32 down(f(f(f(f(fresh_constant))))) 542.07/241.32 down(g(g(g(g(a))))) 542.07/241.32 down(g(g(g(g(f(x0)))))) 542.07/241.32 down(g(g(g(g(b))))) 542.07/241.32 down(g(g(g(g(c))))) 542.07/241.32 down(g(g(g(g(fresh_constant))))) 542.07/241.32 down(f(f(f(f(f(a)))))) 542.07/241.32 down(f(f(f(f(f(b)))))) 542.07/241.32 down(f(f(f(f(f(g(x0))))))) 542.07/241.32 down(f(f(f(f(f(c)))))) 542.07/241.32 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.32 down(g(g(g(g(g(a)))))) 542.07/241.32 down(g(g(g(g(g(f(x0))))))) 542.07/241.32 down(g(g(g(g(g(b)))))) 542.07/241.32 down(g(g(g(g(g(c)))))) 542.07/241.32 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.32 down(f(f(f(f(f(f(a))))))) 542.07/241.32 down(f(f(f(f(f(f(b))))))) 542.07/241.32 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.32 down(f(f(f(f(f(f(c))))))) 542.07/241.32 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.32 down(g(g(g(g(g(g(a))))))) 542.07/241.32 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.32 down(g(g(g(g(g(g(b))))))) 542.07/241.32 down(g(g(g(g(g(g(c))))))) 542.07/241.32 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.32 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 f_flat(up(x0)) 542.07/241.32 g_flat(up(x0)) 542.07/241.32 542.07/241.32 We have to consider all minimal (P,Q,R)-chains. 542.07/241.32 ---------------------------------------- 542.07/241.32 542.07/241.32 (95) DependencyGraphProof (EQUIVALENT) 542.07/241.32 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 542.07/241.32 ---------------------------------------- 542.07/241.32 542.07/241.32 (96) 542.07/241.32 Obligation: 542.07/241.32 Q DP problem: 542.07/241.32 The TRS P consists of the following rules: 542.07/241.32 542.07/241.32 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.32 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.32 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) 542.07/241.32 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.32 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.32 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.32 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.32 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.32 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.32 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.32 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.32 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.32 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.32 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.32 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.32 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.32 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.32 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.32 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.32 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.32 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.32 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.32 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.32 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.32 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.32 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.32 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.32 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.32 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.32 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.32 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.32 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.32 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.32 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.32 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.32 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.32 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.07/241.32 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.07/241.32 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.32 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.32 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.07/241.32 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.07/241.32 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.07/241.32 542.07/241.32 The TRS R consists of the following rules: 542.07/241.32 542.07/241.32 down(a) -> up(f(a)) 542.07/241.32 down(b) -> up(g(b)) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.32 down(f(a)) -> f_flat(down(a)) 542.07/241.32 down(f(b)) -> f_flat(down(b)) 542.07/241.32 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.32 down(f(c)) -> f_flat(down(c)) 542.07/241.32 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.32 down(g(a)) -> g_flat(down(a)) 542.07/241.32 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.32 down(g(b)) -> g_flat(down(b)) 542.07/241.32 down(g(c)) -> g_flat(down(c)) 542.07/241.32 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.32 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.32 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.32 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.32 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.32 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.32 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.32 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.32 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.32 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.32 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.32 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.32 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.32 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.32 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.32 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.32 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.32 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.32 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.32 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.32 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.32 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.32 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.32 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.32 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.32 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.32 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.32 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.32 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.32 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.32 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.32 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.32 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.32 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.32 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.32 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.32 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.32 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.32 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.32 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.32 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.32 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.32 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.32 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.32 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.32 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.32 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.32 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.32 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.32 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.32 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.32 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.32 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.32 542.07/241.32 The set Q consists of the following terms: 542.07/241.32 542.07/241.32 down(a) 542.07/241.32 down(b) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.32 down(f(a)) 542.07/241.32 down(f(b)) 542.07/241.32 down(f(g(x0))) 542.07/241.32 down(f(c)) 542.07/241.32 down(f(fresh_constant)) 542.07/241.32 down(g(a)) 542.07/241.32 down(g(f(x0))) 542.07/241.32 down(g(b)) 542.07/241.32 down(g(c)) 542.07/241.32 down(g(fresh_constant)) 542.07/241.32 down(f(f(a))) 542.07/241.32 down(f(f(b))) 542.07/241.32 down(f(f(g(x0)))) 542.07/241.32 down(f(f(c))) 542.07/241.32 down(f(f(fresh_constant))) 542.07/241.32 down(g(g(a))) 542.07/241.32 down(g(g(f(x0)))) 542.07/241.32 down(g(g(b))) 542.07/241.32 down(g(g(c))) 542.07/241.32 down(g(g(fresh_constant))) 542.07/241.32 down(f(f(f(a)))) 542.07/241.32 down(f(f(f(b)))) 542.07/241.32 down(f(f(f(g(x0))))) 542.07/241.32 down(f(f(f(c)))) 542.07/241.32 down(f(f(f(fresh_constant)))) 542.07/241.32 down(g(g(g(a)))) 542.07/241.32 down(g(g(g(f(x0))))) 542.07/241.32 down(g(g(g(b)))) 542.07/241.32 down(g(g(g(c)))) 542.07/241.32 down(g(g(g(fresh_constant)))) 542.07/241.32 down(f(f(f(f(a))))) 542.07/241.32 down(f(f(f(f(b))))) 542.07/241.32 down(f(f(f(f(g(x0)))))) 542.07/241.32 down(f(f(f(f(c))))) 542.07/241.32 down(f(f(f(f(fresh_constant))))) 542.07/241.32 down(g(g(g(g(a))))) 542.07/241.32 down(g(g(g(g(f(x0)))))) 542.07/241.32 down(g(g(g(g(b))))) 542.07/241.32 down(g(g(g(g(c))))) 542.07/241.32 down(g(g(g(g(fresh_constant))))) 542.07/241.32 down(f(f(f(f(f(a)))))) 542.07/241.32 down(f(f(f(f(f(b)))))) 542.07/241.32 down(f(f(f(f(f(g(x0))))))) 542.07/241.32 down(f(f(f(f(f(c)))))) 542.07/241.32 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.32 down(g(g(g(g(g(a)))))) 542.07/241.32 down(g(g(g(g(g(f(x0))))))) 542.07/241.32 down(g(g(g(g(g(b)))))) 542.07/241.32 down(g(g(g(g(g(c)))))) 542.07/241.32 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.32 down(f(f(f(f(f(f(a))))))) 542.07/241.32 down(f(f(f(f(f(f(b))))))) 542.07/241.32 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.32 down(f(f(f(f(f(f(c))))))) 542.07/241.32 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.32 down(g(g(g(g(g(g(a))))))) 542.07/241.32 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.32 down(g(g(g(g(g(g(b))))))) 542.07/241.32 down(g(g(g(g(g(g(c))))))) 542.07/241.32 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.32 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 f_flat(up(x0)) 542.07/241.32 g_flat(up(x0)) 542.07/241.32 542.07/241.32 We have to consider all minimal (P,Q,R)-chains. 542.07/241.32 ---------------------------------------- 542.07/241.32 542.07/241.32 (97) TransformationProof (EQUIVALENT) 542.07/241.32 By rewriting [LPAR04] the rule TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(down(f(fresh_constant)))) at position [0,0] we obtained the following new rules [LPAR04]: 542.07/241.32 542.07/241.32 (TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(f_flat(down(fresh_constant)))),TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(f_flat(down(fresh_constant))))) 542.07/241.32 542.07/241.32 542.07/241.32 ---------------------------------------- 542.07/241.32 542.07/241.32 (98) 542.07/241.32 Obligation: 542.07/241.32 Q DP problem: 542.07/241.32 The TRS P consists of the following rules: 542.07/241.32 542.07/241.32 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.32 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.32 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.32 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.32 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.32 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.32 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.32 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.32 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.32 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.32 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.32 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.32 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.32 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.32 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.32 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.32 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.32 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.32 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.32 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.32 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.32 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.32 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.32 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.32 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.32 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.32 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.32 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.32 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.32 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.32 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.32 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.32 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.32 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.32 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.32 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.07/241.32 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.07/241.32 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.32 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.32 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.07/241.32 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.07/241.32 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.07/241.32 TOP(up(f(f(fresh_constant)))) -> TOP(f_flat(f_flat(down(fresh_constant)))) 542.07/241.32 542.07/241.32 The TRS R consists of the following rules: 542.07/241.32 542.07/241.32 down(a) -> up(f(a)) 542.07/241.32 down(b) -> up(g(b)) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.07/241.32 down(f(a)) -> f_flat(down(a)) 542.07/241.32 down(f(b)) -> f_flat(down(b)) 542.07/241.32 down(f(g(y4))) -> f_flat(down(g(y4))) 542.07/241.32 down(f(c)) -> f_flat(down(c)) 542.07/241.32 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.07/241.32 down(g(a)) -> g_flat(down(a)) 542.07/241.32 down(g(f(y6))) -> g_flat(down(f(y6))) 542.07/241.32 down(g(b)) -> g_flat(down(b)) 542.07/241.32 down(g(c)) -> g_flat(down(c)) 542.07/241.32 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.07/241.32 down(f(f(a))) -> f_flat(down(f(a))) 542.07/241.32 down(f(f(b))) -> f_flat(down(f(b))) 542.07/241.32 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.07/241.32 down(f(f(c))) -> f_flat(down(f(c))) 542.07/241.32 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.07/241.32 down(g(g(a))) -> g_flat(down(g(a))) 542.07/241.32 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.07/241.32 down(g(g(b))) -> g_flat(down(g(b))) 542.07/241.32 down(g(g(c))) -> g_flat(down(g(c))) 542.07/241.32 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.07/241.32 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.07/241.32 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.07/241.32 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.07/241.32 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.07/241.32 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.07/241.32 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.07/241.32 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.07/241.32 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.07/241.32 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.07/241.32 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.07/241.32 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.07/241.32 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.07/241.32 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.07/241.32 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.07/241.32 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.07/241.32 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.07/241.32 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.07/241.32 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.07/241.32 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.07/241.32 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.07/241.32 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.07/241.32 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.07/241.32 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.07/241.32 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.07/241.32 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.07/241.32 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.07/241.32 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.07/241.32 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.07/241.32 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.07/241.32 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.07/241.32 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.07/241.32 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.07/241.32 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.07/241.32 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.07/241.32 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.07/241.32 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.07/241.32 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.07/241.32 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.07/241.32 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.07/241.32 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.07/241.32 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 g_flat(up(x_1)) -> up(g(x_1)) 542.07/241.32 f_flat(up(x_1)) -> up(f(x_1)) 542.07/241.32 542.07/241.32 The set Q consists of the following terms: 542.07/241.32 542.07/241.32 down(a) 542.07/241.32 down(b) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.07/241.32 down(f(a)) 542.07/241.32 down(f(b)) 542.07/241.32 down(f(g(x0))) 542.07/241.32 down(f(c)) 542.07/241.32 down(f(fresh_constant)) 542.07/241.32 down(g(a)) 542.07/241.32 down(g(f(x0))) 542.07/241.32 down(g(b)) 542.07/241.32 down(g(c)) 542.07/241.32 down(g(fresh_constant)) 542.07/241.32 down(f(f(a))) 542.07/241.32 down(f(f(b))) 542.07/241.32 down(f(f(g(x0)))) 542.07/241.32 down(f(f(c))) 542.07/241.32 down(f(f(fresh_constant))) 542.07/241.32 down(g(g(a))) 542.07/241.32 down(g(g(f(x0)))) 542.07/241.32 down(g(g(b))) 542.07/241.32 down(g(g(c))) 542.07/241.32 down(g(g(fresh_constant))) 542.07/241.32 down(f(f(f(a)))) 542.07/241.32 down(f(f(f(b)))) 542.07/241.32 down(f(f(f(g(x0))))) 542.07/241.32 down(f(f(f(c)))) 542.07/241.32 down(f(f(f(fresh_constant)))) 542.07/241.32 down(g(g(g(a)))) 542.07/241.32 down(g(g(g(f(x0))))) 542.07/241.32 down(g(g(g(b)))) 542.07/241.32 down(g(g(g(c)))) 542.07/241.32 down(g(g(g(fresh_constant)))) 542.07/241.32 down(f(f(f(f(a))))) 542.07/241.32 down(f(f(f(f(b))))) 542.07/241.32 down(f(f(f(f(g(x0)))))) 542.07/241.32 down(f(f(f(f(c))))) 542.07/241.32 down(f(f(f(f(fresh_constant))))) 542.07/241.32 down(g(g(g(g(a))))) 542.07/241.32 down(g(g(g(g(f(x0)))))) 542.07/241.32 down(g(g(g(g(b))))) 542.07/241.32 down(g(g(g(g(c))))) 542.07/241.32 down(g(g(g(g(fresh_constant))))) 542.07/241.32 down(f(f(f(f(f(a)))))) 542.07/241.32 down(f(f(f(f(f(b)))))) 542.07/241.32 down(f(f(f(f(f(g(x0))))))) 542.07/241.32 down(f(f(f(f(f(c)))))) 542.07/241.32 down(f(f(f(f(f(fresh_constant)))))) 542.07/241.32 down(g(g(g(g(g(a)))))) 542.07/241.32 down(g(g(g(g(g(f(x0))))))) 542.07/241.32 down(g(g(g(g(g(b)))))) 542.07/241.32 down(g(g(g(g(g(c)))))) 542.07/241.32 down(g(g(g(g(g(fresh_constant)))))) 542.07/241.32 down(f(f(f(f(f(f(a))))))) 542.07/241.32 down(f(f(f(f(f(f(b))))))) 542.07/241.32 down(f(f(f(f(f(f(g(x0)))))))) 542.07/241.32 down(f(f(f(f(f(f(c))))))) 542.07/241.32 down(f(f(f(f(f(f(fresh_constant))))))) 542.07/241.32 down(g(g(g(g(g(g(a))))))) 542.07/241.32 down(g(g(g(g(g(g(f(x0)))))))) 542.07/241.32 down(g(g(g(g(g(g(b))))))) 542.07/241.32 down(g(g(g(g(g(g(c))))))) 542.07/241.32 down(g(g(g(g(g(g(fresh_constant))))))) 542.07/241.32 down(f(f(f(f(f(f(f(a)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(b)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(g(x0))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(c)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(a)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(f(x0))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(b)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(c)))))))) 542.07/241.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(a))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(b))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(c))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(a))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(b))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(c))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 f_flat(up(x0)) 542.07/241.32 g_flat(up(x0)) 542.07/241.32 542.07/241.32 We have to consider all minimal (P,Q,R)-chains. 542.07/241.32 ---------------------------------------- 542.07/241.32 542.07/241.32 (99) DependencyGraphProof (EQUIVALENT) 542.07/241.32 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 542.07/241.32 ---------------------------------------- 542.07/241.32 542.07/241.32 (100) 542.07/241.32 Obligation: 542.07/241.32 Q DP problem: 542.07/241.32 The TRS P consists of the following rules: 542.07/241.32 542.07/241.32 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.07/241.32 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.07/241.32 TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) 542.07/241.32 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.07/241.32 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.07/241.32 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.07/241.32 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.07/241.32 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.07/241.32 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.07/241.32 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.07/241.32 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.07/241.32 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.07/241.32 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.07/241.32 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.07/241.32 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.07/241.32 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.07/241.32 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.07/241.32 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.07/241.32 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.07/241.32 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.07/241.32 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.07/241.32 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.07/241.32 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.07/241.32 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.07/241.32 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.07/241.32 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.07/241.32 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.07/241.32 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.07/241.32 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.07/241.32 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.07/241.32 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.07/241.32 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.07/241.32 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.07/241.32 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.07/241.32 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.07/241.32 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.07/241.32 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.07/241.32 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.07/241.32 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.07/241.32 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.07/241.32 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.07/241.32 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.07/241.32 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.07/241.32 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.07/241.32 542.07/241.32 The TRS R consists of the following rules: 542.19/241.32 542.19/241.32 down(a) -> up(f(a)) 542.19/241.32 down(b) -> up(g(b)) 542.19/241.32 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.32 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.32 down(f(a)) -> f_flat(down(a)) 542.19/241.32 down(f(b)) -> f_flat(down(b)) 542.19/241.32 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.32 down(f(c)) -> f_flat(down(c)) 542.19/241.32 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.32 down(g(a)) -> g_flat(down(a)) 542.19/241.32 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.32 down(g(b)) -> g_flat(down(b)) 542.19/241.32 down(g(c)) -> g_flat(down(c)) 542.19/241.32 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.32 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.32 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.32 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.32 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.32 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.32 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.32 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.32 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.32 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.32 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.32 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.32 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.32 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.32 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.32 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.32 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.32 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.32 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.32 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.32 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.32 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.32 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.32 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.32 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.32 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.32 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.32 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.32 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.32 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.33 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.33 542.19/241.33 The set Q consists of the following terms: 542.19/241.33 542.19/241.33 down(a) 542.19/241.33 down(b) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.33 down(f(a)) 542.19/241.33 down(f(b)) 542.19/241.33 down(f(g(x0))) 542.19/241.33 down(f(c)) 542.19/241.33 down(f(fresh_constant)) 542.19/241.33 down(g(a)) 542.19/241.33 down(g(f(x0))) 542.19/241.33 down(g(b)) 542.19/241.33 down(g(c)) 542.19/241.33 down(g(fresh_constant)) 542.19/241.33 down(f(f(a))) 542.19/241.33 down(f(f(b))) 542.19/241.33 down(f(f(g(x0)))) 542.19/241.33 down(f(f(c))) 542.19/241.33 down(f(f(fresh_constant))) 542.19/241.33 down(g(g(a))) 542.19/241.33 down(g(g(f(x0)))) 542.19/241.33 down(g(g(b))) 542.19/241.33 down(g(g(c))) 542.19/241.33 down(g(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) 542.19/241.33 down(f(f(f(g(x0))))) 542.19/241.33 down(f(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) 542.19/241.33 down(g(g(g(f(x0))))) 542.19/241.33 down(g(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(x0)))))) 542.19/241.33 down(f(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(x0)))))) 542.19/241.33 down(g(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(x0))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(x0))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 f_flat(up(x0)) 542.19/241.33 g_flat(up(x0)) 542.19/241.33 542.19/241.33 We have to consider all minimal (P,Q,R)-chains. 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (101) TransformationProof (EQUIVALENT) 542.19/241.33 By rewriting [LPAR04] the rule TOP(up(g(g(b)))) -> TOP(g_flat(down(g(b)))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.33 542.19/241.33 (TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))),TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b))))) 542.19/241.33 542.19/241.33 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (102) 542.19/241.33 Obligation: 542.19/241.33 Q DP problem: 542.19/241.33 The TRS P consists of the following rules: 542.19/241.33 542.19/241.33 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.33 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.33 TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) 542.19/241.33 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.19/241.33 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.33 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.33 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.19/241.33 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.19/241.33 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.19/241.33 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.19/241.33 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.19/241.33 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.33 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.33 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.33 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.33 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.33 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.33 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.33 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.33 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.33 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.33 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.33 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.33 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.33 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.33 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.33 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.33 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.33 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.33 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.33 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.33 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.33 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.33 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.33 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.33 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.33 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.33 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.33 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.33 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.33 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.33 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.33 542.19/241.33 The TRS R consists of the following rules: 542.19/241.33 542.19/241.33 down(a) -> up(f(a)) 542.19/241.33 down(b) -> up(g(b)) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.33 down(f(a)) -> f_flat(down(a)) 542.19/241.33 down(f(b)) -> f_flat(down(b)) 542.19/241.33 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.33 down(f(c)) -> f_flat(down(c)) 542.19/241.33 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.33 down(g(a)) -> g_flat(down(a)) 542.19/241.33 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.33 down(g(b)) -> g_flat(down(b)) 542.19/241.33 down(g(c)) -> g_flat(down(c)) 542.19/241.33 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.33 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.33 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.33 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.33 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.33 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.33 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.33 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.33 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.33 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.33 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.33 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.33 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.33 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.33 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.33 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.33 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.33 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.33 542.19/241.33 The set Q consists of the following terms: 542.19/241.33 542.19/241.33 down(a) 542.19/241.33 down(b) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.33 down(f(a)) 542.19/241.33 down(f(b)) 542.19/241.33 down(f(g(x0))) 542.19/241.33 down(f(c)) 542.19/241.33 down(f(fresh_constant)) 542.19/241.33 down(g(a)) 542.19/241.33 down(g(f(x0))) 542.19/241.33 down(g(b)) 542.19/241.33 down(g(c)) 542.19/241.33 down(g(fresh_constant)) 542.19/241.33 down(f(f(a))) 542.19/241.33 down(f(f(b))) 542.19/241.33 down(f(f(g(x0)))) 542.19/241.33 down(f(f(c))) 542.19/241.33 down(f(f(fresh_constant))) 542.19/241.33 down(g(g(a))) 542.19/241.33 down(g(g(f(x0)))) 542.19/241.33 down(g(g(b))) 542.19/241.33 down(g(g(c))) 542.19/241.33 down(g(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) 542.19/241.33 down(f(f(f(g(x0))))) 542.19/241.33 down(f(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) 542.19/241.33 down(g(g(g(f(x0))))) 542.19/241.33 down(g(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(x0)))))) 542.19/241.33 down(f(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(x0)))))) 542.19/241.33 down(g(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(x0))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(x0))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 f_flat(up(x0)) 542.19/241.33 g_flat(up(x0)) 542.19/241.33 542.19/241.33 We have to consider all minimal (P,Q,R)-chains. 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (103) TransformationProof (EQUIVALENT) 542.19/241.33 By rewriting [LPAR04] the rule TOP(up(g(g(c)))) -> TOP(g_flat(down(g(c)))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.33 542.19/241.33 (TOP(up(g(g(c)))) -> TOP(g_flat(g_flat(down(c)))),TOP(up(g(g(c)))) -> TOP(g_flat(g_flat(down(c))))) 542.19/241.33 542.19/241.33 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (104) 542.19/241.33 Obligation: 542.19/241.33 Q DP problem: 542.19/241.33 The TRS P consists of the following rules: 542.19/241.33 542.19/241.33 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.33 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.33 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.19/241.33 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.33 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.33 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.19/241.33 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.19/241.33 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.19/241.33 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.19/241.33 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.19/241.33 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.33 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.33 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.33 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.33 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.33 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.33 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.33 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.33 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.33 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.33 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.33 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.33 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.33 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.33 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.33 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.33 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.33 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.33 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.33 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.33 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.33 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.33 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.33 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.33 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.33 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.33 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.33 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.33 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.33 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.33 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.33 TOP(up(g(g(c)))) -> TOP(g_flat(g_flat(down(c)))) 542.19/241.33 542.19/241.33 The TRS R consists of the following rules: 542.19/241.33 542.19/241.33 down(a) -> up(f(a)) 542.19/241.33 down(b) -> up(g(b)) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.33 down(f(a)) -> f_flat(down(a)) 542.19/241.33 down(f(b)) -> f_flat(down(b)) 542.19/241.33 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.33 down(f(c)) -> f_flat(down(c)) 542.19/241.33 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.33 down(g(a)) -> g_flat(down(a)) 542.19/241.33 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.33 down(g(b)) -> g_flat(down(b)) 542.19/241.33 down(g(c)) -> g_flat(down(c)) 542.19/241.33 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.33 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.33 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.33 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.33 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.33 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.33 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.33 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.33 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.33 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.33 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.33 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.33 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.33 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.33 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.33 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.33 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.33 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.33 542.19/241.33 The set Q consists of the following terms: 542.19/241.33 542.19/241.33 down(a) 542.19/241.33 down(b) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.33 down(f(a)) 542.19/241.33 down(f(b)) 542.19/241.33 down(f(g(x0))) 542.19/241.33 down(f(c)) 542.19/241.33 down(f(fresh_constant)) 542.19/241.33 down(g(a)) 542.19/241.33 down(g(f(x0))) 542.19/241.33 down(g(b)) 542.19/241.33 down(g(c)) 542.19/241.33 down(g(fresh_constant)) 542.19/241.33 down(f(f(a))) 542.19/241.33 down(f(f(b))) 542.19/241.33 down(f(f(g(x0)))) 542.19/241.33 down(f(f(c))) 542.19/241.33 down(f(f(fresh_constant))) 542.19/241.33 down(g(g(a))) 542.19/241.33 down(g(g(f(x0)))) 542.19/241.33 down(g(g(b))) 542.19/241.33 down(g(g(c))) 542.19/241.33 down(g(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) 542.19/241.33 down(f(f(f(g(x0))))) 542.19/241.33 down(f(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) 542.19/241.33 down(g(g(g(f(x0))))) 542.19/241.33 down(g(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(x0)))))) 542.19/241.33 down(f(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(x0)))))) 542.19/241.33 down(g(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(x0))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(x0))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 f_flat(up(x0)) 542.19/241.33 g_flat(up(x0)) 542.19/241.33 542.19/241.33 We have to consider all minimal (P,Q,R)-chains. 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (105) DependencyGraphProof (EQUIVALENT) 542.19/241.33 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (106) 542.19/241.33 Obligation: 542.19/241.33 Q DP problem: 542.19/241.33 The TRS P consists of the following rules: 542.19/241.33 542.19/241.33 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.33 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.33 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) 542.19/241.33 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.33 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.33 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.19/241.33 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.19/241.33 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.19/241.33 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.19/241.33 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.19/241.33 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.33 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.33 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.33 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.33 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.33 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.33 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.33 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.33 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.33 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.33 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.33 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.33 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.33 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.33 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.33 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.33 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.33 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.33 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.33 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.33 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.33 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.33 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.33 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.33 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.33 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.33 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.33 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.33 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.33 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.33 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.33 542.19/241.33 The TRS R consists of the following rules: 542.19/241.33 542.19/241.33 down(a) -> up(f(a)) 542.19/241.33 down(b) -> up(g(b)) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.33 down(f(a)) -> f_flat(down(a)) 542.19/241.33 down(f(b)) -> f_flat(down(b)) 542.19/241.33 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.33 down(f(c)) -> f_flat(down(c)) 542.19/241.33 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.33 down(g(a)) -> g_flat(down(a)) 542.19/241.33 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.33 down(g(b)) -> g_flat(down(b)) 542.19/241.33 down(g(c)) -> g_flat(down(c)) 542.19/241.33 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.33 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.33 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.33 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.33 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.33 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.33 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.33 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.33 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.33 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.33 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.33 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.33 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.33 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.33 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.33 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.33 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.33 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.33 542.19/241.33 The set Q consists of the following terms: 542.19/241.33 542.19/241.33 down(a) 542.19/241.33 down(b) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.33 down(f(a)) 542.19/241.33 down(f(b)) 542.19/241.33 down(f(g(x0))) 542.19/241.33 down(f(c)) 542.19/241.33 down(f(fresh_constant)) 542.19/241.33 down(g(a)) 542.19/241.33 down(g(f(x0))) 542.19/241.33 down(g(b)) 542.19/241.33 down(g(c)) 542.19/241.33 down(g(fresh_constant)) 542.19/241.33 down(f(f(a))) 542.19/241.33 down(f(f(b))) 542.19/241.33 down(f(f(g(x0)))) 542.19/241.33 down(f(f(c))) 542.19/241.33 down(f(f(fresh_constant))) 542.19/241.33 down(g(g(a))) 542.19/241.33 down(g(g(f(x0)))) 542.19/241.33 down(g(g(b))) 542.19/241.33 down(g(g(c))) 542.19/241.33 down(g(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) 542.19/241.33 down(f(f(f(g(x0))))) 542.19/241.33 down(f(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) 542.19/241.33 down(g(g(g(f(x0))))) 542.19/241.33 down(g(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(x0)))))) 542.19/241.33 down(f(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(x0)))))) 542.19/241.33 down(g(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(x0))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(x0))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 f_flat(up(x0)) 542.19/241.33 g_flat(up(x0)) 542.19/241.33 542.19/241.33 We have to consider all minimal (P,Q,R)-chains. 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (107) TransformationProof (EQUIVALENT) 542.19/241.33 By rewriting [LPAR04] the rule TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(down(g(fresh_constant)))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.33 542.19/241.33 (TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(g_flat(down(fresh_constant)))),TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(g_flat(down(fresh_constant))))) 542.19/241.33 542.19/241.33 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (108) 542.19/241.33 Obligation: 542.19/241.33 Q DP problem: 542.19/241.33 The TRS P consists of the following rules: 542.19/241.33 542.19/241.33 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.33 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.33 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.33 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.33 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.19/241.33 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.19/241.33 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.19/241.33 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.19/241.33 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.19/241.33 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.33 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.33 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.33 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.33 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.33 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.33 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.33 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.33 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.33 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.33 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.33 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.33 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.33 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.33 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.33 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.33 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.33 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.33 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.33 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.33 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.33 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.33 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.33 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.33 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.33 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.33 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.33 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.33 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.33 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.33 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.33 TOP(up(g(g(fresh_constant)))) -> TOP(g_flat(g_flat(down(fresh_constant)))) 542.19/241.33 542.19/241.33 The TRS R consists of the following rules: 542.19/241.33 542.19/241.33 down(a) -> up(f(a)) 542.19/241.33 down(b) -> up(g(b)) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.33 down(f(a)) -> f_flat(down(a)) 542.19/241.33 down(f(b)) -> f_flat(down(b)) 542.19/241.33 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.33 down(f(c)) -> f_flat(down(c)) 542.19/241.33 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.33 down(g(a)) -> g_flat(down(a)) 542.19/241.33 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.33 down(g(b)) -> g_flat(down(b)) 542.19/241.33 down(g(c)) -> g_flat(down(c)) 542.19/241.33 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.33 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.33 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.33 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.33 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.33 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.33 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.33 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.33 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.33 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.33 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.33 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.33 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.33 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.33 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.33 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.33 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.33 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.33 542.19/241.33 The set Q consists of the following terms: 542.19/241.33 542.19/241.33 down(a) 542.19/241.33 down(b) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.33 down(f(a)) 542.19/241.33 down(f(b)) 542.19/241.33 down(f(g(x0))) 542.19/241.33 down(f(c)) 542.19/241.33 down(f(fresh_constant)) 542.19/241.33 down(g(a)) 542.19/241.33 down(g(f(x0))) 542.19/241.33 down(g(b)) 542.19/241.33 down(g(c)) 542.19/241.33 down(g(fresh_constant)) 542.19/241.33 down(f(f(a))) 542.19/241.33 down(f(f(b))) 542.19/241.33 down(f(f(g(x0)))) 542.19/241.33 down(f(f(c))) 542.19/241.33 down(f(f(fresh_constant))) 542.19/241.33 down(g(g(a))) 542.19/241.33 down(g(g(f(x0)))) 542.19/241.33 down(g(g(b))) 542.19/241.33 down(g(g(c))) 542.19/241.33 down(g(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) 542.19/241.33 down(f(f(f(g(x0))))) 542.19/241.33 down(f(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) 542.19/241.33 down(g(g(g(f(x0))))) 542.19/241.33 down(g(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(x0)))))) 542.19/241.33 down(f(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(x0)))))) 542.19/241.33 down(g(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(x0))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(x0))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 f_flat(up(x0)) 542.19/241.33 g_flat(up(x0)) 542.19/241.33 542.19/241.33 We have to consider all minimal (P,Q,R)-chains. 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (109) DependencyGraphProof (EQUIVALENT) 542.19/241.33 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (110) 542.19/241.33 Obligation: 542.19/241.33 Q DP problem: 542.19/241.33 The TRS P consists of the following rules: 542.19/241.33 542.19/241.33 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.33 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.33 TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) 542.19/241.33 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.19/241.33 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.19/241.33 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.19/241.33 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.19/241.33 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.33 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.33 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.33 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.33 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.33 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.33 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.33 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.33 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.33 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.33 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.33 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.33 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.33 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.33 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.33 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.33 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.33 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.33 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.33 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.33 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.33 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.33 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.33 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.33 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.33 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.33 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.33 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.33 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.33 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.33 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.33 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.33 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.33 542.19/241.33 The TRS R consists of the following rules: 542.19/241.33 542.19/241.33 down(a) -> up(f(a)) 542.19/241.33 down(b) -> up(g(b)) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.33 down(f(a)) -> f_flat(down(a)) 542.19/241.33 down(f(b)) -> f_flat(down(b)) 542.19/241.33 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.33 down(f(c)) -> f_flat(down(c)) 542.19/241.33 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.33 down(g(a)) -> g_flat(down(a)) 542.19/241.33 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.33 down(g(b)) -> g_flat(down(b)) 542.19/241.33 down(g(c)) -> g_flat(down(c)) 542.19/241.33 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.33 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.33 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.33 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.33 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.33 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.33 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.33 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.33 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.33 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.33 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.33 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.33 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.33 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.33 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.33 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.33 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.33 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.33 542.19/241.33 The set Q consists of the following terms: 542.19/241.33 542.19/241.33 down(a) 542.19/241.33 down(b) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.33 down(f(a)) 542.19/241.33 down(f(b)) 542.19/241.33 down(f(g(x0))) 542.19/241.33 down(f(c)) 542.19/241.33 down(f(fresh_constant)) 542.19/241.33 down(g(a)) 542.19/241.33 down(g(f(x0))) 542.19/241.33 down(g(b)) 542.19/241.33 down(g(c)) 542.19/241.33 down(g(fresh_constant)) 542.19/241.33 down(f(f(a))) 542.19/241.33 down(f(f(b))) 542.19/241.33 down(f(f(g(x0)))) 542.19/241.33 down(f(f(c))) 542.19/241.33 down(f(f(fresh_constant))) 542.19/241.33 down(g(g(a))) 542.19/241.33 down(g(g(f(x0)))) 542.19/241.33 down(g(g(b))) 542.19/241.33 down(g(g(c))) 542.19/241.33 down(g(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) 542.19/241.33 down(f(f(f(g(x0))))) 542.19/241.33 down(f(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) 542.19/241.33 down(g(g(g(f(x0))))) 542.19/241.33 down(g(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(x0)))))) 542.19/241.33 down(f(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(x0)))))) 542.19/241.33 down(g(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(x0))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(x0))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 f_flat(up(x0)) 542.19/241.33 g_flat(up(x0)) 542.19/241.33 542.19/241.33 We have to consider all minimal (P,Q,R)-chains. 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (111) TransformationProof (EQUIVALENT) 542.19/241.33 By rewriting [LPAR04] the rule TOP(up(f(f(f(a))))) -> TOP(f_flat(down(f(f(a))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.33 542.19/241.33 (TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))),TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a)))))) 542.19/241.33 542.19/241.33 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (112) 542.19/241.33 Obligation: 542.19/241.33 Q DP problem: 542.19/241.33 The TRS P consists of the following rules: 542.19/241.33 542.19/241.33 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.33 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.33 TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) 542.19/241.33 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.19/241.33 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.19/241.33 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.19/241.33 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.33 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.33 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.33 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.33 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.33 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.33 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.33 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.33 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.33 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.33 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.33 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.33 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.33 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.33 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.33 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.33 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.33 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.33 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.33 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.33 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.33 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.33 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.33 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.33 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.33 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.33 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.33 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.33 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.33 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.33 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.33 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.33 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.33 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.33 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.33 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.33 542.19/241.33 The TRS R consists of the following rules: 542.19/241.33 542.19/241.33 down(a) -> up(f(a)) 542.19/241.33 down(b) -> up(g(b)) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.33 down(f(a)) -> f_flat(down(a)) 542.19/241.33 down(f(b)) -> f_flat(down(b)) 542.19/241.33 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.33 down(f(c)) -> f_flat(down(c)) 542.19/241.33 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.33 down(g(a)) -> g_flat(down(a)) 542.19/241.33 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.33 down(g(b)) -> g_flat(down(b)) 542.19/241.33 down(g(c)) -> g_flat(down(c)) 542.19/241.33 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.33 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.33 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.33 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.33 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.33 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.33 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.33 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.33 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.33 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.33 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.33 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.33 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.33 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.33 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.33 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.33 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.33 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.33 542.19/241.33 The set Q consists of the following terms: 542.19/241.33 542.19/241.33 down(a) 542.19/241.33 down(b) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.33 down(f(a)) 542.19/241.33 down(f(b)) 542.19/241.33 down(f(g(x0))) 542.19/241.33 down(f(c)) 542.19/241.33 down(f(fresh_constant)) 542.19/241.33 down(g(a)) 542.19/241.33 down(g(f(x0))) 542.19/241.33 down(g(b)) 542.19/241.33 down(g(c)) 542.19/241.33 down(g(fresh_constant)) 542.19/241.33 down(f(f(a))) 542.19/241.33 down(f(f(b))) 542.19/241.33 down(f(f(g(x0)))) 542.19/241.33 down(f(f(c))) 542.19/241.33 down(f(f(fresh_constant))) 542.19/241.33 down(g(g(a))) 542.19/241.33 down(g(g(f(x0)))) 542.19/241.33 down(g(g(b))) 542.19/241.33 down(g(g(c))) 542.19/241.33 down(g(g(fresh_constant))) 542.19/241.33 down(f(f(f(a)))) 542.19/241.33 down(f(f(f(b)))) 542.19/241.33 down(f(f(f(g(x0))))) 542.19/241.33 down(f(f(f(c)))) 542.19/241.33 down(f(f(f(fresh_constant)))) 542.19/241.33 down(g(g(g(a)))) 542.19/241.33 down(g(g(g(f(x0))))) 542.19/241.33 down(g(g(g(b)))) 542.19/241.33 down(g(g(g(c)))) 542.19/241.33 down(g(g(g(fresh_constant)))) 542.19/241.33 down(f(f(f(f(a))))) 542.19/241.33 down(f(f(f(f(b))))) 542.19/241.33 down(f(f(f(f(g(x0)))))) 542.19/241.33 down(f(f(f(f(c))))) 542.19/241.33 down(f(f(f(f(fresh_constant))))) 542.19/241.33 down(g(g(g(g(a))))) 542.19/241.33 down(g(g(g(g(f(x0)))))) 542.19/241.33 down(g(g(g(g(b))))) 542.19/241.33 down(g(g(g(g(c))))) 542.19/241.33 down(g(g(g(g(fresh_constant))))) 542.19/241.33 down(f(f(f(f(f(a)))))) 542.19/241.33 down(f(f(f(f(f(b)))))) 542.19/241.33 down(f(f(f(f(f(g(x0))))))) 542.19/241.33 down(f(f(f(f(f(c)))))) 542.19/241.33 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.33 down(g(g(g(g(g(a)))))) 542.19/241.33 down(g(g(g(g(g(f(x0))))))) 542.19/241.33 down(g(g(g(g(g(b)))))) 542.19/241.33 down(g(g(g(g(g(c)))))) 542.19/241.33 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.33 down(f(f(f(f(f(f(a))))))) 542.19/241.33 down(f(f(f(f(f(f(b))))))) 542.19/241.33 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.33 down(f(f(f(f(f(f(c))))))) 542.19/241.33 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.33 down(g(g(g(g(g(g(a))))))) 542.19/241.33 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.33 down(g(g(g(g(g(g(b))))))) 542.19/241.33 down(g(g(g(g(g(g(c))))))) 542.19/241.33 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.33 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.33 f_flat(up(x0)) 542.19/241.33 g_flat(up(x0)) 542.19/241.33 542.19/241.33 We have to consider all minimal (P,Q,R)-chains. 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (113) TransformationProof (EQUIVALENT) 542.19/241.33 By rewriting [LPAR04] the rule TOP(up(f(f(f(b))))) -> TOP(f_flat(down(f(f(b))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.33 542.19/241.33 (TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))),TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b)))))) 542.19/241.33 542.19/241.33 542.19/241.33 ---------------------------------------- 542.19/241.33 542.19/241.33 (114) 542.19/241.33 Obligation: 542.19/241.33 Q DP problem: 542.19/241.33 The TRS P consists of the following rules: 542.19/241.33 542.19/241.33 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.33 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.33 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) 542.19/241.33 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.19/241.33 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.19/241.33 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.33 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.33 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.34 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.34 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.34 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.34 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.34 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.34 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.34 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.34 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.34 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.34 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.34 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.34 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.34 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.34 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.34 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.34 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.34 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.34 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.34 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.34 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.34 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.34 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.34 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.34 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.34 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.34 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.34 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.34 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.34 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.34 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.34 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.34 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.34 542.19/241.34 The TRS R consists of the following rules: 542.19/241.34 542.19/241.34 down(a) -> up(f(a)) 542.19/241.34 down(b) -> up(g(b)) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.34 down(f(a)) -> f_flat(down(a)) 542.19/241.34 down(f(b)) -> f_flat(down(b)) 542.19/241.34 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.34 down(f(c)) -> f_flat(down(c)) 542.19/241.34 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.34 down(g(a)) -> g_flat(down(a)) 542.19/241.34 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.34 down(g(b)) -> g_flat(down(b)) 542.19/241.34 down(g(c)) -> g_flat(down(c)) 542.19/241.34 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.34 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.34 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.34 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.34 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.34 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.34 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.34 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.34 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.34 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.34 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.34 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.34 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.34 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.34 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.34 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.34 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.34 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.34 542.19/241.34 The set Q consists of the following terms: 542.19/241.34 542.19/241.34 down(a) 542.19/241.34 down(b) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.34 down(f(a)) 542.19/241.34 down(f(b)) 542.19/241.34 down(f(g(x0))) 542.19/241.34 down(f(c)) 542.19/241.34 down(f(fresh_constant)) 542.19/241.34 down(g(a)) 542.19/241.34 down(g(f(x0))) 542.19/241.34 down(g(b)) 542.19/241.34 down(g(c)) 542.19/241.34 down(g(fresh_constant)) 542.19/241.34 down(f(f(a))) 542.19/241.34 down(f(f(b))) 542.19/241.34 down(f(f(g(x0)))) 542.19/241.34 down(f(f(c))) 542.19/241.34 down(f(f(fresh_constant))) 542.19/241.34 down(g(g(a))) 542.19/241.34 down(g(g(f(x0)))) 542.19/241.34 down(g(g(b))) 542.19/241.34 down(g(g(c))) 542.19/241.34 down(g(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) 542.19/241.34 down(f(f(f(g(x0))))) 542.19/241.34 down(f(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) 542.19/241.34 down(g(g(g(f(x0))))) 542.19/241.34 down(g(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(x0)))))) 542.19/241.34 down(f(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(x0)))))) 542.19/241.34 down(g(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(x0))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(x0))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 f_flat(up(x0)) 542.19/241.34 g_flat(up(x0)) 542.19/241.34 542.19/241.34 We have to consider all minimal (P,Q,R)-chains. 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (115) TransformationProof (EQUIVALENT) 542.19/241.34 By rewriting [LPAR04] the rule TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(down(f(f(g(x0)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.34 542.19/241.34 (TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))),TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0))))))) 542.19/241.34 542.19/241.34 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (116) 542.19/241.34 Obligation: 542.19/241.34 Q DP problem: 542.19/241.34 The TRS P consists of the following rules: 542.19/241.34 542.19/241.34 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.34 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.34 TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) 542.19/241.34 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.19/241.34 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.34 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.34 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.34 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.34 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.34 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.34 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.34 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.34 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.34 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.34 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.34 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.34 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.34 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.34 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.34 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.34 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.34 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.34 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.34 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.34 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.34 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.34 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.34 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.34 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.34 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.34 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.34 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.34 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.34 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.34 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.34 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.34 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.34 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.34 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.34 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.34 542.19/241.34 The TRS R consists of the following rules: 542.19/241.34 542.19/241.34 down(a) -> up(f(a)) 542.19/241.34 down(b) -> up(g(b)) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.34 down(f(a)) -> f_flat(down(a)) 542.19/241.34 down(f(b)) -> f_flat(down(b)) 542.19/241.34 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.34 down(f(c)) -> f_flat(down(c)) 542.19/241.34 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.34 down(g(a)) -> g_flat(down(a)) 542.19/241.34 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.34 down(g(b)) -> g_flat(down(b)) 542.19/241.34 down(g(c)) -> g_flat(down(c)) 542.19/241.34 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.34 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.34 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.34 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.34 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.34 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.34 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.34 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.34 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.34 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.34 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.34 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.34 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.34 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.34 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.34 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.34 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.34 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.34 542.19/241.34 The set Q consists of the following terms: 542.19/241.34 542.19/241.34 down(a) 542.19/241.34 down(b) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.34 down(f(a)) 542.19/241.34 down(f(b)) 542.19/241.34 down(f(g(x0))) 542.19/241.34 down(f(c)) 542.19/241.34 down(f(fresh_constant)) 542.19/241.34 down(g(a)) 542.19/241.34 down(g(f(x0))) 542.19/241.34 down(g(b)) 542.19/241.34 down(g(c)) 542.19/241.34 down(g(fresh_constant)) 542.19/241.34 down(f(f(a))) 542.19/241.34 down(f(f(b))) 542.19/241.34 down(f(f(g(x0)))) 542.19/241.34 down(f(f(c))) 542.19/241.34 down(f(f(fresh_constant))) 542.19/241.34 down(g(g(a))) 542.19/241.34 down(g(g(f(x0)))) 542.19/241.34 down(g(g(b))) 542.19/241.34 down(g(g(c))) 542.19/241.34 down(g(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) 542.19/241.34 down(f(f(f(g(x0))))) 542.19/241.34 down(f(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) 542.19/241.34 down(g(g(g(f(x0))))) 542.19/241.34 down(g(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(x0)))))) 542.19/241.34 down(f(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(x0)))))) 542.19/241.34 down(g(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(x0))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(x0))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 f_flat(up(x0)) 542.19/241.34 g_flat(up(x0)) 542.19/241.34 542.19/241.34 We have to consider all minimal (P,Q,R)-chains. 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (117) TransformationProof (EQUIVALENT) 542.19/241.34 By rewriting [LPAR04] the rule TOP(up(f(f(f(c))))) -> TOP(f_flat(down(f(f(c))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.34 542.19/241.34 (TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))),TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c)))))) 542.19/241.34 542.19/241.34 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (118) 542.19/241.34 Obligation: 542.19/241.34 Q DP problem: 542.19/241.34 The TRS P consists of the following rules: 542.19/241.34 542.19/241.34 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.34 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.34 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) 542.19/241.34 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.34 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.34 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.34 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.34 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.34 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.34 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.34 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.34 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.34 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.34 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.34 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.34 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.34 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.34 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.34 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.34 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.34 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.34 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.34 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.34 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.34 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.34 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.34 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.34 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.34 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.34 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.34 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.34 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.34 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.34 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.34 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.34 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.34 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.34 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.34 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.34 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.34 542.19/241.34 The TRS R consists of the following rules: 542.19/241.34 542.19/241.34 down(a) -> up(f(a)) 542.19/241.34 down(b) -> up(g(b)) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.34 down(f(a)) -> f_flat(down(a)) 542.19/241.34 down(f(b)) -> f_flat(down(b)) 542.19/241.34 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.34 down(f(c)) -> f_flat(down(c)) 542.19/241.34 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.34 down(g(a)) -> g_flat(down(a)) 542.19/241.34 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.34 down(g(b)) -> g_flat(down(b)) 542.19/241.34 down(g(c)) -> g_flat(down(c)) 542.19/241.34 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.34 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.34 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.34 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.34 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.34 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.34 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.34 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.34 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.34 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.34 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.34 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.34 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.34 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.34 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.34 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.34 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.34 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.34 542.19/241.34 The set Q consists of the following terms: 542.19/241.34 542.19/241.34 down(a) 542.19/241.34 down(b) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.34 down(f(a)) 542.19/241.34 down(f(b)) 542.19/241.34 down(f(g(x0))) 542.19/241.34 down(f(c)) 542.19/241.34 down(f(fresh_constant)) 542.19/241.34 down(g(a)) 542.19/241.34 down(g(f(x0))) 542.19/241.34 down(g(b)) 542.19/241.34 down(g(c)) 542.19/241.34 down(g(fresh_constant)) 542.19/241.34 down(f(f(a))) 542.19/241.34 down(f(f(b))) 542.19/241.34 down(f(f(g(x0)))) 542.19/241.34 down(f(f(c))) 542.19/241.34 down(f(f(fresh_constant))) 542.19/241.34 down(g(g(a))) 542.19/241.34 down(g(g(f(x0)))) 542.19/241.34 down(g(g(b))) 542.19/241.34 down(g(g(c))) 542.19/241.34 down(g(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) 542.19/241.34 down(f(f(f(g(x0))))) 542.19/241.34 down(f(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) 542.19/241.34 down(g(g(g(f(x0))))) 542.19/241.34 down(g(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(x0)))))) 542.19/241.34 down(f(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(x0)))))) 542.19/241.34 down(g(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(x0))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(x0))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 f_flat(up(x0)) 542.19/241.34 g_flat(up(x0)) 542.19/241.34 542.19/241.34 We have to consider all minimal (P,Q,R)-chains. 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (119) TransformationProof (EQUIVALENT) 542.19/241.34 By rewriting [LPAR04] the rule TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(down(f(f(fresh_constant))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.34 542.19/241.34 (TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))),TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant)))))) 542.19/241.34 542.19/241.34 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (120) 542.19/241.34 Obligation: 542.19/241.34 Q DP problem: 542.19/241.34 The TRS P consists of the following rules: 542.19/241.34 542.19/241.34 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.34 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.34 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) 542.19/241.34 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.34 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.34 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.34 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.34 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.34 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.34 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.34 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.34 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.34 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.34 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.34 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.34 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.34 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.34 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.34 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.34 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.34 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.34 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.34 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.34 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.34 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.34 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.34 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.34 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.34 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.34 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.34 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.34 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.34 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.34 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.34 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.34 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.34 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.34 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.34 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.34 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.34 542.19/241.34 The TRS R consists of the following rules: 542.19/241.34 542.19/241.34 down(a) -> up(f(a)) 542.19/241.34 down(b) -> up(g(b)) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.34 down(f(a)) -> f_flat(down(a)) 542.19/241.34 down(f(b)) -> f_flat(down(b)) 542.19/241.34 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.34 down(f(c)) -> f_flat(down(c)) 542.19/241.34 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.34 down(g(a)) -> g_flat(down(a)) 542.19/241.34 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.34 down(g(b)) -> g_flat(down(b)) 542.19/241.34 down(g(c)) -> g_flat(down(c)) 542.19/241.34 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.34 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.34 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.34 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.34 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.34 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.34 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.34 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.34 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.34 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.34 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.34 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.34 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.34 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.34 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.34 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.34 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.34 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.34 542.19/241.34 The set Q consists of the following terms: 542.19/241.34 542.19/241.34 down(a) 542.19/241.34 down(b) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.34 down(f(a)) 542.19/241.34 down(f(b)) 542.19/241.34 down(f(g(x0))) 542.19/241.34 down(f(c)) 542.19/241.34 down(f(fresh_constant)) 542.19/241.34 down(g(a)) 542.19/241.34 down(g(f(x0))) 542.19/241.34 down(g(b)) 542.19/241.34 down(g(c)) 542.19/241.34 down(g(fresh_constant)) 542.19/241.34 down(f(f(a))) 542.19/241.34 down(f(f(b))) 542.19/241.34 down(f(f(g(x0)))) 542.19/241.34 down(f(f(c))) 542.19/241.34 down(f(f(fresh_constant))) 542.19/241.34 down(g(g(a))) 542.19/241.34 down(g(g(f(x0)))) 542.19/241.34 down(g(g(b))) 542.19/241.34 down(g(g(c))) 542.19/241.34 down(g(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) 542.19/241.34 down(f(f(f(g(x0))))) 542.19/241.34 down(f(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) 542.19/241.34 down(g(g(g(f(x0))))) 542.19/241.34 down(g(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(x0)))))) 542.19/241.34 down(f(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(x0)))))) 542.19/241.34 down(g(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(x0))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(x0))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 f_flat(up(x0)) 542.19/241.34 g_flat(up(x0)) 542.19/241.34 542.19/241.34 We have to consider all minimal (P,Q,R)-chains. 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (121) TransformationProof (EQUIVALENT) 542.19/241.34 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(down(f(f(f(a)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.34 542.19/241.34 (TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))),TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a))))))) 542.19/241.34 542.19/241.34 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (122) 542.19/241.34 Obligation: 542.19/241.34 Q DP problem: 542.19/241.34 The TRS P consists of the following rules: 542.19/241.34 542.19/241.34 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.34 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.34 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) 542.19/241.34 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.34 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.34 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.34 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.34 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.34 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.34 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.34 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.34 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.34 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.34 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.34 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.34 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.34 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.34 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.34 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.34 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.34 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.34 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.34 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.34 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.34 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.34 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.34 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.34 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.34 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.34 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.34 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.34 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.34 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.34 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.34 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.34 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.34 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.34 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.34 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.34 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.34 542.19/241.34 The TRS R consists of the following rules: 542.19/241.34 542.19/241.34 down(a) -> up(f(a)) 542.19/241.34 down(b) -> up(g(b)) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.34 down(f(a)) -> f_flat(down(a)) 542.19/241.34 down(f(b)) -> f_flat(down(b)) 542.19/241.34 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.34 down(f(c)) -> f_flat(down(c)) 542.19/241.34 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.34 down(g(a)) -> g_flat(down(a)) 542.19/241.34 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.34 down(g(b)) -> g_flat(down(b)) 542.19/241.34 down(g(c)) -> g_flat(down(c)) 542.19/241.34 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.34 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.34 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.34 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.34 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.34 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.34 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.34 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.34 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.34 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.34 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.34 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.34 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.34 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.34 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.34 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.34 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.34 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.34 542.19/241.34 The set Q consists of the following terms: 542.19/241.34 542.19/241.34 down(a) 542.19/241.34 down(b) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.34 down(f(a)) 542.19/241.34 down(f(b)) 542.19/241.34 down(f(g(x0))) 542.19/241.34 down(f(c)) 542.19/241.34 down(f(fresh_constant)) 542.19/241.34 down(g(a)) 542.19/241.34 down(g(f(x0))) 542.19/241.34 down(g(b)) 542.19/241.34 down(g(c)) 542.19/241.34 down(g(fresh_constant)) 542.19/241.34 down(f(f(a))) 542.19/241.34 down(f(f(b))) 542.19/241.34 down(f(f(g(x0)))) 542.19/241.34 down(f(f(c))) 542.19/241.34 down(f(f(fresh_constant))) 542.19/241.34 down(g(g(a))) 542.19/241.34 down(g(g(f(x0)))) 542.19/241.34 down(g(g(b))) 542.19/241.34 down(g(g(c))) 542.19/241.34 down(g(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) 542.19/241.34 down(f(f(f(g(x0))))) 542.19/241.34 down(f(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) 542.19/241.34 down(g(g(g(f(x0))))) 542.19/241.34 down(g(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(x0)))))) 542.19/241.34 down(f(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(x0)))))) 542.19/241.34 down(g(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(x0))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(x0))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 f_flat(up(x0)) 542.19/241.34 g_flat(up(x0)) 542.19/241.34 542.19/241.34 We have to consider all minimal (P,Q,R)-chains. 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (123) TransformationProof (EQUIVALENT) 542.19/241.34 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(down(f(f(f(b)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.34 542.19/241.34 (TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))),TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b))))))) 542.19/241.34 542.19/241.34 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (124) 542.19/241.34 Obligation: 542.19/241.34 Q DP problem: 542.19/241.34 The TRS P consists of the following rules: 542.19/241.34 542.19/241.34 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.34 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.34 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) 542.19/241.34 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.34 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.34 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.34 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.34 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.34 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.34 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.34 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.34 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.34 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.34 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.34 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.34 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.34 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.34 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.34 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.34 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.34 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.34 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.34 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.34 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.34 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.34 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.34 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.34 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.34 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.34 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.34 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.34 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.34 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.34 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.34 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.34 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.34 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.34 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.34 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.34 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.34 542.19/241.34 The TRS R consists of the following rules: 542.19/241.34 542.19/241.34 down(a) -> up(f(a)) 542.19/241.34 down(b) -> up(g(b)) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.34 down(f(a)) -> f_flat(down(a)) 542.19/241.34 down(f(b)) -> f_flat(down(b)) 542.19/241.34 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.34 down(f(c)) -> f_flat(down(c)) 542.19/241.34 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.34 down(g(a)) -> g_flat(down(a)) 542.19/241.34 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.34 down(g(b)) -> g_flat(down(b)) 542.19/241.34 down(g(c)) -> g_flat(down(c)) 542.19/241.34 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.34 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.34 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.34 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.34 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.34 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.34 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.34 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.34 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.34 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.34 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.34 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.34 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.34 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.34 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.34 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.34 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.34 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.34 542.19/241.34 The set Q consists of the following terms: 542.19/241.34 542.19/241.34 down(a) 542.19/241.34 down(b) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.34 down(f(a)) 542.19/241.34 down(f(b)) 542.19/241.34 down(f(g(x0))) 542.19/241.34 down(f(c)) 542.19/241.34 down(f(fresh_constant)) 542.19/241.34 down(g(a)) 542.19/241.34 down(g(f(x0))) 542.19/241.34 down(g(b)) 542.19/241.34 down(g(c)) 542.19/241.34 down(g(fresh_constant)) 542.19/241.34 down(f(f(a))) 542.19/241.34 down(f(f(b))) 542.19/241.34 down(f(f(g(x0)))) 542.19/241.34 down(f(f(c))) 542.19/241.34 down(f(f(fresh_constant))) 542.19/241.34 down(g(g(a))) 542.19/241.34 down(g(g(f(x0)))) 542.19/241.34 down(g(g(b))) 542.19/241.34 down(g(g(c))) 542.19/241.34 down(g(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) 542.19/241.34 down(f(f(f(g(x0))))) 542.19/241.34 down(f(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) 542.19/241.34 down(g(g(g(f(x0))))) 542.19/241.34 down(g(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(x0)))))) 542.19/241.34 down(f(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(x0)))))) 542.19/241.34 down(g(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(x0))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(x0))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.34 down(f(f(f(f(f(f(c))))))) 542.19/241.34 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.34 down(g(g(g(g(g(g(a))))))) 542.19/241.34 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.34 down(g(g(g(g(g(g(b))))))) 542.19/241.34 down(g(g(g(g(g(g(c))))))) 542.19/241.34 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.34 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 f_flat(up(x0)) 542.19/241.34 g_flat(up(x0)) 542.19/241.34 542.19/241.34 We have to consider all minimal (P,Q,R)-chains. 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (125) TransformationProof (EQUIVALENT) 542.19/241.34 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(down(f(f(f(g(x0))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.34 542.19/241.34 (TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))),TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0)))))))) 542.19/241.34 542.19/241.34 542.19/241.34 ---------------------------------------- 542.19/241.34 542.19/241.34 (126) 542.19/241.34 Obligation: 542.19/241.34 Q DP problem: 542.19/241.34 The TRS P consists of the following rules: 542.19/241.34 542.19/241.34 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.34 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.34 TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) 542.19/241.34 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.34 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.34 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.34 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.34 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.34 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.34 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.34 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.34 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.34 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.34 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.34 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.34 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.34 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.34 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.34 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.34 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.34 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.34 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.34 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.34 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.34 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.34 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.34 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.34 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.34 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.34 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.34 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.34 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.34 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.34 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.34 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.34 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.34 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.34 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.34 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.34 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.34 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.34 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.34 542.19/241.34 The TRS R consists of the following rules: 542.19/241.34 542.19/241.34 down(a) -> up(f(a)) 542.19/241.34 down(b) -> up(g(b)) 542.19/241.34 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.34 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.34 down(f(a)) -> f_flat(down(a)) 542.19/241.34 down(f(b)) -> f_flat(down(b)) 542.19/241.34 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.34 down(f(c)) -> f_flat(down(c)) 542.19/241.34 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.34 down(g(a)) -> g_flat(down(a)) 542.19/241.34 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.34 down(g(b)) -> g_flat(down(b)) 542.19/241.34 down(g(c)) -> g_flat(down(c)) 542.19/241.34 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.34 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.34 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.34 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.34 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.34 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.34 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.34 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.34 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.34 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.34 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.34 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.34 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.34 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.34 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.34 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.34 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.34 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.34 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.34 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.34 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.34 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.34 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.34 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.34 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.34 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.34 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.34 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.34 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.34 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.34 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.34 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.34 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.34 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.34 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.34 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.34 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.34 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.34 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.34 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.34 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.34 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.34 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.34 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.35 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.35 542.19/241.35 The set Q consists of the following terms: 542.19/241.35 542.19/241.35 down(a) 542.19/241.35 down(b) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.35 down(f(a)) 542.19/241.35 down(f(b)) 542.19/241.35 down(f(g(x0))) 542.19/241.35 down(f(c)) 542.19/241.35 down(f(fresh_constant)) 542.19/241.35 down(g(a)) 542.19/241.35 down(g(f(x0))) 542.19/241.35 down(g(b)) 542.19/241.35 down(g(c)) 542.19/241.35 down(g(fresh_constant)) 542.19/241.35 down(f(f(a))) 542.19/241.35 down(f(f(b))) 542.19/241.35 down(f(f(g(x0)))) 542.19/241.35 down(f(f(c))) 542.19/241.35 down(f(f(fresh_constant))) 542.19/241.35 down(g(g(a))) 542.19/241.35 down(g(g(f(x0)))) 542.19/241.35 down(g(g(b))) 542.19/241.35 down(g(g(c))) 542.19/241.35 down(g(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) 542.19/241.35 down(f(f(f(g(x0))))) 542.19/241.35 down(f(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) 542.19/241.35 down(g(g(g(f(x0))))) 542.19/241.35 down(g(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(x0)))))) 542.19/241.35 down(f(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(x0)))))) 542.19/241.35 down(g(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(x0))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(x0))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 f_flat(up(x0)) 542.19/241.35 g_flat(up(x0)) 542.19/241.35 542.19/241.35 We have to consider all minimal (P,Q,R)-chains. 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (127) TransformationProof (EQUIVALENT) 542.19/241.35 By rewriting [LPAR04] the rule TOP(up(g(g(g(a))))) -> TOP(g_flat(down(g(g(a))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.35 542.19/241.35 (TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))),TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a)))))) 542.19/241.35 542.19/241.35 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (128) 542.19/241.35 Obligation: 542.19/241.35 Q DP problem: 542.19/241.35 The TRS P consists of the following rules: 542.19/241.35 542.19/241.35 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.35 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.35 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) 542.19/241.35 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.35 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.35 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.35 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.35 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.35 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.35 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.35 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.35 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.35 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.35 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.35 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.35 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.35 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.35 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.35 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.35 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.35 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.35 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.35 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.35 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.35 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.35 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.35 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.35 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.35 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.35 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.35 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.35 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.35 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.35 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.35 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.35 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.35 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.35 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.35 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.35 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.35 542.19/241.35 The TRS R consists of the following rules: 542.19/241.35 542.19/241.35 down(a) -> up(f(a)) 542.19/241.35 down(b) -> up(g(b)) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.35 down(f(a)) -> f_flat(down(a)) 542.19/241.35 down(f(b)) -> f_flat(down(b)) 542.19/241.35 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.35 down(f(c)) -> f_flat(down(c)) 542.19/241.35 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.35 down(g(a)) -> g_flat(down(a)) 542.19/241.35 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.35 down(g(b)) -> g_flat(down(b)) 542.19/241.35 down(g(c)) -> g_flat(down(c)) 542.19/241.35 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.35 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.35 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.35 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.35 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.35 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.35 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.35 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.35 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.35 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.35 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.35 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.35 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.35 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.35 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.35 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.35 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.35 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.35 542.19/241.35 The set Q consists of the following terms: 542.19/241.35 542.19/241.35 down(a) 542.19/241.35 down(b) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.35 down(f(a)) 542.19/241.35 down(f(b)) 542.19/241.35 down(f(g(x0))) 542.19/241.35 down(f(c)) 542.19/241.35 down(f(fresh_constant)) 542.19/241.35 down(g(a)) 542.19/241.35 down(g(f(x0))) 542.19/241.35 down(g(b)) 542.19/241.35 down(g(c)) 542.19/241.35 down(g(fresh_constant)) 542.19/241.35 down(f(f(a))) 542.19/241.35 down(f(f(b))) 542.19/241.35 down(f(f(g(x0)))) 542.19/241.35 down(f(f(c))) 542.19/241.35 down(f(f(fresh_constant))) 542.19/241.35 down(g(g(a))) 542.19/241.35 down(g(g(f(x0)))) 542.19/241.35 down(g(g(b))) 542.19/241.35 down(g(g(c))) 542.19/241.35 down(g(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) 542.19/241.35 down(f(f(f(g(x0))))) 542.19/241.35 down(f(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) 542.19/241.35 down(g(g(g(f(x0))))) 542.19/241.35 down(g(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(x0)))))) 542.19/241.35 down(f(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(x0)))))) 542.19/241.35 down(g(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(x0))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(x0))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 f_flat(up(x0)) 542.19/241.35 g_flat(up(x0)) 542.19/241.35 542.19/241.35 We have to consider all minimal (P,Q,R)-chains. 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (129) TransformationProof (EQUIVALENT) 542.19/241.35 By rewriting [LPAR04] the rule TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(down(g(g(f(x0)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.35 542.19/241.35 (TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))),TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0))))))) 542.19/241.35 542.19/241.35 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (130) 542.19/241.35 Obligation: 542.19/241.35 Q DP problem: 542.19/241.35 The TRS P consists of the following rules: 542.19/241.35 542.19/241.35 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.35 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.35 TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) 542.19/241.35 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.35 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.35 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.35 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.35 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.35 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.35 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.35 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.35 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.35 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.35 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.35 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.35 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.35 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.35 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.35 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.35 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.35 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.35 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.35 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.35 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.35 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.35 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.35 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.35 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.35 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.35 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.35 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.35 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.35 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.35 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.35 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.35 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.35 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.35 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.35 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.35 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.35 542.19/241.35 The TRS R consists of the following rules: 542.19/241.35 542.19/241.35 down(a) -> up(f(a)) 542.19/241.35 down(b) -> up(g(b)) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.35 down(f(a)) -> f_flat(down(a)) 542.19/241.35 down(f(b)) -> f_flat(down(b)) 542.19/241.35 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.35 down(f(c)) -> f_flat(down(c)) 542.19/241.35 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.35 down(g(a)) -> g_flat(down(a)) 542.19/241.35 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.35 down(g(b)) -> g_flat(down(b)) 542.19/241.35 down(g(c)) -> g_flat(down(c)) 542.19/241.35 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.35 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.35 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.35 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.35 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.35 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.35 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.35 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.35 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.35 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.35 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.35 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.35 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.35 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.35 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.35 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.35 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.35 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.35 542.19/241.35 The set Q consists of the following terms: 542.19/241.35 542.19/241.35 down(a) 542.19/241.35 down(b) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.35 down(f(a)) 542.19/241.35 down(f(b)) 542.19/241.35 down(f(g(x0))) 542.19/241.35 down(f(c)) 542.19/241.35 down(f(fresh_constant)) 542.19/241.35 down(g(a)) 542.19/241.35 down(g(f(x0))) 542.19/241.35 down(g(b)) 542.19/241.35 down(g(c)) 542.19/241.35 down(g(fresh_constant)) 542.19/241.35 down(f(f(a))) 542.19/241.35 down(f(f(b))) 542.19/241.35 down(f(f(g(x0)))) 542.19/241.35 down(f(f(c))) 542.19/241.35 down(f(f(fresh_constant))) 542.19/241.35 down(g(g(a))) 542.19/241.35 down(g(g(f(x0)))) 542.19/241.35 down(g(g(b))) 542.19/241.35 down(g(g(c))) 542.19/241.35 down(g(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) 542.19/241.35 down(f(f(f(g(x0))))) 542.19/241.35 down(f(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) 542.19/241.35 down(g(g(g(f(x0))))) 542.19/241.35 down(g(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(x0)))))) 542.19/241.35 down(f(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(x0)))))) 542.19/241.35 down(g(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(x0))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(x0))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 f_flat(up(x0)) 542.19/241.35 g_flat(up(x0)) 542.19/241.35 542.19/241.35 We have to consider all minimal (P,Q,R)-chains. 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (131) TransformationProof (EQUIVALENT) 542.19/241.35 By rewriting [LPAR04] the rule TOP(up(g(g(g(b))))) -> TOP(g_flat(down(g(g(b))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.35 542.19/241.35 (TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))),TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b)))))) 542.19/241.35 542.19/241.35 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (132) 542.19/241.35 Obligation: 542.19/241.35 Q DP problem: 542.19/241.35 The TRS P consists of the following rules: 542.19/241.35 542.19/241.35 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.35 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.35 TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) 542.19/241.35 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.35 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.35 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.35 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.35 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.35 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.35 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.35 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.35 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.35 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.35 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.35 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.35 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.35 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.35 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.35 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.35 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.35 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.35 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.35 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.35 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.35 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.35 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.35 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.35 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.35 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.35 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.35 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.35 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.35 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.35 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.35 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.35 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.35 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.35 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.35 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.35 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.35 542.19/241.35 The TRS R consists of the following rules: 542.19/241.35 542.19/241.35 down(a) -> up(f(a)) 542.19/241.35 down(b) -> up(g(b)) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.35 down(f(a)) -> f_flat(down(a)) 542.19/241.35 down(f(b)) -> f_flat(down(b)) 542.19/241.35 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.35 down(f(c)) -> f_flat(down(c)) 542.19/241.35 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.35 down(g(a)) -> g_flat(down(a)) 542.19/241.35 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.35 down(g(b)) -> g_flat(down(b)) 542.19/241.35 down(g(c)) -> g_flat(down(c)) 542.19/241.35 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.35 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.35 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.35 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.35 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.35 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.35 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.35 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.35 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.35 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.35 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.35 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.35 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.35 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.35 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.35 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.35 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.35 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.35 542.19/241.35 The set Q consists of the following terms: 542.19/241.35 542.19/241.35 down(a) 542.19/241.35 down(b) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.35 down(f(a)) 542.19/241.35 down(f(b)) 542.19/241.35 down(f(g(x0))) 542.19/241.35 down(f(c)) 542.19/241.35 down(f(fresh_constant)) 542.19/241.35 down(g(a)) 542.19/241.35 down(g(f(x0))) 542.19/241.35 down(g(b)) 542.19/241.35 down(g(c)) 542.19/241.35 down(g(fresh_constant)) 542.19/241.35 down(f(f(a))) 542.19/241.35 down(f(f(b))) 542.19/241.35 down(f(f(g(x0)))) 542.19/241.35 down(f(f(c))) 542.19/241.35 down(f(f(fresh_constant))) 542.19/241.35 down(g(g(a))) 542.19/241.35 down(g(g(f(x0)))) 542.19/241.35 down(g(g(b))) 542.19/241.35 down(g(g(c))) 542.19/241.35 down(g(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) 542.19/241.35 down(f(f(f(g(x0))))) 542.19/241.35 down(f(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) 542.19/241.35 down(g(g(g(f(x0))))) 542.19/241.35 down(g(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(x0)))))) 542.19/241.35 down(f(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(x0)))))) 542.19/241.35 down(g(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(x0))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(x0))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 f_flat(up(x0)) 542.19/241.35 g_flat(up(x0)) 542.19/241.35 542.19/241.35 We have to consider all minimal (P,Q,R)-chains. 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (133) TransformationProof (EQUIVALENT) 542.19/241.35 By rewriting [LPAR04] the rule TOP(up(g(g(g(c))))) -> TOP(g_flat(down(g(g(c))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.35 542.19/241.35 (TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))),TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c)))))) 542.19/241.35 542.19/241.35 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (134) 542.19/241.35 Obligation: 542.19/241.35 Q DP problem: 542.19/241.35 The TRS P consists of the following rules: 542.19/241.35 542.19/241.35 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.35 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.35 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) 542.19/241.35 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.35 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.35 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.35 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.35 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.35 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.35 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.35 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.35 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.35 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.35 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.35 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.35 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.35 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.35 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.35 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.35 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.35 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.35 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.35 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.35 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.35 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.35 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.35 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.35 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.35 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.35 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.35 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.35 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.35 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.35 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.35 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.35 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.35 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.35 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.35 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.35 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.35 542.19/241.35 The TRS R consists of the following rules: 542.19/241.35 542.19/241.35 down(a) -> up(f(a)) 542.19/241.35 down(b) -> up(g(b)) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.35 down(f(a)) -> f_flat(down(a)) 542.19/241.35 down(f(b)) -> f_flat(down(b)) 542.19/241.35 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.35 down(f(c)) -> f_flat(down(c)) 542.19/241.35 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.35 down(g(a)) -> g_flat(down(a)) 542.19/241.35 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.35 down(g(b)) -> g_flat(down(b)) 542.19/241.35 down(g(c)) -> g_flat(down(c)) 542.19/241.35 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.35 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.35 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.35 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.35 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.35 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.35 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.35 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.35 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.35 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.35 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.35 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.35 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.35 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.35 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.35 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.35 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.35 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.35 542.19/241.35 The set Q consists of the following terms: 542.19/241.35 542.19/241.35 down(a) 542.19/241.35 down(b) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.35 down(f(a)) 542.19/241.35 down(f(b)) 542.19/241.35 down(f(g(x0))) 542.19/241.35 down(f(c)) 542.19/241.35 down(f(fresh_constant)) 542.19/241.35 down(g(a)) 542.19/241.35 down(g(f(x0))) 542.19/241.35 down(g(b)) 542.19/241.35 down(g(c)) 542.19/241.35 down(g(fresh_constant)) 542.19/241.35 down(f(f(a))) 542.19/241.35 down(f(f(b))) 542.19/241.35 down(f(f(g(x0)))) 542.19/241.35 down(f(f(c))) 542.19/241.35 down(f(f(fresh_constant))) 542.19/241.35 down(g(g(a))) 542.19/241.35 down(g(g(f(x0)))) 542.19/241.35 down(g(g(b))) 542.19/241.35 down(g(g(c))) 542.19/241.35 down(g(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) 542.19/241.35 down(f(f(f(g(x0))))) 542.19/241.35 down(f(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) 542.19/241.35 down(g(g(g(f(x0))))) 542.19/241.35 down(g(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(x0)))))) 542.19/241.35 down(f(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(x0)))))) 542.19/241.35 down(g(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(x0))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(x0))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 f_flat(up(x0)) 542.19/241.35 g_flat(up(x0)) 542.19/241.35 542.19/241.35 We have to consider all minimal (P,Q,R)-chains. 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (135) TransformationProof (EQUIVALENT) 542.19/241.35 By rewriting [LPAR04] the rule TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(down(g(g(fresh_constant))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.35 542.19/241.35 (TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))),TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant)))))) 542.19/241.35 542.19/241.35 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (136) 542.19/241.35 Obligation: 542.19/241.35 Q DP problem: 542.19/241.35 The TRS P consists of the following rules: 542.19/241.35 542.19/241.35 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.35 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.35 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) 542.19/241.35 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.35 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.35 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.35 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.35 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.35 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.35 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.35 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.35 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.35 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.35 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.35 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.35 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.35 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.35 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.35 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.35 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.35 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.35 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.35 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.35 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.35 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.35 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.35 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.35 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.35 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.35 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.35 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.35 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.35 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.35 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.35 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.35 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.35 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.35 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.35 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.35 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.35 542.19/241.35 The TRS R consists of the following rules: 542.19/241.35 542.19/241.35 down(a) -> up(f(a)) 542.19/241.35 down(b) -> up(g(b)) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.35 down(f(a)) -> f_flat(down(a)) 542.19/241.35 down(f(b)) -> f_flat(down(b)) 542.19/241.35 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.35 down(f(c)) -> f_flat(down(c)) 542.19/241.35 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.35 down(g(a)) -> g_flat(down(a)) 542.19/241.35 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.35 down(g(b)) -> g_flat(down(b)) 542.19/241.35 down(g(c)) -> g_flat(down(c)) 542.19/241.35 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.35 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.35 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.35 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.35 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.35 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.35 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.35 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.35 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.35 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.35 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.35 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.35 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.35 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.35 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.35 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.35 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.35 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.35 542.19/241.35 The set Q consists of the following terms: 542.19/241.35 542.19/241.35 down(a) 542.19/241.35 down(b) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.35 down(f(a)) 542.19/241.35 down(f(b)) 542.19/241.35 down(f(g(x0))) 542.19/241.35 down(f(c)) 542.19/241.35 down(f(fresh_constant)) 542.19/241.35 down(g(a)) 542.19/241.35 down(g(f(x0))) 542.19/241.35 down(g(b)) 542.19/241.35 down(g(c)) 542.19/241.35 down(g(fresh_constant)) 542.19/241.35 down(f(f(a))) 542.19/241.35 down(f(f(b))) 542.19/241.35 down(f(f(g(x0)))) 542.19/241.35 down(f(f(c))) 542.19/241.35 down(f(f(fresh_constant))) 542.19/241.35 down(g(g(a))) 542.19/241.35 down(g(g(f(x0)))) 542.19/241.35 down(g(g(b))) 542.19/241.35 down(g(g(c))) 542.19/241.35 down(g(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) 542.19/241.35 down(f(f(f(g(x0))))) 542.19/241.35 down(f(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) 542.19/241.35 down(g(g(g(f(x0))))) 542.19/241.35 down(g(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(x0)))))) 542.19/241.35 down(f(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(x0)))))) 542.19/241.35 down(g(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(x0))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(x0))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 f_flat(up(x0)) 542.19/241.35 g_flat(up(x0)) 542.19/241.35 542.19/241.35 We have to consider all minimal (P,Q,R)-chains. 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (137) TransformationProof (EQUIVALENT) 542.19/241.35 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(down(g(g(g(a)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.35 542.19/241.35 (TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))),TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a))))))) 542.19/241.35 542.19/241.35 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (138) 542.19/241.35 Obligation: 542.19/241.35 Q DP problem: 542.19/241.35 The TRS P consists of the following rules: 542.19/241.35 542.19/241.35 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.35 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.35 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) 542.19/241.35 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.35 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.35 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.35 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.35 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.35 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.35 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.35 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.35 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.35 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.35 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.35 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.35 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.35 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.35 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.35 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.35 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.35 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.35 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.35 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.35 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.35 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.35 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.35 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.35 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.35 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.35 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.35 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.35 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.35 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.35 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.35 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.35 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.35 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.35 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.35 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.35 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.19/241.35 542.19/241.35 The TRS R consists of the following rules: 542.19/241.35 542.19/241.35 down(a) -> up(f(a)) 542.19/241.35 down(b) -> up(g(b)) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.35 down(f(a)) -> f_flat(down(a)) 542.19/241.35 down(f(b)) -> f_flat(down(b)) 542.19/241.35 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.35 down(f(c)) -> f_flat(down(c)) 542.19/241.35 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.35 down(g(a)) -> g_flat(down(a)) 542.19/241.35 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.35 down(g(b)) -> g_flat(down(b)) 542.19/241.35 down(g(c)) -> g_flat(down(c)) 542.19/241.35 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.35 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.35 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.35 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.35 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.35 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.35 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.35 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.35 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.35 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.35 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.35 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.35 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.35 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.35 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.35 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.35 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.35 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.35 542.19/241.35 The set Q consists of the following terms: 542.19/241.35 542.19/241.35 down(a) 542.19/241.35 down(b) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.35 down(f(a)) 542.19/241.35 down(f(b)) 542.19/241.35 down(f(g(x0))) 542.19/241.35 down(f(c)) 542.19/241.35 down(f(fresh_constant)) 542.19/241.35 down(g(a)) 542.19/241.35 down(g(f(x0))) 542.19/241.35 down(g(b)) 542.19/241.35 down(g(c)) 542.19/241.35 down(g(fresh_constant)) 542.19/241.35 down(f(f(a))) 542.19/241.35 down(f(f(b))) 542.19/241.35 down(f(f(g(x0)))) 542.19/241.35 down(f(f(c))) 542.19/241.35 down(f(f(fresh_constant))) 542.19/241.35 down(g(g(a))) 542.19/241.35 down(g(g(f(x0)))) 542.19/241.35 down(g(g(b))) 542.19/241.35 down(g(g(c))) 542.19/241.35 down(g(g(fresh_constant))) 542.19/241.35 down(f(f(f(a)))) 542.19/241.35 down(f(f(f(b)))) 542.19/241.35 down(f(f(f(g(x0))))) 542.19/241.35 down(f(f(f(c)))) 542.19/241.35 down(f(f(f(fresh_constant)))) 542.19/241.35 down(g(g(g(a)))) 542.19/241.35 down(g(g(g(f(x0))))) 542.19/241.35 down(g(g(g(b)))) 542.19/241.35 down(g(g(g(c)))) 542.19/241.35 down(g(g(g(fresh_constant)))) 542.19/241.35 down(f(f(f(f(a))))) 542.19/241.35 down(f(f(f(f(b))))) 542.19/241.35 down(f(f(f(f(g(x0)))))) 542.19/241.35 down(f(f(f(f(c))))) 542.19/241.35 down(f(f(f(f(fresh_constant))))) 542.19/241.35 down(g(g(g(g(a))))) 542.19/241.35 down(g(g(g(g(f(x0)))))) 542.19/241.35 down(g(g(g(g(b))))) 542.19/241.35 down(g(g(g(g(c))))) 542.19/241.35 down(g(g(g(g(fresh_constant))))) 542.19/241.35 down(f(f(f(f(f(a)))))) 542.19/241.35 down(f(f(f(f(f(b)))))) 542.19/241.35 down(f(f(f(f(f(g(x0))))))) 542.19/241.35 down(f(f(f(f(f(c)))))) 542.19/241.35 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.35 down(g(g(g(g(g(a)))))) 542.19/241.35 down(g(g(g(g(g(f(x0))))))) 542.19/241.35 down(g(g(g(g(g(b)))))) 542.19/241.35 down(g(g(g(g(g(c)))))) 542.19/241.35 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.35 down(f(f(f(f(f(f(a))))))) 542.19/241.35 down(f(f(f(f(f(f(b))))))) 542.19/241.35 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.35 down(f(f(f(f(f(f(c))))))) 542.19/241.35 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.35 down(g(g(g(g(g(g(a))))))) 542.19/241.35 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.35 down(g(g(g(g(g(g(b))))))) 542.19/241.35 down(g(g(g(g(g(g(c))))))) 542.19/241.35 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.35 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.35 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 f_flat(up(x0)) 542.19/241.35 g_flat(up(x0)) 542.19/241.35 542.19/241.35 We have to consider all minimal (P,Q,R)-chains. 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (139) TransformationProof (EQUIVALENT) 542.19/241.35 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(down(g(g(g(f(x0))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.35 542.19/241.35 (TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))),TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0)))))))) 542.19/241.35 542.19/241.35 542.19/241.35 ---------------------------------------- 542.19/241.35 542.19/241.35 (140) 542.19/241.35 Obligation: 542.19/241.35 Q DP problem: 542.19/241.35 The TRS P consists of the following rules: 542.19/241.35 542.19/241.35 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.35 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.35 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) 542.19/241.35 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.35 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.35 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.35 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.35 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.35 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.35 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.35 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.35 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.35 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.35 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.35 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.35 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.35 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.35 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.35 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.35 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.35 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.35 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.35 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.35 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.35 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.35 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.35 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.35 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.35 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.35 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.35 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.35 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.35 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.35 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.35 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.35 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.35 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.35 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.35 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.35 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.35 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.19/241.36 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.19/241.36 542.19/241.36 The TRS R consists of the following rules: 542.19/241.36 542.19/241.36 down(a) -> up(f(a)) 542.19/241.36 down(b) -> up(g(b)) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.36 down(f(a)) -> f_flat(down(a)) 542.19/241.36 down(f(b)) -> f_flat(down(b)) 542.19/241.36 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.36 down(f(c)) -> f_flat(down(c)) 542.19/241.36 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.36 down(g(a)) -> g_flat(down(a)) 542.19/241.36 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.36 down(g(b)) -> g_flat(down(b)) 542.19/241.36 down(g(c)) -> g_flat(down(c)) 542.19/241.36 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.36 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.36 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.36 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.36 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.36 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.36 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.36 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.36 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.36 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.36 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.36 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.36 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.36 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.36 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.36 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.36 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.36 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.36 542.19/241.36 The set Q consists of the following terms: 542.19/241.36 542.19/241.36 down(a) 542.19/241.36 down(b) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.36 down(f(a)) 542.19/241.36 down(f(b)) 542.19/241.36 down(f(g(x0))) 542.19/241.36 down(f(c)) 542.19/241.36 down(f(fresh_constant)) 542.19/241.36 down(g(a)) 542.19/241.36 down(g(f(x0))) 542.19/241.36 down(g(b)) 542.19/241.36 down(g(c)) 542.19/241.36 down(g(fresh_constant)) 542.19/241.36 down(f(f(a))) 542.19/241.36 down(f(f(b))) 542.19/241.36 down(f(f(g(x0)))) 542.19/241.36 down(f(f(c))) 542.19/241.36 down(f(f(fresh_constant))) 542.19/241.36 down(g(g(a))) 542.19/241.36 down(g(g(f(x0)))) 542.19/241.36 down(g(g(b))) 542.19/241.36 down(g(g(c))) 542.19/241.36 down(g(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) 542.19/241.36 down(f(f(f(g(x0))))) 542.19/241.36 down(f(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) 542.19/241.36 down(g(g(g(f(x0))))) 542.19/241.36 down(g(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(x0)))))) 542.19/241.36 down(f(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(x0)))))) 542.19/241.36 down(g(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(x0))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(x0))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 f_flat(up(x0)) 542.19/241.36 g_flat(up(x0)) 542.19/241.36 542.19/241.36 We have to consider all minimal (P,Q,R)-chains. 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (141) TransformationProof (EQUIVALENT) 542.19/241.36 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(down(f(f(f(c)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.36 542.19/241.36 (TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))),TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c))))))) 542.19/241.36 542.19/241.36 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (142) 542.19/241.36 Obligation: 542.19/241.36 Q DP problem: 542.19/241.36 The TRS P consists of the following rules: 542.19/241.36 542.19/241.36 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.36 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.36 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) 542.19/241.36 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.36 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.36 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.36 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.36 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.36 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.36 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.36 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.36 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.36 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.36 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.36 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.36 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.36 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.36 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.36 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.36 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.36 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.36 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.36 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.36 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.36 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.36 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.36 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.36 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.36 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.36 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.36 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.36 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.36 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.36 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.36 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.36 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.36 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.36 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.19/241.36 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.19/241.36 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.19/241.36 542.19/241.36 The TRS R consists of the following rules: 542.19/241.36 542.19/241.36 down(a) -> up(f(a)) 542.19/241.36 down(b) -> up(g(b)) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.36 down(f(a)) -> f_flat(down(a)) 542.19/241.36 down(f(b)) -> f_flat(down(b)) 542.19/241.36 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.36 down(f(c)) -> f_flat(down(c)) 542.19/241.36 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.36 down(g(a)) -> g_flat(down(a)) 542.19/241.36 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.36 down(g(b)) -> g_flat(down(b)) 542.19/241.36 down(g(c)) -> g_flat(down(c)) 542.19/241.36 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.36 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.36 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.36 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.36 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.36 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.36 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.36 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.36 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.36 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.36 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.36 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.36 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.36 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.36 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.36 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.36 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.36 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.36 542.19/241.36 The set Q consists of the following terms: 542.19/241.36 542.19/241.36 down(a) 542.19/241.36 down(b) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.36 down(f(a)) 542.19/241.36 down(f(b)) 542.19/241.36 down(f(g(x0))) 542.19/241.36 down(f(c)) 542.19/241.36 down(f(fresh_constant)) 542.19/241.36 down(g(a)) 542.19/241.36 down(g(f(x0))) 542.19/241.36 down(g(b)) 542.19/241.36 down(g(c)) 542.19/241.36 down(g(fresh_constant)) 542.19/241.36 down(f(f(a))) 542.19/241.36 down(f(f(b))) 542.19/241.36 down(f(f(g(x0)))) 542.19/241.36 down(f(f(c))) 542.19/241.36 down(f(f(fresh_constant))) 542.19/241.36 down(g(g(a))) 542.19/241.36 down(g(g(f(x0)))) 542.19/241.36 down(g(g(b))) 542.19/241.36 down(g(g(c))) 542.19/241.36 down(g(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) 542.19/241.36 down(f(f(f(g(x0))))) 542.19/241.36 down(f(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) 542.19/241.36 down(g(g(g(f(x0))))) 542.19/241.36 down(g(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(x0)))))) 542.19/241.36 down(f(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(x0)))))) 542.19/241.36 down(g(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(x0))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(x0))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 f_flat(up(x0)) 542.19/241.36 g_flat(up(x0)) 542.19/241.36 542.19/241.36 We have to consider all minimal (P,Q,R)-chains. 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (143) TransformationProof (EQUIVALENT) 542.19/241.36 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(down(f(f(f(fresh_constant)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.36 542.19/241.36 (TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))),TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.19/241.36 542.19/241.36 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (144) 542.19/241.36 Obligation: 542.19/241.36 Q DP problem: 542.19/241.36 The TRS P consists of the following rules: 542.19/241.36 542.19/241.36 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.36 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.36 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) 542.19/241.36 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.36 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.36 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.36 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.36 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.36 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.36 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.36 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.36 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.36 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.36 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.36 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.36 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.36 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.36 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.36 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.36 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.36 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.36 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.36 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.36 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.36 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.36 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.36 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.36 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.36 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.36 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.36 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.36 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.36 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.36 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.36 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.36 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.36 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.19/241.36 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.19/241.36 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.19/241.36 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.19/241.36 542.19/241.36 The TRS R consists of the following rules: 542.19/241.36 542.19/241.36 down(a) -> up(f(a)) 542.19/241.36 down(b) -> up(g(b)) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.36 down(f(a)) -> f_flat(down(a)) 542.19/241.36 down(f(b)) -> f_flat(down(b)) 542.19/241.36 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.36 down(f(c)) -> f_flat(down(c)) 542.19/241.36 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.36 down(g(a)) -> g_flat(down(a)) 542.19/241.36 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.36 down(g(b)) -> g_flat(down(b)) 542.19/241.36 down(g(c)) -> g_flat(down(c)) 542.19/241.36 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.36 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.36 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.36 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.36 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.36 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.36 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.36 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.36 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.36 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.36 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.36 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.36 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.36 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.36 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.36 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.36 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.36 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.36 542.19/241.36 The set Q consists of the following terms: 542.19/241.36 542.19/241.36 down(a) 542.19/241.36 down(b) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.36 down(f(a)) 542.19/241.36 down(f(b)) 542.19/241.36 down(f(g(x0))) 542.19/241.36 down(f(c)) 542.19/241.36 down(f(fresh_constant)) 542.19/241.36 down(g(a)) 542.19/241.36 down(g(f(x0))) 542.19/241.36 down(g(b)) 542.19/241.36 down(g(c)) 542.19/241.36 down(g(fresh_constant)) 542.19/241.36 down(f(f(a))) 542.19/241.36 down(f(f(b))) 542.19/241.36 down(f(f(g(x0)))) 542.19/241.36 down(f(f(c))) 542.19/241.36 down(f(f(fresh_constant))) 542.19/241.36 down(g(g(a))) 542.19/241.36 down(g(g(f(x0)))) 542.19/241.36 down(g(g(b))) 542.19/241.36 down(g(g(c))) 542.19/241.36 down(g(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) 542.19/241.36 down(f(f(f(g(x0))))) 542.19/241.36 down(f(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) 542.19/241.36 down(g(g(g(f(x0))))) 542.19/241.36 down(g(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(x0)))))) 542.19/241.36 down(f(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(x0)))))) 542.19/241.36 down(g(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(x0))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(x0))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 f_flat(up(x0)) 542.19/241.36 g_flat(up(x0)) 542.19/241.36 542.19/241.36 We have to consider all minimal (P,Q,R)-chains. 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (145) TransformationProof (EQUIVALENT) 542.19/241.36 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(down(f(f(f(f(a))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.36 542.19/241.36 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a)))))))) 542.19/241.36 542.19/241.36 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (146) 542.19/241.36 Obligation: 542.19/241.36 Q DP problem: 542.19/241.36 The TRS P consists of the following rules: 542.19/241.36 542.19/241.36 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.36 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.36 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) 542.19/241.36 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.36 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.36 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.36 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.36 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.36 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.36 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.36 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.36 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.36 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.36 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.36 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.36 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.36 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.36 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.36 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.36 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.36 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.36 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.36 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.36 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.36 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.36 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.36 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.36 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.36 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.36 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.36 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.36 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.36 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.36 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.36 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.36 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.19/241.36 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.19/241.36 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.19/241.36 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.19/241.36 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.19/241.36 542.19/241.36 The TRS R consists of the following rules: 542.19/241.36 542.19/241.36 down(a) -> up(f(a)) 542.19/241.36 down(b) -> up(g(b)) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.36 down(f(a)) -> f_flat(down(a)) 542.19/241.36 down(f(b)) -> f_flat(down(b)) 542.19/241.36 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.36 down(f(c)) -> f_flat(down(c)) 542.19/241.36 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.36 down(g(a)) -> g_flat(down(a)) 542.19/241.36 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.36 down(g(b)) -> g_flat(down(b)) 542.19/241.36 down(g(c)) -> g_flat(down(c)) 542.19/241.36 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.36 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.36 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.36 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.36 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.36 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.36 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.36 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.36 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.36 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.36 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.36 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.36 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.36 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.36 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.36 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.36 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.36 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.36 542.19/241.36 The set Q consists of the following terms: 542.19/241.36 542.19/241.36 down(a) 542.19/241.36 down(b) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.36 down(f(a)) 542.19/241.36 down(f(b)) 542.19/241.36 down(f(g(x0))) 542.19/241.36 down(f(c)) 542.19/241.36 down(f(fresh_constant)) 542.19/241.36 down(g(a)) 542.19/241.36 down(g(f(x0))) 542.19/241.36 down(g(b)) 542.19/241.36 down(g(c)) 542.19/241.36 down(g(fresh_constant)) 542.19/241.36 down(f(f(a))) 542.19/241.36 down(f(f(b))) 542.19/241.36 down(f(f(g(x0)))) 542.19/241.36 down(f(f(c))) 542.19/241.36 down(f(f(fresh_constant))) 542.19/241.36 down(g(g(a))) 542.19/241.36 down(g(g(f(x0)))) 542.19/241.36 down(g(g(b))) 542.19/241.36 down(g(g(c))) 542.19/241.36 down(g(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) 542.19/241.36 down(f(f(f(g(x0))))) 542.19/241.36 down(f(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) 542.19/241.36 down(g(g(g(f(x0))))) 542.19/241.36 down(g(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(x0)))))) 542.19/241.36 down(f(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(x0)))))) 542.19/241.36 down(g(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(x0))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(x0))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 f_flat(up(x0)) 542.19/241.36 g_flat(up(x0)) 542.19/241.36 542.19/241.36 We have to consider all minimal (P,Q,R)-chains. 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (147) TransformationProof (EQUIVALENT) 542.19/241.36 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(down(f(f(f(f(b))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.36 542.19/241.36 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b)))))))) 542.19/241.36 542.19/241.36 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (148) 542.19/241.36 Obligation: 542.19/241.36 Q DP problem: 542.19/241.36 The TRS P consists of the following rules: 542.19/241.36 542.19/241.36 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.36 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.36 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) 542.19/241.36 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.36 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.36 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.36 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.36 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.36 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.36 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.36 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.36 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.36 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.36 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.36 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.36 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.36 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.36 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.36 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.36 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.36 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.36 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.36 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.36 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.36 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.36 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.36 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.36 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.36 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.36 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.36 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.36 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.36 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.36 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.36 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.19/241.36 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.19/241.36 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.19/241.36 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.19/241.36 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.19/241.36 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.19/241.36 542.19/241.36 The TRS R consists of the following rules: 542.19/241.36 542.19/241.36 down(a) -> up(f(a)) 542.19/241.36 down(b) -> up(g(b)) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.36 down(f(a)) -> f_flat(down(a)) 542.19/241.36 down(f(b)) -> f_flat(down(b)) 542.19/241.36 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.36 down(f(c)) -> f_flat(down(c)) 542.19/241.36 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.36 down(g(a)) -> g_flat(down(a)) 542.19/241.36 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.36 down(g(b)) -> g_flat(down(b)) 542.19/241.36 down(g(c)) -> g_flat(down(c)) 542.19/241.36 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.36 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.36 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.36 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.36 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.36 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.36 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.36 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.36 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.36 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.36 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.36 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.36 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.36 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.36 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.36 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.36 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.36 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.36 542.19/241.36 The set Q consists of the following terms: 542.19/241.36 542.19/241.36 down(a) 542.19/241.36 down(b) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.36 down(f(a)) 542.19/241.36 down(f(b)) 542.19/241.36 down(f(g(x0))) 542.19/241.36 down(f(c)) 542.19/241.36 down(f(fresh_constant)) 542.19/241.36 down(g(a)) 542.19/241.36 down(g(f(x0))) 542.19/241.36 down(g(b)) 542.19/241.36 down(g(c)) 542.19/241.36 down(g(fresh_constant)) 542.19/241.36 down(f(f(a))) 542.19/241.36 down(f(f(b))) 542.19/241.36 down(f(f(g(x0)))) 542.19/241.36 down(f(f(c))) 542.19/241.36 down(f(f(fresh_constant))) 542.19/241.36 down(g(g(a))) 542.19/241.36 down(g(g(f(x0)))) 542.19/241.36 down(g(g(b))) 542.19/241.36 down(g(g(c))) 542.19/241.36 down(g(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) 542.19/241.36 down(f(f(f(g(x0))))) 542.19/241.36 down(f(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) 542.19/241.36 down(g(g(g(f(x0))))) 542.19/241.36 down(g(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(x0)))))) 542.19/241.36 down(f(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(x0)))))) 542.19/241.36 down(g(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(x0))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(x0))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 f_flat(up(x0)) 542.19/241.36 g_flat(up(x0)) 542.19/241.36 542.19/241.36 We have to consider all minimal (P,Q,R)-chains. 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (149) TransformationProof (EQUIVALENT) 542.19/241.36 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(down(f(f(f(f(g(x0)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.36 542.19/241.36 (TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))),TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.19/241.36 542.19/241.36 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (150) 542.19/241.36 Obligation: 542.19/241.36 Q DP problem: 542.19/241.36 The TRS P consists of the following rules: 542.19/241.36 542.19/241.36 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.36 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.36 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) 542.19/241.36 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.36 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.36 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.36 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.36 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.36 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.36 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.36 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.36 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.36 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.36 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.36 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.36 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.36 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.36 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.36 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.36 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.36 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.36 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.36 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.36 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.36 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.36 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.36 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.36 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.36 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.36 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.36 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.36 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.36 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.36 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.19/241.36 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.19/241.36 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.19/241.36 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.19/241.36 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.19/241.36 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.19/241.36 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.19/241.36 542.19/241.36 The TRS R consists of the following rules: 542.19/241.36 542.19/241.36 down(a) -> up(f(a)) 542.19/241.36 down(b) -> up(g(b)) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.36 down(f(a)) -> f_flat(down(a)) 542.19/241.36 down(f(b)) -> f_flat(down(b)) 542.19/241.36 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.36 down(f(c)) -> f_flat(down(c)) 542.19/241.36 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.36 down(g(a)) -> g_flat(down(a)) 542.19/241.36 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.36 down(g(b)) -> g_flat(down(b)) 542.19/241.36 down(g(c)) -> g_flat(down(c)) 542.19/241.36 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.36 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.36 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.36 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.36 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.36 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.36 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.36 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.36 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.36 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.36 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.36 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.36 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.36 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.36 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.36 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.36 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.36 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.36 542.19/241.36 The set Q consists of the following terms: 542.19/241.36 542.19/241.36 down(a) 542.19/241.36 down(b) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.36 down(f(a)) 542.19/241.36 down(f(b)) 542.19/241.36 down(f(g(x0))) 542.19/241.36 down(f(c)) 542.19/241.36 down(f(fresh_constant)) 542.19/241.36 down(g(a)) 542.19/241.36 down(g(f(x0))) 542.19/241.36 down(g(b)) 542.19/241.36 down(g(c)) 542.19/241.36 down(g(fresh_constant)) 542.19/241.36 down(f(f(a))) 542.19/241.36 down(f(f(b))) 542.19/241.36 down(f(f(g(x0)))) 542.19/241.36 down(f(f(c))) 542.19/241.36 down(f(f(fresh_constant))) 542.19/241.36 down(g(g(a))) 542.19/241.36 down(g(g(f(x0)))) 542.19/241.36 down(g(g(b))) 542.19/241.36 down(g(g(c))) 542.19/241.36 down(g(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) 542.19/241.36 down(f(f(f(g(x0))))) 542.19/241.36 down(f(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) 542.19/241.36 down(g(g(g(f(x0))))) 542.19/241.36 down(g(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(x0)))))) 542.19/241.36 down(f(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(x0)))))) 542.19/241.36 down(g(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(x0))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(x0))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 f_flat(up(x0)) 542.19/241.36 g_flat(up(x0)) 542.19/241.36 542.19/241.36 We have to consider all minimal (P,Q,R)-chains. 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (151) TransformationProof (EQUIVALENT) 542.19/241.36 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(down(g(g(g(b)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.36 542.19/241.36 (TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))),TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b))))))) 542.19/241.36 542.19/241.36 542.19/241.36 ---------------------------------------- 542.19/241.36 542.19/241.36 (152) 542.19/241.36 Obligation: 542.19/241.36 Q DP problem: 542.19/241.36 The TRS P consists of the following rules: 542.19/241.36 542.19/241.36 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.36 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.36 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) 542.19/241.36 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.36 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.36 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.36 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.36 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.36 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.36 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.36 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.36 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.36 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.36 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.36 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.36 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.36 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.36 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.36 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.36 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.36 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.36 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.36 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.36 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.36 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.36 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.36 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.36 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.36 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.36 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.36 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.36 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.36 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.36 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.36 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.19/241.36 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.19/241.36 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.19/241.36 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.19/241.36 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.19/241.36 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.19/241.36 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.19/241.36 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.19/241.36 542.19/241.36 The TRS R consists of the following rules: 542.19/241.36 542.19/241.36 down(a) -> up(f(a)) 542.19/241.36 down(b) -> up(g(b)) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.36 down(f(a)) -> f_flat(down(a)) 542.19/241.36 down(f(b)) -> f_flat(down(b)) 542.19/241.36 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.36 down(f(c)) -> f_flat(down(c)) 542.19/241.36 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.36 down(g(a)) -> g_flat(down(a)) 542.19/241.36 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.36 down(g(b)) -> g_flat(down(b)) 542.19/241.36 down(g(c)) -> g_flat(down(c)) 542.19/241.36 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.36 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.36 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.36 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.36 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.36 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.36 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.36 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.36 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.36 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.36 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.36 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.36 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.36 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.36 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.36 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.36 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.36 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.36 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.36 542.19/241.36 The set Q consists of the following terms: 542.19/241.36 542.19/241.36 down(a) 542.19/241.36 down(b) 542.19/241.36 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.36 down(f(a)) 542.19/241.36 down(f(b)) 542.19/241.36 down(f(g(x0))) 542.19/241.36 down(f(c)) 542.19/241.36 down(f(fresh_constant)) 542.19/241.36 down(g(a)) 542.19/241.36 down(g(f(x0))) 542.19/241.36 down(g(b)) 542.19/241.36 down(g(c)) 542.19/241.36 down(g(fresh_constant)) 542.19/241.36 down(f(f(a))) 542.19/241.36 down(f(f(b))) 542.19/241.36 down(f(f(g(x0)))) 542.19/241.36 down(f(f(c))) 542.19/241.36 down(f(f(fresh_constant))) 542.19/241.36 down(g(g(a))) 542.19/241.36 down(g(g(f(x0)))) 542.19/241.36 down(g(g(b))) 542.19/241.36 down(g(g(c))) 542.19/241.36 down(g(g(fresh_constant))) 542.19/241.36 down(f(f(f(a)))) 542.19/241.36 down(f(f(f(b)))) 542.19/241.36 down(f(f(f(g(x0))))) 542.19/241.36 down(f(f(f(c)))) 542.19/241.36 down(f(f(f(fresh_constant)))) 542.19/241.36 down(g(g(g(a)))) 542.19/241.36 down(g(g(g(f(x0))))) 542.19/241.36 down(g(g(g(b)))) 542.19/241.36 down(g(g(g(c)))) 542.19/241.36 down(g(g(g(fresh_constant)))) 542.19/241.36 down(f(f(f(f(a))))) 542.19/241.36 down(f(f(f(f(b))))) 542.19/241.36 down(f(f(f(f(g(x0)))))) 542.19/241.36 down(f(f(f(f(c))))) 542.19/241.36 down(f(f(f(f(fresh_constant))))) 542.19/241.36 down(g(g(g(g(a))))) 542.19/241.36 down(g(g(g(g(f(x0)))))) 542.19/241.36 down(g(g(g(g(b))))) 542.19/241.36 down(g(g(g(g(c))))) 542.19/241.36 down(g(g(g(g(fresh_constant))))) 542.19/241.36 down(f(f(f(f(f(a)))))) 542.19/241.36 down(f(f(f(f(f(b)))))) 542.19/241.36 down(f(f(f(f(f(g(x0))))))) 542.19/241.36 down(f(f(f(f(f(c)))))) 542.19/241.36 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.36 down(g(g(g(g(g(a)))))) 542.19/241.36 down(g(g(g(g(g(f(x0))))))) 542.19/241.36 down(g(g(g(g(g(b)))))) 542.19/241.36 down(g(g(g(g(g(c)))))) 542.19/241.36 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.36 down(f(f(f(f(f(f(a))))))) 542.19/241.36 down(f(f(f(f(f(f(b))))))) 542.19/241.36 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.36 down(f(f(f(f(f(f(c))))))) 542.19/241.36 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.36 down(g(g(g(g(g(g(a))))))) 542.19/241.36 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.36 down(g(g(g(g(g(g(b))))))) 542.19/241.36 down(g(g(g(g(g(g(c))))))) 542.19/241.36 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.36 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.36 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.36 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.36 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.36 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.37 f_flat(up(x0)) 542.19/241.37 g_flat(up(x0)) 542.19/241.37 542.19/241.37 We have to consider all minimal (P,Q,R)-chains. 542.19/241.37 ---------------------------------------- 542.19/241.37 542.19/241.37 (153) TransformationProof (EQUIVALENT) 542.19/241.37 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(down(g(g(g(c)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.37 542.19/241.37 (TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))),TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c))))))) 542.19/241.37 542.19/241.37 542.19/241.37 ---------------------------------------- 542.19/241.37 542.19/241.37 (154) 542.19/241.37 Obligation: 542.19/241.37 Q DP problem: 542.19/241.37 The TRS P consists of the following rules: 542.19/241.37 542.19/241.37 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.37 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.37 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) 542.19/241.37 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.37 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.37 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.37 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.37 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.37 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.37 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.37 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.37 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.37 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.37 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.37 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.37 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.37 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.37 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.37 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.37 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.37 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.37 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.37 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.37 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.37 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.37 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.37 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.37 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.37 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.37 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.37 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.37 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.19/241.37 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.19/241.37 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.19/241.37 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.19/241.37 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.19/241.37 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.19/241.37 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.19/241.37 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.19/241.37 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.19/241.37 542.19/241.37 The TRS R consists of the following rules: 542.19/241.37 542.19/241.37 down(a) -> up(f(a)) 542.19/241.37 down(b) -> up(g(b)) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.19/241.37 down(f(a)) -> f_flat(down(a)) 542.19/241.37 down(f(b)) -> f_flat(down(b)) 542.19/241.37 down(f(g(y4))) -> f_flat(down(g(y4))) 542.19/241.37 down(f(c)) -> f_flat(down(c)) 542.19/241.37 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.19/241.37 down(g(a)) -> g_flat(down(a)) 542.19/241.37 down(g(f(y6))) -> g_flat(down(f(y6))) 542.19/241.37 down(g(b)) -> g_flat(down(b)) 542.19/241.37 down(g(c)) -> g_flat(down(c)) 542.19/241.37 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.19/241.37 down(f(f(a))) -> f_flat(down(f(a))) 542.19/241.37 down(f(f(b))) -> f_flat(down(f(b))) 542.19/241.37 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.19/241.37 down(f(f(c))) -> f_flat(down(f(c))) 542.19/241.37 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.19/241.37 down(g(g(a))) -> g_flat(down(g(a))) 542.19/241.37 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.19/241.37 down(g(g(b))) -> g_flat(down(g(b))) 542.19/241.37 down(g(g(c))) -> g_flat(down(g(c))) 542.19/241.37 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.19/241.37 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.19/241.37 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.19/241.37 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.19/241.37 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.19/241.37 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.19/241.37 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.19/241.37 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.19/241.37 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.19/241.37 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.19/241.37 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.19/241.37 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.19/241.37 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.19/241.37 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.19/241.37 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.19/241.37 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.19/241.37 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.19/241.37 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.19/241.37 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.19/241.37 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.19/241.37 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.19/241.37 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.19/241.37 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.19/241.37 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.19/241.37 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.19/241.37 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.19/241.37 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.19/241.37 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.19/241.37 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.19/241.37 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.19/241.37 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.19/241.37 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.19/241.37 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.19/241.37 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.19/241.37 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.19/241.37 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.19/241.37 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.19/241.37 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.19/241.37 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.19/241.37 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.19/241.37 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.19/241.37 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.19/241.37 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.19/241.37 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.19/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.37 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.19/241.37 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.19/241.37 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.19/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.37 g_flat(up(x_1)) -> up(g(x_1)) 542.19/241.37 f_flat(up(x_1)) -> up(f(x_1)) 542.19/241.37 542.19/241.37 The set Q consists of the following terms: 542.19/241.37 542.19/241.37 down(a) 542.19/241.37 down(b) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.19/241.37 down(f(a)) 542.19/241.37 down(f(b)) 542.19/241.37 down(f(g(x0))) 542.19/241.37 down(f(c)) 542.19/241.37 down(f(fresh_constant)) 542.19/241.37 down(g(a)) 542.19/241.37 down(g(f(x0))) 542.19/241.37 down(g(b)) 542.19/241.37 down(g(c)) 542.19/241.37 down(g(fresh_constant)) 542.19/241.37 down(f(f(a))) 542.19/241.37 down(f(f(b))) 542.19/241.37 down(f(f(g(x0)))) 542.19/241.37 down(f(f(c))) 542.19/241.37 down(f(f(fresh_constant))) 542.19/241.37 down(g(g(a))) 542.19/241.37 down(g(g(f(x0)))) 542.19/241.37 down(g(g(b))) 542.19/241.37 down(g(g(c))) 542.19/241.37 down(g(g(fresh_constant))) 542.19/241.37 down(f(f(f(a)))) 542.19/241.37 down(f(f(f(b)))) 542.19/241.37 down(f(f(f(g(x0))))) 542.19/241.37 down(f(f(f(c)))) 542.19/241.37 down(f(f(f(fresh_constant)))) 542.19/241.37 down(g(g(g(a)))) 542.19/241.37 down(g(g(g(f(x0))))) 542.19/241.37 down(g(g(g(b)))) 542.19/241.37 down(g(g(g(c)))) 542.19/241.37 down(g(g(g(fresh_constant)))) 542.19/241.37 down(f(f(f(f(a))))) 542.19/241.37 down(f(f(f(f(b))))) 542.19/241.37 down(f(f(f(f(g(x0)))))) 542.19/241.37 down(f(f(f(f(c))))) 542.19/241.37 down(f(f(f(f(fresh_constant))))) 542.19/241.37 down(g(g(g(g(a))))) 542.19/241.37 down(g(g(g(g(f(x0)))))) 542.19/241.37 down(g(g(g(g(b))))) 542.19/241.37 down(g(g(g(g(c))))) 542.19/241.37 down(g(g(g(g(fresh_constant))))) 542.19/241.37 down(f(f(f(f(f(a)))))) 542.19/241.37 down(f(f(f(f(f(b)))))) 542.19/241.37 down(f(f(f(f(f(g(x0))))))) 542.19/241.37 down(f(f(f(f(f(c)))))) 542.19/241.37 down(f(f(f(f(f(fresh_constant)))))) 542.19/241.37 down(g(g(g(g(g(a)))))) 542.19/241.37 down(g(g(g(g(g(f(x0))))))) 542.19/241.37 down(g(g(g(g(g(b)))))) 542.19/241.37 down(g(g(g(g(g(c)))))) 542.19/241.37 down(g(g(g(g(g(fresh_constant)))))) 542.19/241.37 down(f(f(f(f(f(f(a))))))) 542.19/241.37 down(f(f(f(f(f(f(b))))))) 542.19/241.37 down(f(f(f(f(f(f(g(x0)))))))) 542.19/241.37 down(f(f(f(f(f(f(c))))))) 542.19/241.37 down(f(f(f(f(f(f(fresh_constant))))))) 542.19/241.37 down(g(g(g(g(g(g(a))))))) 542.19/241.37 down(g(g(g(g(g(g(f(x0)))))))) 542.19/241.37 down(g(g(g(g(g(g(b))))))) 542.19/241.37 down(g(g(g(g(g(g(c))))))) 542.19/241.37 down(g(g(g(g(g(g(fresh_constant))))))) 542.19/241.37 down(f(f(f(f(f(f(f(a)))))))) 542.19/241.37 down(f(f(f(f(f(f(f(b)))))))) 542.19/241.37 down(f(f(f(f(f(f(f(g(x0))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(c)))))))) 542.19/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.19/241.37 down(g(g(g(g(g(g(g(a)))))))) 542.19/241.37 down(g(g(g(g(g(g(g(f(x0))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(b)))))))) 542.19/241.37 down(g(g(g(g(g(g(g(c)))))))) 542.19/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(a))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(b))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(c))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(a))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(b))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(c))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.19/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.19/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.37 f_flat(up(x0)) 542.19/241.37 g_flat(up(x0)) 542.19/241.37 542.19/241.37 We have to consider all minimal (P,Q,R)-chains. 542.19/241.37 ---------------------------------------- 542.19/241.37 542.19/241.37 (155) TransformationProof (EQUIVALENT) 542.19/241.37 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(down(g(g(g(fresh_constant)))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.19/241.37 542.19/241.37 (TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))),TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.19/241.37 542.19/241.37 542.19/241.37 ---------------------------------------- 542.19/241.37 542.19/241.37 (156) 542.19/241.37 Obligation: 542.19/241.37 Q DP problem: 542.19/241.37 The TRS P consists of the following rules: 542.19/241.37 542.19/241.37 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.19/241.37 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.19/241.37 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) 542.19/241.37 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.19/241.37 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.19/241.37 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.19/241.37 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.19/241.37 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.19/241.37 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.19/241.37 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.19/241.37 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.19/241.37 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.19/241.37 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.19/241.37 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.19/241.37 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.19/241.37 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.19/241.37 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.19/241.37 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.19/241.37 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.19/241.37 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.19/241.37 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.19/241.37 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.19/241.37 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.19/241.37 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.19/241.37 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.19/241.37 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.19/241.37 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.19/241.37 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.19/241.37 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.19/241.37 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.19/241.37 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.19/241.37 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.19/241.37 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.37 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.37 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.37 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.37 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.37 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.37 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.37 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.37 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.37 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.37 542.34/241.37 The TRS R consists of the following rules: 542.34/241.37 542.34/241.37 down(a) -> up(f(a)) 542.34/241.37 down(b) -> up(g(b)) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.37 down(f(a)) -> f_flat(down(a)) 542.34/241.37 down(f(b)) -> f_flat(down(b)) 542.34/241.37 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.37 down(f(c)) -> f_flat(down(c)) 542.34/241.37 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.37 down(g(a)) -> g_flat(down(a)) 542.34/241.37 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.37 down(g(b)) -> g_flat(down(b)) 542.34/241.37 down(g(c)) -> g_flat(down(c)) 542.34/241.37 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.37 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.37 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.37 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.37 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.37 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.37 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.37 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.37 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.37 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.37 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.37 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.37 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.37 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.37 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.37 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.37 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.37 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.37 542.34/241.37 The set Q consists of the following terms: 542.34/241.37 542.34/241.37 down(a) 542.34/241.37 down(b) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.37 down(f(a)) 542.34/241.37 down(f(b)) 542.34/241.37 down(f(g(x0))) 542.34/241.37 down(f(c)) 542.34/241.37 down(f(fresh_constant)) 542.34/241.37 down(g(a)) 542.34/241.37 down(g(f(x0))) 542.34/241.37 down(g(b)) 542.34/241.37 down(g(c)) 542.34/241.37 down(g(fresh_constant)) 542.34/241.37 down(f(f(a))) 542.34/241.37 down(f(f(b))) 542.34/241.37 down(f(f(g(x0)))) 542.34/241.37 down(f(f(c))) 542.34/241.37 down(f(f(fresh_constant))) 542.34/241.37 down(g(g(a))) 542.34/241.37 down(g(g(f(x0)))) 542.34/241.37 down(g(g(b))) 542.34/241.37 down(g(g(c))) 542.34/241.37 down(g(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) 542.34/241.37 down(f(f(f(g(x0))))) 542.34/241.37 down(f(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) 542.34/241.37 down(g(g(g(f(x0))))) 542.34/241.37 down(g(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(x0)))))) 542.34/241.37 down(f(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(x0)))))) 542.34/241.37 down(g(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(x0))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(x0))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 f_flat(up(x0)) 542.34/241.37 g_flat(up(x0)) 542.34/241.37 542.34/241.37 We have to consider all minimal (P,Q,R)-chains. 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (157) TransformationProof (EQUIVALENT) 542.34/241.37 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(down(g(g(g(g(a))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.37 542.34/241.37 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a)))))))) 542.34/241.37 542.34/241.37 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (158) 542.34/241.37 Obligation: 542.34/241.37 Q DP problem: 542.34/241.37 The TRS P consists of the following rules: 542.34/241.37 542.34/241.37 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.37 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.37 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.34/241.37 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.34/241.37 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.34/241.37 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.37 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.37 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.37 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.37 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.37 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.37 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.37 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.37 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.37 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.37 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.37 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.37 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.37 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.37 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.37 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.37 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.37 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.37 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.37 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.37 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.37 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.37 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.37 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.37 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.37 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.37 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.37 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.37 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.37 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.37 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.37 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.37 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.37 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.37 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.37 542.34/241.37 The TRS R consists of the following rules: 542.34/241.37 542.34/241.37 down(a) -> up(f(a)) 542.34/241.37 down(b) -> up(g(b)) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.37 down(f(a)) -> f_flat(down(a)) 542.34/241.37 down(f(b)) -> f_flat(down(b)) 542.34/241.37 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.37 down(f(c)) -> f_flat(down(c)) 542.34/241.37 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.37 down(g(a)) -> g_flat(down(a)) 542.34/241.37 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.37 down(g(b)) -> g_flat(down(b)) 542.34/241.37 down(g(c)) -> g_flat(down(c)) 542.34/241.37 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.37 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.37 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.37 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.37 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.37 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.37 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.37 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.37 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.37 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.37 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.37 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.37 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.37 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.37 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.37 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.37 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.37 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.37 542.34/241.37 The set Q consists of the following terms: 542.34/241.37 542.34/241.37 down(a) 542.34/241.37 down(b) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.37 down(f(a)) 542.34/241.37 down(f(b)) 542.34/241.37 down(f(g(x0))) 542.34/241.37 down(f(c)) 542.34/241.37 down(f(fresh_constant)) 542.34/241.37 down(g(a)) 542.34/241.37 down(g(f(x0))) 542.34/241.37 down(g(b)) 542.34/241.37 down(g(c)) 542.34/241.37 down(g(fresh_constant)) 542.34/241.37 down(f(f(a))) 542.34/241.37 down(f(f(b))) 542.34/241.37 down(f(f(g(x0)))) 542.34/241.37 down(f(f(c))) 542.34/241.37 down(f(f(fresh_constant))) 542.34/241.37 down(g(g(a))) 542.34/241.37 down(g(g(f(x0)))) 542.34/241.37 down(g(g(b))) 542.34/241.37 down(g(g(c))) 542.34/241.37 down(g(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) 542.34/241.37 down(f(f(f(g(x0))))) 542.34/241.37 down(f(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) 542.34/241.37 down(g(g(g(f(x0))))) 542.34/241.37 down(g(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(x0)))))) 542.34/241.37 down(f(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(x0)))))) 542.34/241.37 down(g(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(x0))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(x0))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 f_flat(up(x0)) 542.34/241.37 g_flat(up(x0)) 542.34/241.37 542.34/241.37 We have to consider all minimal (P,Q,R)-chains. 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (159) TransformationProof (EQUIVALENT) 542.34/241.37 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(down(g(g(g(g(f(x0)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.37 542.34/241.37 (TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))),TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.34/241.37 542.34/241.37 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (160) 542.34/241.37 Obligation: 542.34/241.37 Q DP problem: 542.34/241.37 The TRS P consists of the following rules: 542.34/241.37 542.34/241.37 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.37 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.37 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) 542.34/241.37 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.34/241.37 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.34/241.37 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.37 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.37 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.37 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.37 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.37 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.37 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.37 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.37 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.37 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.37 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.37 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.37 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.37 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.37 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.37 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.37 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.37 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.37 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.37 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.37 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.37 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.37 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.37 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.37 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.37 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.37 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.37 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.37 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.37 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.37 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.37 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.37 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.37 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.37 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.37 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.37 542.34/241.37 The TRS R consists of the following rules: 542.34/241.37 542.34/241.37 down(a) -> up(f(a)) 542.34/241.37 down(b) -> up(g(b)) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.37 down(f(a)) -> f_flat(down(a)) 542.34/241.37 down(f(b)) -> f_flat(down(b)) 542.34/241.37 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.37 down(f(c)) -> f_flat(down(c)) 542.34/241.37 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.37 down(g(a)) -> g_flat(down(a)) 542.34/241.37 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.37 down(g(b)) -> g_flat(down(b)) 542.34/241.37 down(g(c)) -> g_flat(down(c)) 542.34/241.37 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.37 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.37 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.37 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.37 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.37 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.37 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.37 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.37 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.37 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.37 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.37 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.37 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.37 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.37 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.37 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.37 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.37 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.37 542.34/241.37 The set Q consists of the following terms: 542.34/241.37 542.34/241.37 down(a) 542.34/241.37 down(b) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.37 down(f(a)) 542.34/241.37 down(f(b)) 542.34/241.37 down(f(g(x0))) 542.34/241.37 down(f(c)) 542.34/241.37 down(f(fresh_constant)) 542.34/241.37 down(g(a)) 542.34/241.37 down(g(f(x0))) 542.34/241.37 down(g(b)) 542.34/241.37 down(g(c)) 542.34/241.37 down(g(fresh_constant)) 542.34/241.37 down(f(f(a))) 542.34/241.37 down(f(f(b))) 542.34/241.37 down(f(f(g(x0)))) 542.34/241.37 down(f(f(c))) 542.34/241.37 down(f(f(fresh_constant))) 542.34/241.37 down(g(g(a))) 542.34/241.37 down(g(g(f(x0)))) 542.34/241.37 down(g(g(b))) 542.34/241.37 down(g(g(c))) 542.34/241.37 down(g(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) 542.34/241.37 down(f(f(f(g(x0))))) 542.34/241.37 down(f(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) 542.34/241.37 down(g(g(g(f(x0))))) 542.34/241.37 down(g(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(x0)))))) 542.34/241.37 down(f(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(x0)))))) 542.34/241.37 down(g(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(x0))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(x0))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 f_flat(up(x0)) 542.34/241.37 g_flat(up(x0)) 542.34/241.37 542.34/241.37 We have to consider all minimal (P,Q,R)-chains. 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (161) TransformationProof (EQUIVALENT) 542.34/241.37 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(down(f(f(f(f(c))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.37 542.34/241.37 (TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))),TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c)))))))) 542.34/241.37 542.34/241.37 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (162) 542.34/241.37 Obligation: 542.34/241.37 Q DP problem: 542.34/241.37 The TRS P consists of the following rules: 542.34/241.37 542.34/241.37 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.37 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.37 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.34/241.37 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.34/241.37 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.37 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.37 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.37 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.37 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.37 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.37 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.37 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.37 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.37 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.37 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.37 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.37 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.37 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.37 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.37 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.37 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.37 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.37 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.37 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.37 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.37 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.37 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.37 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.37 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.37 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.37 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.37 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.37 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.37 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.37 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.37 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.37 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.37 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.37 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.37 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.37 542.34/241.37 The TRS R consists of the following rules: 542.34/241.37 542.34/241.37 down(a) -> up(f(a)) 542.34/241.37 down(b) -> up(g(b)) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.37 down(f(a)) -> f_flat(down(a)) 542.34/241.37 down(f(b)) -> f_flat(down(b)) 542.34/241.37 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.37 down(f(c)) -> f_flat(down(c)) 542.34/241.37 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.37 down(g(a)) -> g_flat(down(a)) 542.34/241.37 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.37 down(g(b)) -> g_flat(down(b)) 542.34/241.37 down(g(c)) -> g_flat(down(c)) 542.34/241.37 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.37 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.37 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.37 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.37 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.37 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.37 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.37 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.37 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.37 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.37 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.37 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.37 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.37 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.37 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.37 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.37 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.37 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.37 542.34/241.37 The set Q consists of the following terms: 542.34/241.37 542.34/241.37 down(a) 542.34/241.37 down(b) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.37 down(f(a)) 542.34/241.37 down(f(b)) 542.34/241.37 down(f(g(x0))) 542.34/241.37 down(f(c)) 542.34/241.37 down(f(fresh_constant)) 542.34/241.37 down(g(a)) 542.34/241.37 down(g(f(x0))) 542.34/241.37 down(g(b)) 542.34/241.37 down(g(c)) 542.34/241.37 down(g(fresh_constant)) 542.34/241.37 down(f(f(a))) 542.34/241.37 down(f(f(b))) 542.34/241.37 down(f(f(g(x0)))) 542.34/241.37 down(f(f(c))) 542.34/241.37 down(f(f(fresh_constant))) 542.34/241.37 down(g(g(a))) 542.34/241.37 down(g(g(f(x0)))) 542.34/241.37 down(g(g(b))) 542.34/241.37 down(g(g(c))) 542.34/241.37 down(g(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) 542.34/241.37 down(f(f(f(g(x0))))) 542.34/241.37 down(f(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) 542.34/241.37 down(g(g(g(f(x0))))) 542.34/241.37 down(g(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(x0)))))) 542.34/241.37 down(f(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(x0)))))) 542.34/241.37 down(g(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(x0))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(x0))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 f_flat(up(x0)) 542.34/241.37 g_flat(up(x0)) 542.34/241.37 542.34/241.37 We have to consider all minimal (P,Q,R)-chains. 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (163) TransformationProof (EQUIVALENT) 542.34/241.37 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(down(f(f(f(f(fresh_constant))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.37 542.34/241.37 (TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))),TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.34/241.37 542.34/241.37 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (164) 542.34/241.37 Obligation: 542.34/241.37 Q DP problem: 542.34/241.37 The TRS P consists of the following rules: 542.34/241.37 542.34/241.37 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.37 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.37 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.34/241.37 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.34/241.37 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.37 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.37 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.37 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.37 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.37 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.37 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.37 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.37 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.37 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.37 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.37 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.37 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.37 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.37 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.37 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.37 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.37 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.37 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.37 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.37 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.37 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.37 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.37 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.37 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.37 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.37 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.37 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.37 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.37 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.37 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.37 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.37 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.37 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.37 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.37 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.37 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.37 542.34/241.37 The TRS R consists of the following rules: 542.34/241.37 542.34/241.37 down(a) -> up(f(a)) 542.34/241.37 down(b) -> up(g(b)) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.37 down(f(a)) -> f_flat(down(a)) 542.34/241.37 down(f(b)) -> f_flat(down(b)) 542.34/241.37 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.37 down(f(c)) -> f_flat(down(c)) 542.34/241.37 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.37 down(g(a)) -> g_flat(down(a)) 542.34/241.37 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.37 down(g(b)) -> g_flat(down(b)) 542.34/241.37 down(g(c)) -> g_flat(down(c)) 542.34/241.37 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.37 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.37 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.37 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.37 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.37 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.37 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.37 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.37 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.37 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.37 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.37 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.37 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.37 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.37 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.37 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.37 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.37 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.37 542.34/241.37 The set Q consists of the following terms: 542.34/241.37 542.34/241.37 down(a) 542.34/241.37 down(b) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.37 down(f(a)) 542.34/241.37 down(f(b)) 542.34/241.37 down(f(g(x0))) 542.34/241.37 down(f(c)) 542.34/241.37 down(f(fresh_constant)) 542.34/241.37 down(g(a)) 542.34/241.37 down(g(f(x0))) 542.34/241.37 down(g(b)) 542.34/241.37 down(g(c)) 542.34/241.37 down(g(fresh_constant)) 542.34/241.37 down(f(f(a))) 542.34/241.37 down(f(f(b))) 542.34/241.37 down(f(f(g(x0)))) 542.34/241.37 down(f(f(c))) 542.34/241.37 down(f(f(fresh_constant))) 542.34/241.37 down(g(g(a))) 542.34/241.37 down(g(g(f(x0)))) 542.34/241.37 down(g(g(b))) 542.34/241.37 down(g(g(c))) 542.34/241.37 down(g(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) 542.34/241.37 down(f(f(f(g(x0))))) 542.34/241.37 down(f(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) 542.34/241.37 down(g(g(g(f(x0))))) 542.34/241.37 down(g(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(x0)))))) 542.34/241.37 down(f(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(x0)))))) 542.34/241.37 down(g(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) 542.34/241.37 down(f(f(f(f(f(b)))))) 542.34/241.37 down(f(f(f(f(f(g(x0))))))) 542.34/241.37 down(f(f(f(f(f(c)))))) 542.34/241.37 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.37 down(g(g(g(g(g(a)))))) 542.34/241.37 down(g(g(g(g(g(f(x0))))))) 542.34/241.37 down(g(g(g(g(g(b)))))) 542.34/241.37 down(g(g(g(g(g(c)))))) 542.34/241.37 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.37 down(f(f(f(f(f(f(a))))))) 542.34/241.37 down(f(f(f(f(f(f(b))))))) 542.34/241.37 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.37 down(f(f(f(f(f(f(c))))))) 542.34/241.37 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.37 down(g(g(g(g(g(g(a))))))) 542.34/241.37 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.37 down(g(g(g(g(g(g(b))))))) 542.34/241.37 down(g(g(g(g(g(g(c))))))) 542.34/241.37 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.37 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.37 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 f_flat(up(x0)) 542.34/241.37 g_flat(up(x0)) 542.34/241.37 542.34/241.37 We have to consider all minimal (P,Q,R)-chains. 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (165) TransformationProof (EQUIVALENT) 542.34/241.37 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(down(f(f(f(f(f(a)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.37 542.34/241.37 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.34/241.37 542.34/241.37 542.34/241.37 ---------------------------------------- 542.34/241.37 542.34/241.37 (166) 542.34/241.37 Obligation: 542.34/241.37 Q DP problem: 542.34/241.37 The TRS P consists of the following rules: 542.34/241.37 542.34/241.37 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.37 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.37 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.34/241.37 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.34/241.37 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.37 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.37 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.37 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.37 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.37 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.37 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.37 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.37 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.37 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.37 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.37 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.37 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.37 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.37 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.37 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.37 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.37 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.37 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.37 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.37 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.37 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.37 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.37 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.37 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.37 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.37 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.37 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.37 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.37 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.37 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.37 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.37 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.37 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.37 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.37 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.37 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.37 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.37 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.37 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.37 542.34/241.37 The TRS R consists of the following rules: 542.34/241.37 542.34/241.37 down(a) -> up(f(a)) 542.34/241.37 down(b) -> up(g(b)) 542.34/241.37 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.37 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.37 down(f(a)) -> f_flat(down(a)) 542.34/241.37 down(f(b)) -> f_flat(down(b)) 542.34/241.37 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.37 down(f(c)) -> f_flat(down(c)) 542.34/241.37 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.37 down(g(a)) -> g_flat(down(a)) 542.34/241.37 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.37 down(g(b)) -> g_flat(down(b)) 542.34/241.37 down(g(c)) -> g_flat(down(c)) 542.34/241.37 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.37 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.37 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.37 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.37 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.37 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.37 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.37 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.37 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.37 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.37 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.37 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.37 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.37 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.37 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.37 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.37 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.37 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.37 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.37 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.37 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.37 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.37 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.37 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.37 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.37 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.37 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.37 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.37 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.37 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.37 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.37 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.38 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.38 542.34/241.38 The set Q consists of the following terms: 542.34/241.38 542.34/241.38 down(a) 542.34/241.38 down(b) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.38 down(f(a)) 542.34/241.38 down(f(b)) 542.34/241.38 down(f(g(x0))) 542.34/241.38 down(f(c)) 542.34/241.38 down(f(fresh_constant)) 542.34/241.38 down(g(a)) 542.34/241.38 down(g(f(x0))) 542.34/241.38 down(g(b)) 542.34/241.38 down(g(c)) 542.34/241.38 down(g(fresh_constant)) 542.34/241.38 down(f(f(a))) 542.34/241.38 down(f(f(b))) 542.34/241.38 down(f(f(g(x0)))) 542.34/241.38 down(f(f(c))) 542.34/241.38 down(f(f(fresh_constant))) 542.34/241.38 down(g(g(a))) 542.34/241.38 down(g(g(f(x0)))) 542.34/241.38 down(g(g(b))) 542.34/241.38 down(g(g(c))) 542.34/241.38 down(g(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) 542.34/241.38 down(f(f(f(g(x0))))) 542.34/241.38 down(f(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) 542.34/241.38 down(g(g(g(f(x0))))) 542.34/241.38 down(g(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(x0)))))) 542.34/241.38 down(f(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(x0)))))) 542.34/241.38 down(g(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(x0))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(x0))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 f_flat(up(x0)) 542.34/241.38 g_flat(up(x0)) 542.34/241.38 542.34/241.38 We have to consider all minimal (P,Q,R)-chains. 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (167) TransformationProof (EQUIVALENT) 542.34/241.38 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(down(f(f(f(f(f(b)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.38 542.34/241.38 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.34/241.38 542.34/241.38 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (168) 542.34/241.38 Obligation: 542.34/241.38 Q DP problem: 542.34/241.38 The TRS P consists of the following rules: 542.34/241.38 542.34/241.38 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.38 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.38 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.34/241.38 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.34/241.38 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.38 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.38 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.38 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.38 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.38 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.38 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.38 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.38 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.38 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.38 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.38 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.38 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.38 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.38 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.38 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.38 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.38 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.38 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.38 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.38 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.38 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.38 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.38 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.38 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.38 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.38 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.38 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.38 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.38 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.38 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.38 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.38 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.38 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.38 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.38 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.38 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.38 542.34/241.38 The TRS R consists of the following rules: 542.34/241.38 542.34/241.38 down(a) -> up(f(a)) 542.34/241.38 down(b) -> up(g(b)) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.38 down(f(a)) -> f_flat(down(a)) 542.34/241.38 down(f(b)) -> f_flat(down(b)) 542.34/241.38 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.38 down(f(c)) -> f_flat(down(c)) 542.34/241.38 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.38 down(g(a)) -> g_flat(down(a)) 542.34/241.38 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.38 down(g(b)) -> g_flat(down(b)) 542.34/241.38 down(g(c)) -> g_flat(down(c)) 542.34/241.38 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.38 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.38 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.38 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.38 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.38 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.38 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.38 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.38 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.38 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.38 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.38 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.38 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.38 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.38 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.38 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.38 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.38 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.38 542.34/241.38 The set Q consists of the following terms: 542.34/241.38 542.34/241.38 down(a) 542.34/241.38 down(b) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.38 down(f(a)) 542.34/241.38 down(f(b)) 542.34/241.38 down(f(g(x0))) 542.34/241.38 down(f(c)) 542.34/241.38 down(f(fresh_constant)) 542.34/241.38 down(g(a)) 542.34/241.38 down(g(f(x0))) 542.34/241.38 down(g(b)) 542.34/241.38 down(g(c)) 542.34/241.38 down(g(fresh_constant)) 542.34/241.38 down(f(f(a))) 542.34/241.38 down(f(f(b))) 542.34/241.38 down(f(f(g(x0)))) 542.34/241.38 down(f(f(c))) 542.34/241.38 down(f(f(fresh_constant))) 542.34/241.38 down(g(g(a))) 542.34/241.38 down(g(g(f(x0)))) 542.34/241.38 down(g(g(b))) 542.34/241.38 down(g(g(c))) 542.34/241.38 down(g(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) 542.34/241.38 down(f(f(f(g(x0))))) 542.34/241.38 down(f(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) 542.34/241.38 down(g(g(g(f(x0))))) 542.34/241.38 down(g(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(x0)))))) 542.34/241.38 down(f(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(x0)))))) 542.34/241.38 down(g(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(x0))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(x0))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 f_flat(up(x0)) 542.34/241.38 g_flat(up(x0)) 542.34/241.38 542.34/241.38 We have to consider all minimal (P,Q,R)-chains. 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (169) TransformationProof (EQUIVALENT) 542.34/241.38 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(down(f(f(f(f(f(g(x0))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.38 542.34/241.38 (TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))),TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.34/241.38 542.34/241.38 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (170) 542.34/241.38 Obligation: 542.34/241.38 Q DP problem: 542.34/241.38 The TRS P consists of the following rules: 542.34/241.38 542.34/241.38 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.38 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.38 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) 542.34/241.38 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.34/241.38 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.38 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.38 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.38 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.38 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.38 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.38 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.38 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.38 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.38 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.38 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.38 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.38 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.38 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.38 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.38 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.38 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.38 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.38 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.38 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.38 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.38 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.38 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.38 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.38 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.38 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.38 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.38 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.38 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.38 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.38 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.38 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.38 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.38 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.38 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.38 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.38 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.38 542.34/241.38 The TRS R consists of the following rules: 542.34/241.38 542.34/241.38 down(a) -> up(f(a)) 542.34/241.38 down(b) -> up(g(b)) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.38 down(f(a)) -> f_flat(down(a)) 542.34/241.38 down(f(b)) -> f_flat(down(b)) 542.34/241.38 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.38 down(f(c)) -> f_flat(down(c)) 542.34/241.38 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.38 down(g(a)) -> g_flat(down(a)) 542.34/241.38 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.38 down(g(b)) -> g_flat(down(b)) 542.34/241.38 down(g(c)) -> g_flat(down(c)) 542.34/241.38 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.38 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.38 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.38 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.38 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.38 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.38 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.38 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.38 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.38 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.38 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.38 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.38 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.38 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.38 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.38 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.38 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.38 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.38 542.34/241.38 The set Q consists of the following terms: 542.34/241.38 542.34/241.38 down(a) 542.34/241.38 down(b) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.38 down(f(a)) 542.34/241.38 down(f(b)) 542.34/241.38 down(f(g(x0))) 542.34/241.38 down(f(c)) 542.34/241.38 down(f(fresh_constant)) 542.34/241.38 down(g(a)) 542.34/241.38 down(g(f(x0))) 542.34/241.38 down(g(b)) 542.34/241.38 down(g(c)) 542.34/241.38 down(g(fresh_constant)) 542.34/241.38 down(f(f(a))) 542.34/241.38 down(f(f(b))) 542.34/241.38 down(f(f(g(x0)))) 542.34/241.38 down(f(f(c))) 542.34/241.38 down(f(f(fresh_constant))) 542.34/241.38 down(g(g(a))) 542.34/241.38 down(g(g(f(x0)))) 542.34/241.38 down(g(g(b))) 542.34/241.38 down(g(g(c))) 542.34/241.38 down(g(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) 542.34/241.38 down(f(f(f(g(x0))))) 542.34/241.38 down(f(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) 542.34/241.38 down(g(g(g(f(x0))))) 542.34/241.38 down(g(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(x0)))))) 542.34/241.38 down(f(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(x0)))))) 542.34/241.38 down(g(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(x0))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(x0))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 f_flat(up(x0)) 542.34/241.38 g_flat(up(x0)) 542.34/241.38 542.34/241.38 We have to consider all minimal (P,Q,R)-chains. 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (171) TransformationProof (EQUIVALENT) 542.34/241.38 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(down(g(g(g(g(b))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.38 542.34/241.38 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b)))))))) 542.34/241.38 542.34/241.38 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (172) 542.34/241.38 Obligation: 542.34/241.38 Q DP problem: 542.34/241.38 The TRS P consists of the following rules: 542.34/241.38 542.34/241.38 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.38 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.38 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) 542.34/241.38 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.38 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.38 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.38 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.38 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.38 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.38 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.38 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.38 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.38 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.38 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.38 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.38 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.38 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.38 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.38 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.38 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.38 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.38 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.38 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.38 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.38 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.38 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.38 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.38 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.38 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.38 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.38 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.38 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.38 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.38 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.38 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.38 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.38 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.38 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.38 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.38 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.38 542.34/241.38 The TRS R consists of the following rules: 542.34/241.38 542.34/241.38 down(a) -> up(f(a)) 542.34/241.38 down(b) -> up(g(b)) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.38 down(f(a)) -> f_flat(down(a)) 542.34/241.38 down(f(b)) -> f_flat(down(b)) 542.34/241.38 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.38 down(f(c)) -> f_flat(down(c)) 542.34/241.38 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.38 down(g(a)) -> g_flat(down(a)) 542.34/241.38 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.38 down(g(b)) -> g_flat(down(b)) 542.34/241.38 down(g(c)) -> g_flat(down(c)) 542.34/241.38 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.38 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.38 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.38 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.38 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.38 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.38 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.38 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.38 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.38 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.38 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.38 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.38 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.38 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.38 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.38 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.38 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.38 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.38 542.34/241.38 The set Q consists of the following terms: 542.34/241.38 542.34/241.38 down(a) 542.34/241.38 down(b) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.38 down(f(a)) 542.34/241.38 down(f(b)) 542.34/241.38 down(f(g(x0))) 542.34/241.38 down(f(c)) 542.34/241.38 down(f(fresh_constant)) 542.34/241.38 down(g(a)) 542.34/241.38 down(g(f(x0))) 542.34/241.38 down(g(b)) 542.34/241.38 down(g(c)) 542.34/241.38 down(g(fresh_constant)) 542.34/241.38 down(f(f(a))) 542.34/241.38 down(f(f(b))) 542.34/241.38 down(f(f(g(x0)))) 542.34/241.38 down(f(f(c))) 542.34/241.38 down(f(f(fresh_constant))) 542.34/241.38 down(g(g(a))) 542.34/241.38 down(g(g(f(x0)))) 542.34/241.38 down(g(g(b))) 542.34/241.38 down(g(g(c))) 542.34/241.38 down(g(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) 542.34/241.38 down(f(f(f(g(x0))))) 542.34/241.38 down(f(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) 542.34/241.38 down(g(g(g(f(x0))))) 542.34/241.38 down(g(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(x0)))))) 542.34/241.38 down(f(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(x0)))))) 542.34/241.38 down(g(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(x0))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(x0))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 f_flat(up(x0)) 542.34/241.38 g_flat(up(x0)) 542.34/241.38 542.34/241.38 We have to consider all minimal (P,Q,R)-chains. 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (173) TransformationProof (EQUIVALENT) 542.34/241.38 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(down(g(g(g(g(c))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.38 542.34/241.38 (TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))),TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c)))))))) 542.34/241.38 542.34/241.38 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (174) 542.34/241.38 Obligation: 542.34/241.38 Q DP problem: 542.34/241.38 The TRS P consists of the following rules: 542.34/241.38 542.34/241.38 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.38 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.38 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.38 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.38 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.38 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.38 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.38 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.38 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.38 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.38 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.38 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.38 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.38 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.38 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.38 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.38 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.38 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.38 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.38 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.38 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.38 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.38 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.38 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.38 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.38 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.38 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.38 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.38 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.38 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.38 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.38 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.38 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.38 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.38 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.38 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.38 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.38 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.38 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.38 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.38 542.34/241.38 The TRS R consists of the following rules: 542.34/241.38 542.34/241.38 down(a) -> up(f(a)) 542.34/241.38 down(b) -> up(g(b)) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.38 down(f(a)) -> f_flat(down(a)) 542.34/241.38 down(f(b)) -> f_flat(down(b)) 542.34/241.38 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.38 down(f(c)) -> f_flat(down(c)) 542.34/241.38 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.38 down(g(a)) -> g_flat(down(a)) 542.34/241.38 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.38 down(g(b)) -> g_flat(down(b)) 542.34/241.38 down(g(c)) -> g_flat(down(c)) 542.34/241.38 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.38 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.38 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.38 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.38 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.38 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.38 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.38 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.38 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.38 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.38 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.38 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.38 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.38 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.38 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.38 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.38 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.38 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.38 542.34/241.38 The set Q consists of the following terms: 542.34/241.38 542.34/241.38 down(a) 542.34/241.38 down(b) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.38 down(f(a)) 542.34/241.38 down(f(b)) 542.34/241.38 down(f(g(x0))) 542.34/241.38 down(f(c)) 542.34/241.38 down(f(fresh_constant)) 542.34/241.38 down(g(a)) 542.34/241.38 down(g(f(x0))) 542.34/241.38 down(g(b)) 542.34/241.38 down(g(c)) 542.34/241.38 down(g(fresh_constant)) 542.34/241.38 down(f(f(a))) 542.34/241.38 down(f(f(b))) 542.34/241.38 down(f(f(g(x0)))) 542.34/241.38 down(f(f(c))) 542.34/241.38 down(f(f(fresh_constant))) 542.34/241.38 down(g(g(a))) 542.34/241.38 down(g(g(f(x0)))) 542.34/241.38 down(g(g(b))) 542.34/241.38 down(g(g(c))) 542.34/241.38 down(g(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) 542.34/241.38 down(f(f(f(g(x0))))) 542.34/241.38 down(f(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) 542.34/241.38 down(g(g(g(f(x0))))) 542.34/241.38 down(g(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(x0)))))) 542.34/241.38 down(f(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(x0)))))) 542.34/241.38 down(g(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(x0))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(x0))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 f_flat(up(x0)) 542.34/241.38 g_flat(up(x0)) 542.34/241.38 542.34/241.38 We have to consider all minimal (P,Q,R)-chains. 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (175) TransformationProof (EQUIVALENT) 542.34/241.38 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(down(g(g(g(g(fresh_constant))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.38 542.34/241.38 (TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))),TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.34/241.38 542.34/241.38 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (176) 542.34/241.38 Obligation: 542.34/241.38 Q DP problem: 542.34/241.38 The TRS P consists of the following rules: 542.34/241.38 542.34/241.38 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.38 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.38 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.38 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.38 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.38 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.38 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.38 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.38 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.38 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.38 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.38 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.38 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.38 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.38 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.38 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.38 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.38 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.38 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.38 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.38 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.38 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.38 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.38 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.38 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.38 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.38 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.38 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.38 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.38 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.38 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.38 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.38 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.38 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.38 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.38 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.38 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.38 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.38 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.38 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.38 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.38 542.34/241.38 The TRS R consists of the following rules: 542.34/241.38 542.34/241.38 down(a) -> up(f(a)) 542.34/241.38 down(b) -> up(g(b)) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.38 down(f(a)) -> f_flat(down(a)) 542.34/241.38 down(f(b)) -> f_flat(down(b)) 542.34/241.38 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.38 down(f(c)) -> f_flat(down(c)) 542.34/241.38 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.38 down(g(a)) -> g_flat(down(a)) 542.34/241.38 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.38 down(g(b)) -> g_flat(down(b)) 542.34/241.38 down(g(c)) -> g_flat(down(c)) 542.34/241.38 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.38 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.38 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.38 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.38 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.38 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.38 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.38 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.38 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.38 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.38 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.38 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.38 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.38 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.38 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.38 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.38 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.38 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.38 542.34/241.38 The set Q consists of the following terms: 542.34/241.38 542.34/241.38 down(a) 542.34/241.38 down(b) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.38 down(f(a)) 542.34/241.38 down(f(b)) 542.34/241.38 down(f(g(x0))) 542.34/241.38 down(f(c)) 542.34/241.38 down(f(fresh_constant)) 542.34/241.38 down(g(a)) 542.34/241.38 down(g(f(x0))) 542.34/241.38 down(g(b)) 542.34/241.38 down(g(c)) 542.34/241.38 down(g(fresh_constant)) 542.34/241.38 down(f(f(a))) 542.34/241.38 down(f(f(b))) 542.34/241.38 down(f(f(g(x0)))) 542.34/241.38 down(f(f(c))) 542.34/241.38 down(f(f(fresh_constant))) 542.34/241.38 down(g(g(a))) 542.34/241.38 down(g(g(f(x0)))) 542.34/241.38 down(g(g(b))) 542.34/241.38 down(g(g(c))) 542.34/241.38 down(g(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) 542.34/241.38 down(f(f(f(g(x0))))) 542.34/241.38 down(f(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) 542.34/241.38 down(g(g(g(f(x0))))) 542.34/241.38 down(g(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(x0)))))) 542.34/241.38 down(f(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(x0)))))) 542.34/241.38 down(g(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(x0))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(x0))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 f_flat(up(x0)) 542.34/241.38 g_flat(up(x0)) 542.34/241.38 542.34/241.38 We have to consider all minimal (P,Q,R)-chains. 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (177) TransformationProof (EQUIVALENT) 542.34/241.38 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(down(g(g(g(g(g(a)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.38 542.34/241.38 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.34/241.38 542.34/241.38 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (178) 542.34/241.38 Obligation: 542.34/241.38 Q DP problem: 542.34/241.38 The TRS P consists of the following rules: 542.34/241.38 542.34/241.38 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.38 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.38 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.38 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.38 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.38 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.38 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.38 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.38 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.38 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.38 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.38 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.38 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.38 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.38 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.38 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.38 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.38 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.38 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.38 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.38 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.38 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.38 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.38 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.38 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.38 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.38 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.38 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.38 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.38 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.38 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.38 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.38 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.38 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.38 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.38 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.38 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.38 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.38 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.38 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.38 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.38 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.38 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.38 542.34/241.38 The TRS R consists of the following rules: 542.34/241.38 542.34/241.38 down(a) -> up(f(a)) 542.34/241.38 down(b) -> up(g(b)) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.38 down(f(a)) -> f_flat(down(a)) 542.34/241.38 down(f(b)) -> f_flat(down(b)) 542.34/241.38 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.38 down(f(c)) -> f_flat(down(c)) 542.34/241.38 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.38 down(g(a)) -> g_flat(down(a)) 542.34/241.38 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.38 down(g(b)) -> g_flat(down(b)) 542.34/241.38 down(g(c)) -> g_flat(down(c)) 542.34/241.38 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.38 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.38 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.38 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.38 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.38 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.38 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.38 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.38 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.38 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.38 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.38 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.38 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.38 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.38 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.38 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.38 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.38 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.38 542.34/241.38 The set Q consists of the following terms: 542.34/241.38 542.34/241.38 down(a) 542.34/241.38 down(b) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.38 down(f(a)) 542.34/241.38 down(f(b)) 542.34/241.38 down(f(g(x0))) 542.34/241.38 down(f(c)) 542.34/241.38 down(f(fresh_constant)) 542.34/241.38 down(g(a)) 542.34/241.38 down(g(f(x0))) 542.34/241.38 down(g(b)) 542.34/241.38 down(g(c)) 542.34/241.38 down(g(fresh_constant)) 542.34/241.38 down(f(f(a))) 542.34/241.38 down(f(f(b))) 542.34/241.38 down(f(f(g(x0)))) 542.34/241.38 down(f(f(c))) 542.34/241.38 down(f(f(fresh_constant))) 542.34/241.38 down(g(g(a))) 542.34/241.38 down(g(g(f(x0)))) 542.34/241.38 down(g(g(b))) 542.34/241.38 down(g(g(c))) 542.34/241.38 down(g(g(fresh_constant))) 542.34/241.38 down(f(f(f(a)))) 542.34/241.38 down(f(f(f(b)))) 542.34/241.38 down(f(f(f(g(x0))))) 542.34/241.38 down(f(f(f(c)))) 542.34/241.38 down(f(f(f(fresh_constant)))) 542.34/241.38 down(g(g(g(a)))) 542.34/241.38 down(g(g(g(f(x0))))) 542.34/241.38 down(g(g(g(b)))) 542.34/241.38 down(g(g(g(c)))) 542.34/241.38 down(g(g(g(fresh_constant)))) 542.34/241.38 down(f(f(f(f(a))))) 542.34/241.38 down(f(f(f(f(b))))) 542.34/241.38 down(f(f(f(f(g(x0)))))) 542.34/241.38 down(f(f(f(f(c))))) 542.34/241.38 down(f(f(f(f(fresh_constant))))) 542.34/241.38 down(g(g(g(g(a))))) 542.34/241.38 down(g(g(g(g(f(x0)))))) 542.34/241.38 down(g(g(g(g(b))))) 542.34/241.38 down(g(g(g(g(c))))) 542.34/241.38 down(g(g(g(g(fresh_constant))))) 542.34/241.38 down(f(f(f(f(f(a)))))) 542.34/241.38 down(f(f(f(f(f(b)))))) 542.34/241.38 down(f(f(f(f(f(g(x0))))))) 542.34/241.38 down(f(f(f(f(f(c)))))) 542.34/241.38 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.38 down(g(g(g(g(g(a)))))) 542.34/241.38 down(g(g(g(g(g(f(x0))))))) 542.34/241.38 down(g(g(g(g(g(b)))))) 542.34/241.38 down(g(g(g(g(g(c)))))) 542.34/241.38 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.38 down(f(f(f(f(f(f(a))))))) 542.34/241.38 down(f(f(f(f(f(f(b))))))) 542.34/241.38 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.38 down(f(f(f(f(f(f(c))))))) 542.34/241.38 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.38 down(g(g(g(g(g(g(a))))))) 542.34/241.38 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.38 down(g(g(g(g(g(g(b))))))) 542.34/241.38 down(g(g(g(g(g(g(c))))))) 542.34/241.38 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.38 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.38 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.38 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.38 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.38 f_flat(up(x0)) 542.34/241.38 g_flat(up(x0)) 542.34/241.38 542.34/241.38 We have to consider all minimal (P,Q,R)-chains. 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (179) TransformationProof (EQUIVALENT) 542.34/241.38 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(down(g(g(g(g(g(f(x0))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.38 542.34/241.38 (TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))),TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.34/241.38 542.34/241.38 542.34/241.38 ---------------------------------------- 542.34/241.38 542.34/241.38 (180) 542.34/241.38 Obligation: 542.34/241.38 Q DP problem: 542.34/241.38 The TRS P consists of the following rules: 542.34/241.38 542.34/241.38 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.38 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.38 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.38 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.39 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.39 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.39 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.39 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.39 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.39 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.39 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.39 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.39 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.39 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.39 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.39 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.39 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.39 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.39 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.39 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.39 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.39 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.39 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.39 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.39 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.39 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.39 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.39 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.39 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.39 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.39 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.39 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.39 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.39 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.39 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.39 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.39 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.39 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.39 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.39 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.39 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.39 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.39 542.34/241.39 The TRS R consists of the following rules: 542.34/241.39 542.34/241.39 down(a) -> up(f(a)) 542.34/241.39 down(b) -> up(g(b)) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.39 down(f(a)) -> f_flat(down(a)) 542.34/241.39 down(f(b)) -> f_flat(down(b)) 542.34/241.39 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.39 down(f(c)) -> f_flat(down(c)) 542.34/241.39 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.39 down(g(a)) -> g_flat(down(a)) 542.34/241.39 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.39 down(g(b)) -> g_flat(down(b)) 542.34/241.39 down(g(c)) -> g_flat(down(c)) 542.34/241.39 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.39 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.39 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.39 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.39 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.39 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.39 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.39 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.39 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.39 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.39 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.39 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.39 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.39 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.39 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.39 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.39 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.39 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.39 542.34/241.39 The set Q consists of the following terms: 542.34/241.39 542.34/241.39 down(a) 542.34/241.39 down(b) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.39 down(f(a)) 542.34/241.39 down(f(b)) 542.34/241.39 down(f(g(x0))) 542.34/241.39 down(f(c)) 542.34/241.39 down(f(fresh_constant)) 542.34/241.39 down(g(a)) 542.34/241.39 down(g(f(x0))) 542.34/241.39 down(g(b)) 542.34/241.39 down(g(c)) 542.34/241.39 down(g(fresh_constant)) 542.34/241.39 down(f(f(a))) 542.34/241.39 down(f(f(b))) 542.34/241.39 down(f(f(g(x0)))) 542.34/241.39 down(f(f(c))) 542.34/241.39 down(f(f(fresh_constant))) 542.34/241.39 down(g(g(a))) 542.34/241.39 down(g(g(f(x0)))) 542.34/241.39 down(g(g(b))) 542.34/241.39 down(g(g(c))) 542.34/241.39 down(g(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) 542.34/241.39 down(f(f(f(g(x0))))) 542.34/241.39 down(f(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) 542.34/241.39 down(g(g(g(f(x0))))) 542.34/241.39 down(g(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(x0)))))) 542.34/241.39 down(f(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(x0)))))) 542.34/241.39 down(g(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(x0))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(x0))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 f_flat(up(x0)) 542.34/241.39 g_flat(up(x0)) 542.34/241.39 542.34/241.39 We have to consider all minimal (P,Q,R)-chains. 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (181) TransformationProof (EQUIVALENT) 542.34/241.39 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(down(f(f(f(f(f(c)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.39 542.34/241.39 (TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))),TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.34/241.39 542.34/241.39 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (182) 542.34/241.39 Obligation: 542.34/241.39 Q DP problem: 542.34/241.39 The TRS P consists of the following rules: 542.34/241.39 542.34/241.39 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.39 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.39 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.39 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.39 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.39 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.39 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.39 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.39 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.39 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.39 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.39 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.39 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.39 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.39 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.39 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.39 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.39 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.39 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.39 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.39 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.39 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.39 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.39 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.39 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.39 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.39 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.39 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.39 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.39 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.39 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.39 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.39 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.39 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.39 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.39 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.39 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.39 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.39 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.39 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.39 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.39 542.34/241.39 The TRS R consists of the following rules: 542.34/241.39 542.34/241.39 down(a) -> up(f(a)) 542.34/241.39 down(b) -> up(g(b)) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.39 down(f(a)) -> f_flat(down(a)) 542.34/241.39 down(f(b)) -> f_flat(down(b)) 542.34/241.39 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.39 down(f(c)) -> f_flat(down(c)) 542.34/241.39 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.39 down(g(a)) -> g_flat(down(a)) 542.34/241.39 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.39 down(g(b)) -> g_flat(down(b)) 542.34/241.39 down(g(c)) -> g_flat(down(c)) 542.34/241.39 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.39 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.39 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.39 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.39 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.39 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.39 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.39 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.39 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.39 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.39 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.39 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.39 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.39 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.39 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.39 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.39 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.39 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.39 542.34/241.39 The set Q consists of the following terms: 542.34/241.39 542.34/241.39 down(a) 542.34/241.39 down(b) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.39 down(f(a)) 542.34/241.39 down(f(b)) 542.34/241.39 down(f(g(x0))) 542.34/241.39 down(f(c)) 542.34/241.39 down(f(fresh_constant)) 542.34/241.39 down(g(a)) 542.34/241.39 down(g(f(x0))) 542.34/241.39 down(g(b)) 542.34/241.39 down(g(c)) 542.34/241.39 down(g(fresh_constant)) 542.34/241.39 down(f(f(a))) 542.34/241.39 down(f(f(b))) 542.34/241.39 down(f(f(g(x0)))) 542.34/241.39 down(f(f(c))) 542.34/241.39 down(f(f(fresh_constant))) 542.34/241.39 down(g(g(a))) 542.34/241.39 down(g(g(f(x0)))) 542.34/241.39 down(g(g(b))) 542.34/241.39 down(g(g(c))) 542.34/241.39 down(g(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) 542.34/241.39 down(f(f(f(g(x0))))) 542.34/241.39 down(f(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) 542.34/241.39 down(g(g(g(f(x0))))) 542.34/241.39 down(g(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(x0)))))) 542.34/241.39 down(f(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(x0)))))) 542.34/241.39 down(g(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(x0))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(x0))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 f_flat(up(x0)) 542.34/241.39 g_flat(up(x0)) 542.34/241.39 542.34/241.39 We have to consider all minimal (P,Q,R)-chains. 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (183) TransformationProof (EQUIVALENT) 542.34/241.39 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(down(f(f(f(f(f(fresh_constant)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.39 542.34/241.39 (TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))),TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.34/241.39 542.34/241.39 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (184) 542.34/241.39 Obligation: 542.34/241.39 Q DP problem: 542.34/241.39 The TRS P consists of the following rules: 542.34/241.39 542.34/241.39 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.39 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.39 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.39 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.39 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.39 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.39 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.39 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.39 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.39 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.39 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.39 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.39 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.39 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.39 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.39 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.39 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.39 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.39 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.39 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.39 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.39 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.39 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.39 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.39 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.39 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.39 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.39 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.39 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.39 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.39 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.39 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.39 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.39 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.39 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.39 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.39 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.39 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.39 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.39 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.39 542.34/241.39 The TRS R consists of the following rules: 542.34/241.39 542.34/241.39 down(a) -> up(f(a)) 542.34/241.39 down(b) -> up(g(b)) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.39 down(f(a)) -> f_flat(down(a)) 542.34/241.39 down(f(b)) -> f_flat(down(b)) 542.34/241.39 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.39 down(f(c)) -> f_flat(down(c)) 542.34/241.39 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.39 down(g(a)) -> g_flat(down(a)) 542.34/241.39 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.39 down(g(b)) -> g_flat(down(b)) 542.34/241.39 down(g(c)) -> g_flat(down(c)) 542.34/241.39 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.39 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.39 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.39 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.39 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.39 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.39 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.39 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.39 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.39 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.39 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.39 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.39 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.39 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.39 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.39 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.39 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.39 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.39 542.34/241.39 The set Q consists of the following terms: 542.34/241.39 542.34/241.39 down(a) 542.34/241.39 down(b) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.39 down(f(a)) 542.34/241.39 down(f(b)) 542.34/241.39 down(f(g(x0))) 542.34/241.39 down(f(c)) 542.34/241.39 down(f(fresh_constant)) 542.34/241.39 down(g(a)) 542.34/241.39 down(g(f(x0))) 542.34/241.39 down(g(b)) 542.34/241.39 down(g(c)) 542.34/241.39 down(g(fresh_constant)) 542.34/241.39 down(f(f(a))) 542.34/241.39 down(f(f(b))) 542.34/241.39 down(f(f(g(x0)))) 542.34/241.39 down(f(f(c))) 542.34/241.39 down(f(f(fresh_constant))) 542.34/241.39 down(g(g(a))) 542.34/241.39 down(g(g(f(x0)))) 542.34/241.39 down(g(g(b))) 542.34/241.39 down(g(g(c))) 542.34/241.39 down(g(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) 542.34/241.39 down(f(f(f(g(x0))))) 542.34/241.39 down(f(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) 542.34/241.39 down(g(g(g(f(x0))))) 542.34/241.39 down(g(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(x0)))))) 542.34/241.39 down(f(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(x0)))))) 542.34/241.39 down(g(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(x0))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(x0))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 f_flat(up(x0)) 542.34/241.39 g_flat(up(x0)) 542.34/241.39 542.34/241.39 We have to consider all minimal (P,Q,R)-chains. 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (185) TransformationProof (EQUIVALENT) 542.34/241.39 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(a))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.39 542.34/241.39 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.34/241.39 542.34/241.39 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (186) 542.34/241.39 Obligation: 542.34/241.39 Q DP problem: 542.34/241.39 The TRS P consists of the following rules: 542.34/241.39 542.34/241.39 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.39 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.39 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.39 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.39 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.39 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.39 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.39 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.39 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.39 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.39 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.39 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.39 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.39 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.39 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.39 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.39 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.39 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.39 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.39 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.39 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.39 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.39 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.39 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.39 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.39 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.39 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.39 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.39 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.39 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.39 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.39 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.39 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.39 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.39 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.39 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.39 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.39 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.39 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.39 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.39 542.34/241.39 The TRS R consists of the following rules: 542.34/241.39 542.34/241.39 down(a) -> up(f(a)) 542.34/241.39 down(b) -> up(g(b)) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.39 down(f(a)) -> f_flat(down(a)) 542.34/241.39 down(f(b)) -> f_flat(down(b)) 542.34/241.39 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.39 down(f(c)) -> f_flat(down(c)) 542.34/241.39 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.39 down(g(a)) -> g_flat(down(a)) 542.34/241.39 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.39 down(g(b)) -> g_flat(down(b)) 542.34/241.39 down(g(c)) -> g_flat(down(c)) 542.34/241.39 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.39 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.39 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.39 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.39 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.39 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.39 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.39 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.39 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.39 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.39 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.39 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.39 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.39 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.39 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.39 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.39 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.39 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.39 542.34/241.39 The set Q consists of the following terms: 542.34/241.39 542.34/241.39 down(a) 542.34/241.39 down(b) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.39 down(f(a)) 542.34/241.39 down(f(b)) 542.34/241.39 down(f(g(x0))) 542.34/241.39 down(f(c)) 542.34/241.39 down(f(fresh_constant)) 542.34/241.39 down(g(a)) 542.34/241.39 down(g(f(x0))) 542.34/241.39 down(g(b)) 542.34/241.39 down(g(c)) 542.34/241.39 down(g(fresh_constant)) 542.34/241.39 down(f(f(a))) 542.34/241.39 down(f(f(b))) 542.34/241.39 down(f(f(g(x0)))) 542.34/241.39 down(f(f(c))) 542.34/241.39 down(f(f(fresh_constant))) 542.34/241.39 down(g(g(a))) 542.34/241.39 down(g(g(f(x0)))) 542.34/241.39 down(g(g(b))) 542.34/241.39 down(g(g(c))) 542.34/241.39 down(g(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) 542.34/241.39 down(f(f(f(g(x0))))) 542.34/241.39 down(f(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) 542.34/241.39 down(g(g(g(f(x0))))) 542.34/241.39 down(g(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(x0)))))) 542.34/241.39 down(f(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(x0)))))) 542.34/241.39 down(g(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(x0))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(x0))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 f_flat(up(x0)) 542.34/241.39 g_flat(up(x0)) 542.34/241.39 542.34/241.39 We have to consider all minimal (P,Q,R)-chains. 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (187) TransformationProof (EQUIVALENT) 542.34/241.39 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(b))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.39 542.34/241.39 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.34/241.39 542.34/241.39 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (188) 542.34/241.39 Obligation: 542.34/241.39 Q DP problem: 542.34/241.39 The TRS P consists of the following rules: 542.34/241.39 542.34/241.39 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.39 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.39 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.39 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.39 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.39 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.39 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.39 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.39 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.39 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.39 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.39 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.39 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.39 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.39 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.39 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.39 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.39 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.39 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.39 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.39 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.39 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.39 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.39 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.39 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.39 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.39 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.39 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.39 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.39 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.39 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.39 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.39 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.39 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.39 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.39 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.39 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.39 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.39 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.39 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.39 542.34/241.39 The TRS R consists of the following rules: 542.34/241.39 542.34/241.39 down(a) -> up(f(a)) 542.34/241.39 down(b) -> up(g(b)) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.39 down(f(a)) -> f_flat(down(a)) 542.34/241.39 down(f(b)) -> f_flat(down(b)) 542.34/241.39 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.39 down(f(c)) -> f_flat(down(c)) 542.34/241.39 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.39 down(g(a)) -> g_flat(down(a)) 542.34/241.39 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.39 down(g(b)) -> g_flat(down(b)) 542.34/241.39 down(g(c)) -> g_flat(down(c)) 542.34/241.39 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.39 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.39 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.39 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.39 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.39 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.39 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.39 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.39 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.39 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.39 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.39 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.39 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.39 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.39 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.39 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.39 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.39 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.39 542.34/241.39 The set Q consists of the following terms: 542.34/241.39 542.34/241.39 down(a) 542.34/241.39 down(b) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.39 down(f(a)) 542.34/241.39 down(f(b)) 542.34/241.39 down(f(g(x0))) 542.34/241.39 down(f(c)) 542.34/241.39 down(f(fresh_constant)) 542.34/241.39 down(g(a)) 542.34/241.39 down(g(f(x0))) 542.34/241.39 down(g(b)) 542.34/241.39 down(g(c)) 542.34/241.39 down(g(fresh_constant)) 542.34/241.39 down(f(f(a))) 542.34/241.39 down(f(f(b))) 542.34/241.39 down(f(f(g(x0)))) 542.34/241.39 down(f(f(c))) 542.34/241.39 down(f(f(fresh_constant))) 542.34/241.39 down(g(g(a))) 542.34/241.39 down(g(g(f(x0)))) 542.34/241.39 down(g(g(b))) 542.34/241.39 down(g(g(c))) 542.34/241.39 down(g(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) 542.34/241.39 down(f(f(f(g(x0))))) 542.34/241.39 down(f(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) 542.34/241.39 down(g(g(g(f(x0))))) 542.34/241.39 down(g(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(x0)))))) 542.34/241.39 down(f(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(x0)))))) 542.34/241.39 down(g(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(x0))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(x0))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 f_flat(up(x0)) 542.34/241.39 g_flat(up(x0)) 542.34/241.39 542.34/241.39 We have to consider all minimal (P,Q,R)-chains. 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (189) TransformationProof (EQUIVALENT) 542.34/241.39 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(g(x0)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.39 542.34/241.39 (TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))),TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 542.34/241.39 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (190) 542.34/241.39 Obligation: 542.34/241.39 Q DP problem: 542.34/241.39 The TRS P consists of the following rules: 542.34/241.39 542.34/241.39 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.39 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.39 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.39 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.39 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.39 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.39 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.39 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.39 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.39 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.39 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.39 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.39 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.39 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.39 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.39 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.39 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.39 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.39 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.39 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.39 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.39 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.39 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.39 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.39 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.39 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.39 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.39 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.39 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.39 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.39 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.39 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.39 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.39 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.39 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.39 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.39 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.39 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.39 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.39 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.39 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 542.34/241.39 The TRS R consists of the following rules: 542.34/241.39 542.34/241.39 down(a) -> up(f(a)) 542.34/241.39 down(b) -> up(g(b)) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.39 down(f(a)) -> f_flat(down(a)) 542.34/241.39 down(f(b)) -> f_flat(down(b)) 542.34/241.39 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.39 down(f(c)) -> f_flat(down(c)) 542.34/241.39 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.39 down(g(a)) -> g_flat(down(a)) 542.34/241.39 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.39 down(g(b)) -> g_flat(down(b)) 542.34/241.39 down(g(c)) -> g_flat(down(c)) 542.34/241.39 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.39 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.39 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.39 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.39 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.39 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.39 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.39 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.39 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.39 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.39 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.39 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.39 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.39 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.39 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.39 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.39 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.39 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.39 542.34/241.39 The set Q consists of the following terms: 542.34/241.39 542.34/241.39 down(a) 542.34/241.39 down(b) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.39 down(f(a)) 542.34/241.39 down(f(b)) 542.34/241.39 down(f(g(x0))) 542.34/241.39 down(f(c)) 542.34/241.39 down(f(fresh_constant)) 542.34/241.39 down(g(a)) 542.34/241.39 down(g(f(x0))) 542.34/241.39 down(g(b)) 542.34/241.39 down(g(c)) 542.34/241.39 down(g(fresh_constant)) 542.34/241.39 down(f(f(a))) 542.34/241.39 down(f(f(b))) 542.34/241.39 down(f(f(g(x0)))) 542.34/241.39 down(f(f(c))) 542.34/241.39 down(f(f(fresh_constant))) 542.34/241.39 down(g(g(a))) 542.34/241.39 down(g(g(f(x0)))) 542.34/241.39 down(g(g(b))) 542.34/241.39 down(g(g(c))) 542.34/241.39 down(g(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) 542.34/241.39 down(f(f(f(g(x0))))) 542.34/241.39 down(f(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) 542.34/241.39 down(g(g(g(f(x0))))) 542.34/241.39 down(g(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(x0)))))) 542.34/241.39 down(f(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(x0)))))) 542.34/241.39 down(g(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(x0))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(x0))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 f_flat(up(x0)) 542.34/241.39 g_flat(up(x0)) 542.34/241.39 542.34/241.39 We have to consider all minimal (P,Q,R)-chains. 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (191) TransformationProof (EQUIVALENT) 542.34/241.39 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(down(g(g(g(g(g(b)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.39 542.34/241.39 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.34/241.39 542.34/241.39 542.34/241.39 ---------------------------------------- 542.34/241.39 542.34/241.39 (192) 542.34/241.39 Obligation: 542.34/241.39 Q DP problem: 542.34/241.39 The TRS P consists of the following rules: 542.34/241.39 542.34/241.39 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.39 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.39 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.39 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.39 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.39 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.39 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.39 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.39 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.39 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.39 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.39 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.39 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.39 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.39 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.39 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.39 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.39 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.39 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.39 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.39 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.39 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.39 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.39 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.39 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.39 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.39 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.39 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.39 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.39 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.39 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.39 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.39 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.39 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.39 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.39 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.39 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.39 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.39 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.39 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.39 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.39 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.39 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.39 542.34/241.39 The TRS R consists of the following rules: 542.34/241.39 542.34/241.39 down(a) -> up(f(a)) 542.34/241.39 down(b) -> up(g(b)) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.39 down(f(a)) -> f_flat(down(a)) 542.34/241.39 down(f(b)) -> f_flat(down(b)) 542.34/241.39 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.39 down(f(c)) -> f_flat(down(c)) 542.34/241.39 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.39 down(g(a)) -> g_flat(down(a)) 542.34/241.39 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.39 down(g(b)) -> g_flat(down(b)) 542.34/241.39 down(g(c)) -> g_flat(down(c)) 542.34/241.39 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.39 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.39 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.39 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.39 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.39 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.39 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.39 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.39 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.39 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.39 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.39 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.39 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.39 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.39 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.39 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.39 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.39 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.39 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.39 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.39 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.39 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.39 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.39 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.39 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.39 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.39 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.39 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.39 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.39 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.39 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.39 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.39 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.39 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.39 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.39 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.39 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.39 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.39 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.39 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.39 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.39 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.39 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.39 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.39 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.39 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.39 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.39 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.39 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.39 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.39 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.39 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.39 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.39 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.39 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.39 542.34/241.39 The set Q consists of the following terms: 542.34/241.39 542.34/241.39 down(a) 542.34/241.39 down(b) 542.34/241.39 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.39 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.39 down(f(a)) 542.34/241.39 down(f(b)) 542.34/241.39 down(f(g(x0))) 542.34/241.39 down(f(c)) 542.34/241.39 down(f(fresh_constant)) 542.34/241.39 down(g(a)) 542.34/241.39 down(g(f(x0))) 542.34/241.39 down(g(b)) 542.34/241.39 down(g(c)) 542.34/241.39 down(g(fresh_constant)) 542.34/241.39 down(f(f(a))) 542.34/241.39 down(f(f(b))) 542.34/241.39 down(f(f(g(x0)))) 542.34/241.39 down(f(f(c))) 542.34/241.39 down(f(f(fresh_constant))) 542.34/241.39 down(g(g(a))) 542.34/241.39 down(g(g(f(x0)))) 542.34/241.40 down(g(g(b))) 542.34/241.40 down(g(g(c))) 542.34/241.40 down(g(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) 542.34/241.40 down(f(f(f(g(x0))))) 542.34/241.40 down(f(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) 542.34/241.40 down(g(g(g(f(x0))))) 542.34/241.40 down(g(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(x0)))))) 542.34/241.40 down(f(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(x0)))))) 542.34/241.40 down(g(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(x0))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(x0))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 f_flat(up(x0)) 542.34/241.40 g_flat(up(x0)) 542.34/241.40 542.34/241.40 We have to consider all minimal (P,Q,R)-chains. 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (193) TransformationProof (EQUIVALENT) 542.34/241.40 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(down(g(g(g(g(g(c)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.40 542.34/241.40 (TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))),TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c))))))))) 542.34/241.40 542.34/241.40 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (194) 542.34/241.40 Obligation: 542.34/241.40 Q DP problem: 542.34/241.40 The TRS P consists of the following rules: 542.34/241.40 542.34/241.40 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.40 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.40 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.40 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.40 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.40 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.40 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.40 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.40 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.40 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.40 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.40 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.40 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.40 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.40 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.40 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.40 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.40 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.40 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.40 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.40 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.40 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.40 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.40 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.40 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.40 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.40 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.40 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.40 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.40 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.40 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.40 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.40 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.40 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.40 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.40 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.40 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.40 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.40 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.40 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.40 542.34/241.40 The TRS R consists of the following rules: 542.34/241.40 542.34/241.40 down(a) -> up(f(a)) 542.34/241.40 down(b) -> up(g(b)) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.40 down(f(a)) -> f_flat(down(a)) 542.34/241.40 down(f(b)) -> f_flat(down(b)) 542.34/241.40 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.40 down(f(c)) -> f_flat(down(c)) 542.34/241.40 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.40 down(g(a)) -> g_flat(down(a)) 542.34/241.40 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.40 down(g(b)) -> g_flat(down(b)) 542.34/241.40 down(g(c)) -> g_flat(down(c)) 542.34/241.40 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.40 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.40 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.40 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.40 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.40 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.40 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.40 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.40 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.40 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.40 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.40 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.40 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.40 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.40 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.40 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.40 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.40 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.40 542.34/241.40 The set Q consists of the following terms: 542.34/241.40 542.34/241.40 down(a) 542.34/241.40 down(b) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.40 down(f(a)) 542.34/241.40 down(f(b)) 542.34/241.40 down(f(g(x0))) 542.34/241.40 down(f(c)) 542.34/241.40 down(f(fresh_constant)) 542.34/241.40 down(g(a)) 542.34/241.40 down(g(f(x0))) 542.34/241.40 down(g(b)) 542.34/241.40 down(g(c)) 542.34/241.40 down(g(fresh_constant)) 542.34/241.40 down(f(f(a))) 542.34/241.40 down(f(f(b))) 542.34/241.40 down(f(f(g(x0)))) 542.34/241.40 down(f(f(c))) 542.34/241.40 down(f(f(fresh_constant))) 542.34/241.40 down(g(g(a))) 542.34/241.40 down(g(g(f(x0)))) 542.34/241.40 down(g(g(b))) 542.34/241.40 down(g(g(c))) 542.34/241.40 down(g(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) 542.34/241.40 down(f(f(f(g(x0))))) 542.34/241.40 down(f(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) 542.34/241.40 down(g(g(g(f(x0))))) 542.34/241.40 down(g(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(x0)))))) 542.34/241.40 down(f(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(x0)))))) 542.34/241.40 down(g(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(x0))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(x0))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 f_flat(up(x0)) 542.34/241.40 g_flat(up(x0)) 542.34/241.40 542.34/241.40 We have to consider all minimal (P,Q,R)-chains. 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (195) TransformationProof (EQUIVALENT) 542.34/241.40 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(down(g(g(g(g(g(fresh_constant)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.40 542.34/241.40 (TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))),TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 542.34/241.40 542.34/241.40 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (196) 542.34/241.40 Obligation: 542.34/241.40 Q DP problem: 542.34/241.40 The TRS P consists of the following rules: 542.34/241.40 542.34/241.40 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.40 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.40 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.40 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.40 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.40 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.40 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.40 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.40 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.40 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.40 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.40 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.40 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.40 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.40 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.40 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.40 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.40 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.40 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.40 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.40 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.40 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.40 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.40 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.40 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.40 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.40 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.40 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.40 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.40 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.40 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.40 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.40 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.40 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.40 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.40 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.40 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.40 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.40 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.40 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.40 542.34/241.40 The TRS R consists of the following rules: 542.34/241.40 542.34/241.40 down(a) -> up(f(a)) 542.34/241.40 down(b) -> up(g(b)) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.40 down(f(a)) -> f_flat(down(a)) 542.34/241.40 down(f(b)) -> f_flat(down(b)) 542.34/241.40 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.40 down(f(c)) -> f_flat(down(c)) 542.34/241.40 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.40 down(g(a)) -> g_flat(down(a)) 542.34/241.40 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.40 down(g(b)) -> g_flat(down(b)) 542.34/241.40 down(g(c)) -> g_flat(down(c)) 542.34/241.40 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.40 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.40 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.40 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.40 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.40 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.40 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.40 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.40 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.40 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.40 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.40 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.40 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.40 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.40 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.40 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.40 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.40 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.40 542.34/241.40 The set Q consists of the following terms: 542.34/241.40 542.34/241.40 down(a) 542.34/241.40 down(b) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.40 down(f(a)) 542.34/241.40 down(f(b)) 542.34/241.40 down(f(g(x0))) 542.34/241.40 down(f(c)) 542.34/241.40 down(f(fresh_constant)) 542.34/241.40 down(g(a)) 542.34/241.40 down(g(f(x0))) 542.34/241.40 down(g(b)) 542.34/241.40 down(g(c)) 542.34/241.40 down(g(fresh_constant)) 542.34/241.40 down(f(f(a))) 542.34/241.40 down(f(f(b))) 542.34/241.40 down(f(f(g(x0)))) 542.34/241.40 down(f(f(c))) 542.34/241.40 down(f(f(fresh_constant))) 542.34/241.40 down(g(g(a))) 542.34/241.40 down(g(g(f(x0)))) 542.34/241.40 down(g(g(b))) 542.34/241.40 down(g(g(c))) 542.34/241.40 down(g(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) 542.34/241.40 down(f(f(f(g(x0))))) 542.34/241.40 down(f(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) 542.34/241.40 down(g(g(g(f(x0))))) 542.34/241.40 down(g(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(x0)))))) 542.34/241.40 down(f(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(x0)))))) 542.34/241.40 down(g(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(x0))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(x0))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 f_flat(up(x0)) 542.34/241.40 g_flat(up(x0)) 542.34/241.40 542.34/241.40 We have to consider all minimal (P,Q,R)-chains. 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (197) TransformationProof (EQUIVALENT) 542.34/241.40 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(a))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.40 542.34/241.40 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 542.34/241.40 542.34/241.40 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (198) 542.34/241.40 Obligation: 542.34/241.40 Q DP problem: 542.34/241.40 The TRS P consists of the following rules: 542.34/241.40 542.34/241.40 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.40 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.40 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.40 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.40 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.40 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.40 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.40 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.40 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.40 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.40 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.40 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.40 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.40 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.40 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.40 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.40 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.40 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.40 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.40 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.40 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.40 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.40 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.40 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.40 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.40 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.40 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.40 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.40 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.40 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.40 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.40 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.40 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.40 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.40 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.40 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.40 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.40 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.40 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.40 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.40 542.34/241.40 The TRS R consists of the following rules: 542.34/241.40 542.34/241.40 down(a) -> up(f(a)) 542.34/241.40 down(b) -> up(g(b)) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.40 down(f(a)) -> f_flat(down(a)) 542.34/241.40 down(f(b)) -> f_flat(down(b)) 542.34/241.40 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.40 down(f(c)) -> f_flat(down(c)) 542.34/241.40 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.40 down(g(a)) -> g_flat(down(a)) 542.34/241.40 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.40 down(g(b)) -> g_flat(down(b)) 542.34/241.40 down(g(c)) -> g_flat(down(c)) 542.34/241.40 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.40 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.40 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.40 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.40 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.40 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.40 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.40 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.40 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.40 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.40 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.40 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.40 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.40 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.40 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.40 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.40 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.40 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.40 542.34/241.40 The set Q consists of the following terms: 542.34/241.40 542.34/241.40 down(a) 542.34/241.40 down(b) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.40 down(f(a)) 542.34/241.40 down(f(b)) 542.34/241.40 down(f(g(x0))) 542.34/241.40 down(f(c)) 542.34/241.40 down(f(fresh_constant)) 542.34/241.40 down(g(a)) 542.34/241.40 down(g(f(x0))) 542.34/241.40 down(g(b)) 542.34/241.40 down(g(c)) 542.34/241.40 down(g(fresh_constant)) 542.34/241.40 down(f(f(a))) 542.34/241.40 down(f(f(b))) 542.34/241.40 down(f(f(g(x0)))) 542.34/241.40 down(f(f(c))) 542.34/241.40 down(f(f(fresh_constant))) 542.34/241.40 down(g(g(a))) 542.34/241.40 down(g(g(f(x0)))) 542.34/241.40 down(g(g(b))) 542.34/241.40 down(g(g(c))) 542.34/241.40 down(g(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) 542.34/241.40 down(f(f(f(g(x0))))) 542.34/241.40 down(f(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) 542.34/241.40 down(g(g(g(f(x0))))) 542.34/241.40 down(g(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(x0)))))) 542.34/241.40 down(f(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(x0)))))) 542.34/241.40 down(g(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(x0))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(x0))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 f_flat(up(x0)) 542.34/241.40 g_flat(up(x0)) 542.34/241.40 542.34/241.40 We have to consider all minimal (P,Q,R)-chains. 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (199) TransformationProof (EQUIVALENT) 542.34/241.40 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(f(x0)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.40 542.34/241.40 (TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))),TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 542.34/241.40 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (200) 542.34/241.40 Obligation: 542.34/241.40 Q DP problem: 542.34/241.40 The TRS P consists of the following rules: 542.34/241.40 542.34/241.40 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.40 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.40 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.40 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.40 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.40 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.40 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.40 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.40 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.40 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.40 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.40 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.40 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.40 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.40 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.40 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.40 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.40 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.40 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.40 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.40 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.40 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.40 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.40 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.40 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.40 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.40 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.40 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.40 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.40 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.40 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.40 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.40 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.40 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.40 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.40 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.40 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.40 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.40 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.40 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 542.34/241.40 The TRS R consists of the following rules: 542.34/241.40 542.34/241.40 down(a) -> up(f(a)) 542.34/241.40 down(b) -> up(g(b)) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.40 down(f(a)) -> f_flat(down(a)) 542.34/241.40 down(f(b)) -> f_flat(down(b)) 542.34/241.40 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.40 down(f(c)) -> f_flat(down(c)) 542.34/241.40 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.40 down(g(a)) -> g_flat(down(a)) 542.34/241.40 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.40 down(g(b)) -> g_flat(down(b)) 542.34/241.40 down(g(c)) -> g_flat(down(c)) 542.34/241.40 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.40 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.40 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.40 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.40 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.40 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.40 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.40 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.40 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.40 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.40 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.40 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.40 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.40 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.40 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.40 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.40 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.40 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.40 542.34/241.40 The set Q consists of the following terms: 542.34/241.40 542.34/241.40 down(a) 542.34/241.40 down(b) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.40 down(f(a)) 542.34/241.40 down(f(b)) 542.34/241.40 down(f(g(x0))) 542.34/241.40 down(f(c)) 542.34/241.40 down(f(fresh_constant)) 542.34/241.40 down(g(a)) 542.34/241.40 down(g(f(x0))) 542.34/241.40 down(g(b)) 542.34/241.40 down(g(c)) 542.34/241.40 down(g(fresh_constant)) 542.34/241.40 down(f(f(a))) 542.34/241.40 down(f(f(b))) 542.34/241.40 down(f(f(g(x0)))) 542.34/241.40 down(f(f(c))) 542.34/241.40 down(f(f(fresh_constant))) 542.34/241.40 down(g(g(a))) 542.34/241.40 down(g(g(f(x0)))) 542.34/241.40 down(g(g(b))) 542.34/241.40 down(g(g(c))) 542.34/241.40 down(g(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) 542.34/241.40 down(f(f(f(g(x0))))) 542.34/241.40 down(f(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) 542.34/241.40 down(g(g(g(f(x0))))) 542.34/241.40 down(g(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(x0)))))) 542.34/241.40 down(f(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(x0)))))) 542.34/241.40 down(g(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(x0))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(x0))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 f_flat(up(x0)) 542.34/241.40 g_flat(up(x0)) 542.34/241.40 542.34/241.40 We have to consider all minimal (P,Q,R)-chains. 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (201) TransformationProof (EQUIVALENT) 542.34/241.40 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(c))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.40 542.34/241.40 (TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))),TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 542.34/241.40 542.34/241.40 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (202) 542.34/241.40 Obligation: 542.34/241.40 Q DP problem: 542.34/241.40 The TRS P consists of the following rules: 542.34/241.40 542.34/241.40 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.40 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.40 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.40 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.40 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.40 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.40 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.40 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.40 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.40 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.40 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.40 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.40 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.40 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.40 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.40 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.40 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.40 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.40 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.40 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.40 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.40 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.40 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.40 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.40 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.40 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.40 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.40 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.40 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.40 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.40 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.40 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.40 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.40 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.40 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.40 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.40 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.40 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.40 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.40 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.40 542.34/241.40 The TRS R consists of the following rules: 542.34/241.40 542.34/241.40 down(a) -> up(f(a)) 542.34/241.40 down(b) -> up(g(b)) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.40 down(f(a)) -> f_flat(down(a)) 542.34/241.40 down(f(b)) -> f_flat(down(b)) 542.34/241.40 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.40 down(f(c)) -> f_flat(down(c)) 542.34/241.40 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.40 down(g(a)) -> g_flat(down(a)) 542.34/241.40 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.40 down(g(b)) -> g_flat(down(b)) 542.34/241.40 down(g(c)) -> g_flat(down(c)) 542.34/241.40 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.40 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.40 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.40 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.40 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.40 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.40 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.40 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.40 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.40 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.40 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.40 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.40 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.40 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.40 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.40 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.40 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.40 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.40 542.34/241.40 The set Q consists of the following terms: 542.34/241.40 542.34/241.40 down(a) 542.34/241.40 down(b) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.40 down(f(a)) 542.34/241.40 down(f(b)) 542.34/241.40 down(f(g(x0))) 542.34/241.40 down(f(c)) 542.34/241.40 down(f(fresh_constant)) 542.34/241.40 down(g(a)) 542.34/241.40 down(g(f(x0))) 542.34/241.40 down(g(b)) 542.34/241.40 down(g(c)) 542.34/241.40 down(g(fresh_constant)) 542.34/241.40 down(f(f(a))) 542.34/241.40 down(f(f(b))) 542.34/241.40 down(f(f(g(x0)))) 542.34/241.40 down(f(f(c))) 542.34/241.40 down(f(f(fresh_constant))) 542.34/241.40 down(g(g(a))) 542.34/241.40 down(g(g(f(x0)))) 542.34/241.40 down(g(g(b))) 542.34/241.40 down(g(g(c))) 542.34/241.40 down(g(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) 542.34/241.40 down(f(f(f(g(x0))))) 542.34/241.40 down(f(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) 542.34/241.40 down(g(g(g(f(x0))))) 542.34/241.40 down(g(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(x0)))))) 542.34/241.40 down(f(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(x0)))))) 542.34/241.40 down(g(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(x0))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(x0))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 f_flat(up(x0)) 542.34/241.40 g_flat(up(x0)) 542.34/241.40 542.34/241.40 We have to consider all minimal (P,Q,R)-chains. 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (203) TransformationProof (EQUIVALENT) 542.34/241.40 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.40 542.34/241.40 (TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))),TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 542.34/241.40 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (204) 542.34/241.40 Obligation: 542.34/241.40 Q DP problem: 542.34/241.40 The TRS P consists of the following rules: 542.34/241.40 542.34/241.40 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.40 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.40 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.40 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.40 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.40 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.40 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.40 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.40 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.40 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.40 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.40 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.40 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.40 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.40 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.40 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.40 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.40 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.40 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.40 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.40 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.40 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.40 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.40 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.40 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.40 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.40 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.40 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.40 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.40 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.40 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.40 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.40 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.40 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.40 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.40 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.40 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.40 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.40 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.40 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 542.34/241.40 The TRS R consists of the following rules: 542.34/241.40 542.34/241.40 down(a) -> up(f(a)) 542.34/241.40 down(b) -> up(g(b)) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.40 down(f(a)) -> f_flat(down(a)) 542.34/241.40 down(f(b)) -> f_flat(down(b)) 542.34/241.40 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.40 down(f(c)) -> f_flat(down(c)) 542.34/241.40 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.40 down(g(a)) -> g_flat(down(a)) 542.34/241.40 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.40 down(g(b)) -> g_flat(down(b)) 542.34/241.40 down(g(c)) -> g_flat(down(c)) 542.34/241.40 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.40 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.40 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.40 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.40 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.40 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.40 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.40 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.40 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.40 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.40 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.40 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.40 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.40 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.40 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.40 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.40 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.40 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.40 542.34/241.40 The set Q consists of the following terms: 542.34/241.40 542.34/241.40 down(a) 542.34/241.40 down(b) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.40 down(f(a)) 542.34/241.40 down(f(b)) 542.34/241.40 down(f(g(x0))) 542.34/241.40 down(f(c)) 542.34/241.40 down(f(fresh_constant)) 542.34/241.40 down(g(a)) 542.34/241.40 down(g(f(x0))) 542.34/241.40 down(g(b)) 542.34/241.40 down(g(c)) 542.34/241.40 down(g(fresh_constant)) 542.34/241.40 down(f(f(a))) 542.34/241.40 down(f(f(b))) 542.34/241.40 down(f(f(g(x0)))) 542.34/241.40 down(f(f(c))) 542.34/241.40 down(f(f(fresh_constant))) 542.34/241.40 down(g(g(a))) 542.34/241.40 down(g(g(f(x0)))) 542.34/241.40 down(g(g(b))) 542.34/241.40 down(g(g(c))) 542.34/241.40 down(g(g(fresh_constant))) 542.34/241.40 down(f(f(f(a)))) 542.34/241.40 down(f(f(f(b)))) 542.34/241.40 down(f(f(f(g(x0))))) 542.34/241.40 down(f(f(f(c)))) 542.34/241.40 down(f(f(f(fresh_constant)))) 542.34/241.40 down(g(g(g(a)))) 542.34/241.40 down(g(g(g(f(x0))))) 542.34/241.40 down(g(g(g(b)))) 542.34/241.40 down(g(g(g(c)))) 542.34/241.40 down(g(g(g(fresh_constant)))) 542.34/241.40 down(f(f(f(f(a))))) 542.34/241.40 down(f(f(f(f(b))))) 542.34/241.40 down(f(f(f(f(g(x0)))))) 542.34/241.40 down(f(f(f(f(c))))) 542.34/241.40 down(f(f(f(f(fresh_constant))))) 542.34/241.40 down(g(g(g(g(a))))) 542.34/241.40 down(g(g(g(g(f(x0)))))) 542.34/241.40 down(g(g(g(g(b))))) 542.34/241.40 down(g(g(g(g(c))))) 542.34/241.40 down(g(g(g(g(fresh_constant))))) 542.34/241.40 down(f(f(f(f(f(a)))))) 542.34/241.40 down(f(f(f(f(f(b)))))) 542.34/241.40 down(f(f(f(f(f(g(x0))))))) 542.34/241.40 down(f(f(f(f(f(c)))))) 542.34/241.40 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.40 down(g(g(g(g(g(a)))))) 542.34/241.40 down(g(g(g(g(g(f(x0))))))) 542.34/241.40 down(g(g(g(g(g(b)))))) 542.34/241.40 down(g(g(g(g(g(c)))))) 542.34/241.40 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.40 down(f(f(f(f(f(f(a))))))) 542.34/241.40 down(f(f(f(f(f(f(b))))))) 542.34/241.40 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.40 down(f(f(f(f(f(f(c))))))) 542.34/241.40 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.40 down(g(g(g(g(g(g(a))))))) 542.34/241.40 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.40 down(g(g(g(g(g(g(b))))))) 542.34/241.40 down(g(g(g(g(g(g(c))))))) 542.34/241.40 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.40 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.40 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 f_flat(up(x0)) 542.34/241.40 g_flat(up(x0)) 542.34/241.40 542.34/241.40 We have to consider all minimal (P,Q,R)-chains. 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (205) TransformationProof (EQUIVALENT) 542.34/241.40 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(a)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.40 542.34/241.40 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 542.34/241.40 542.34/241.40 542.34/241.40 ---------------------------------------- 542.34/241.40 542.34/241.40 (206) 542.34/241.40 Obligation: 542.34/241.40 Q DP problem: 542.34/241.40 The TRS P consists of the following rules: 542.34/241.40 542.34/241.40 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.40 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.40 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.40 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.40 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.40 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.40 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.40 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.40 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.40 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.40 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.40 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.40 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.40 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.40 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.40 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.40 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.40 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.40 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.40 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.40 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.40 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.40 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.40 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.40 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.40 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.40 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.40 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.40 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.40 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.40 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.40 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.40 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.40 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.40 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.40 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.40 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.40 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.40 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.40 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.40 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.40 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.40 542.34/241.40 The TRS R consists of the following rules: 542.34/241.40 542.34/241.40 down(a) -> up(f(a)) 542.34/241.40 down(b) -> up(g(b)) 542.34/241.40 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.40 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.40 down(f(a)) -> f_flat(down(a)) 542.34/241.40 down(f(b)) -> f_flat(down(b)) 542.34/241.40 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.40 down(f(c)) -> f_flat(down(c)) 542.34/241.40 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.40 down(g(a)) -> g_flat(down(a)) 542.34/241.40 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.40 down(g(b)) -> g_flat(down(b)) 542.34/241.40 down(g(c)) -> g_flat(down(c)) 542.34/241.40 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.40 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.40 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.40 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.40 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.40 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.41 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.41 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.41 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.41 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.41 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.41 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.41 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.41 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.41 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.41 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.41 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.41 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.41 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.41 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.41 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.41 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.41 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.41 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.41 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.41 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.41 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.41 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.41 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.41 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.41 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.41 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.41 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.41 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.41 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.41 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.41 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.41 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.41 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.41 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.41 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.41 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.41 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.41 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.41 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.41 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.41 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.41 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.41 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.41 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.41 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.41 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.41 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.41 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.41 542.34/241.41 The set Q consists of the following terms: 542.34/241.41 542.34/241.41 down(a) 542.34/241.41 down(b) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.41 down(f(a)) 542.34/241.41 down(f(b)) 542.34/241.41 down(f(g(x0))) 542.34/241.41 down(f(c)) 542.34/241.41 down(f(fresh_constant)) 542.34/241.41 down(g(a)) 542.34/241.41 down(g(f(x0))) 542.34/241.41 down(g(b)) 542.34/241.41 down(g(c)) 542.34/241.41 down(g(fresh_constant)) 542.34/241.41 down(f(f(a))) 542.34/241.41 down(f(f(b))) 542.34/241.41 down(f(f(g(x0)))) 542.34/241.41 down(f(f(c))) 542.34/241.41 down(f(f(fresh_constant))) 542.34/241.41 down(g(g(a))) 542.34/241.41 down(g(g(f(x0)))) 542.34/241.41 down(g(g(b))) 542.34/241.41 down(g(g(c))) 542.34/241.41 down(g(g(fresh_constant))) 542.34/241.41 down(f(f(f(a)))) 542.34/241.41 down(f(f(f(b)))) 542.34/241.41 down(f(f(f(g(x0))))) 542.34/241.41 down(f(f(f(c)))) 542.34/241.41 down(f(f(f(fresh_constant)))) 542.34/241.41 down(g(g(g(a)))) 542.34/241.41 down(g(g(g(f(x0))))) 542.34/241.41 down(g(g(g(b)))) 542.34/241.41 down(g(g(g(c)))) 542.34/241.41 down(g(g(g(fresh_constant)))) 542.34/241.41 down(f(f(f(f(a))))) 542.34/241.41 down(f(f(f(f(b))))) 542.34/241.41 down(f(f(f(f(g(x0)))))) 542.34/241.41 down(f(f(f(f(c))))) 542.34/241.41 down(f(f(f(f(fresh_constant))))) 542.34/241.41 down(g(g(g(g(a))))) 542.34/241.41 down(g(g(g(g(f(x0)))))) 542.34/241.41 down(g(g(g(g(b))))) 542.34/241.41 down(g(g(g(g(c))))) 542.34/241.41 down(g(g(g(g(fresh_constant))))) 542.34/241.41 down(f(f(f(f(f(a)))))) 542.34/241.41 down(f(f(f(f(f(b)))))) 542.34/241.41 down(f(f(f(f(f(g(x0))))))) 542.34/241.41 down(f(f(f(f(f(c)))))) 542.34/241.41 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.41 down(g(g(g(g(g(a)))))) 542.34/241.41 down(g(g(g(g(g(f(x0))))))) 542.34/241.41 down(g(g(g(g(g(b)))))) 542.34/241.41 down(g(g(g(g(g(c)))))) 542.34/241.41 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.41 down(f(f(f(f(f(f(a))))))) 542.34/241.41 down(f(f(f(f(f(f(b))))))) 542.34/241.41 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.41 down(f(f(f(f(f(f(c))))))) 542.34/241.41 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.41 down(g(g(g(g(g(g(a))))))) 542.34/241.41 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.41 down(g(g(g(g(g(g(b))))))) 542.34/241.41 down(g(g(g(g(g(g(c))))))) 542.34/241.41 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.41 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.41 f_flat(up(x0)) 542.34/241.41 g_flat(up(x0)) 542.34/241.41 542.34/241.41 We have to consider all minimal (P,Q,R)-chains. 542.34/241.41 ---------------------------------------- 542.34/241.41 542.34/241.41 (207) TransformationProof (EQUIVALENT) 542.34/241.41 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(b)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.41 542.34/241.41 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 542.34/241.41 542.34/241.41 542.34/241.41 ---------------------------------------- 542.34/241.41 542.34/241.41 (208) 542.34/241.41 Obligation: 542.34/241.41 Q DP problem: 542.34/241.41 The TRS P consists of the following rules: 542.34/241.41 542.34/241.41 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.41 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.41 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.41 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.41 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.41 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.41 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.41 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.41 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.41 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.41 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.41 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.41 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.41 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.41 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.41 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.41 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.41 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.41 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.41 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.41 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.41 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.41 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.41 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.41 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.41 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.41 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.41 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.41 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.41 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.41 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.41 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.41 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.41 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.41 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.41 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.41 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.41 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.41 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.41 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.41 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.41 542.34/241.41 The TRS R consists of the following rules: 542.34/241.41 542.34/241.41 down(a) -> up(f(a)) 542.34/241.41 down(b) -> up(g(b)) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.41 down(f(a)) -> f_flat(down(a)) 542.34/241.41 down(f(b)) -> f_flat(down(b)) 542.34/241.41 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.41 down(f(c)) -> f_flat(down(c)) 542.34/241.41 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.41 down(g(a)) -> g_flat(down(a)) 542.34/241.41 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.41 down(g(b)) -> g_flat(down(b)) 542.34/241.41 down(g(c)) -> g_flat(down(c)) 542.34/241.41 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.41 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.41 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.41 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.41 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.41 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.41 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.41 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.41 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.41 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.41 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.41 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.41 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.41 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.41 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.41 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.41 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.41 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.41 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.41 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.41 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.41 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.41 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.41 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.41 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.41 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.41 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.41 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.41 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.41 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.41 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.41 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.41 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.41 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.41 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.41 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.41 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.41 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.41 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.41 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.41 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.41 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.41 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.41 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.41 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.41 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.41 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.41 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.41 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.41 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.41 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.41 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.41 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.41 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.41 542.34/241.41 The set Q consists of the following terms: 542.34/241.41 542.34/241.41 down(a) 542.34/241.41 down(b) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.41 down(f(a)) 542.34/241.41 down(f(b)) 542.34/241.41 down(f(g(x0))) 542.34/241.41 down(f(c)) 542.34/241.41 down(f(fresh_constant)) 542.34/241.41 down(g(a)) 542.34/241.41 down(g(f(x0))) 542.34/241.41 down(g(b)) 542.34/241.41 down(g(c)) 542.34/241.41 down(g(fresh_constant)) 542.34/241.41 down(f(f(a))) 542.34/241.41 down(f(f(b))) 542.34/241.41 down(f(f(g(x0)))) 542.34/241.41 down(f(f(c))) 542.34/241.41 down(f(f(fresh_constant))) 542.34/241.41 down(g(g(a))) 542.34/241.41 down(g(g(f(x0)))) 542.34/241.41 down(g(g(b))) 542.34/241.41 down(g(g(c))) 542.34/241.41 down(g(g(fresh_constant))) 542.34/241.41 down(f(f(f(a)))) 542.34/241.41 down(f(f(f(b)))) 542.34/241.41 down(f(f(f(g(x0))))) 542.34/241.41 down(f(f(f(c)))) 542.34/241.41 down(f(f(f(fresh_constant)))) 542.34/241.41 down(g(g(g(a)))) 542.34/241.41 down(g(g(g(f(x0))))) 542.34/241.41 down(g(g(g(b)))) 542.34/241.41 down(g(g(g(c)))) 542.34/241.41 down(g(g(g(fresh_constant)))) 542.34/241.41 down(f(f(f(f(a))))) 542.34/241.41 down(f(f(f(f(b))))) 542.34/241.41 down(f(f(f(f(g(x0)))))) 542.34/241.41 down(f(f(f(f(c))))) 542.34/241.41 down(f(f(f(f(fresh_constant))))) 542.34/241.41 down(g(g(g(g(a))))) 542.34/241.41 down(g(g(g(g(f(x0)))))) 542.34/241.41 down(g(g(g(g(b))))) 542.34/241.41 down(g(g(g(g(c))))) 542.34/241.41 down(g(g(g(g(fresh_constant))))) 542.34/241.41 down(f(f(f(f(f(a)))))) 542.34/241.41 down(f(f(f(f(f(b)))))) 542.34/241.41 down(f(f(f(f(f(g(x0))))))) 542.34/241.41 down(f(f(f(f(f(c)))))) 542.34/241.41 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.41 down(g(g(g(g(g(a)))))) 542.34/241.41 down(g(g(g(g(g(f(x0))))))) 542.34/241.41 down(g(g(g(g(g(b)))))) 542.34/241.41 down(g(g(g(g(g(c)))))) 542.34/241.41 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.41 down(f(f(f(f(f(f(a))))))) 542.34/241.41 down(f(f(f(f(f(f(b))))))) 542.34/241.41 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.41 down(f(f(f(f(f(f(c))))))) 542.34/241.41 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.41 down(g(g(g(g(g(g(a))))))) 542.34/241.41 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.41 down(g(g(g(g(g(g(b))))))) 542.34/241.41 down(g(g(g(g(g(g(c))))))) 542.34/241.41 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.41 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.41 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.41 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.41 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.41 f_flat(up(x0)) 542.34/241.41 g_flat(up(x0)) 542.34/241.41 542.34/241.41 We have to consider all minimal (P,Q,R)-chains. 542.34/241.41 ---------------------------------------- 542.34/241.41 542.34/241.41 (209) TransformationProof (EQUIVALENT) 542.34/241.41 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.41 542.34/241.41 (TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))),TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.41 542.34/241.41 542.34/241.41 ---------------------------------------- 542.34/241.41 542.34/241.41 (210) 542.34/241.41 Obligation: 542.34/241.41 Q DP problem: 542.34/241.41 The TRS P consists of the following rules: 542.34/241.41 542.34/241.41 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.41 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.41 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.41 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.41 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.41 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.41 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.41 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.41 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.42 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.42 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.42 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.42 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.42 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.42 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.42 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.42 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.42 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.42 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.42 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.42 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.42 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.42 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.42 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.42 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.42 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.42 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.42 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.42 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.42 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.42 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.42 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.42 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.42 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.42 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.42 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.42 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.42 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.42 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.42 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.42 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.42 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 542.34/241.42 The TRS R consists of the following rules: 542.34/241.42 542.34/241.42 down(a) -> up(f(a)) 542.34/241.42 down(b) -> up(g(b)) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.42 down(f(a)) -> f_flat(down(a)) 542.34/241.42 down(f(b)) -> f_flat(down(b)) 542.34/241.42 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.42 down(f(c)) -> f_flat(down(c)) 542.34/241.42 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.42 down(g(a)) -> g_flat(down(a)) 542.34/241.42 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.42 down(g(b)) -> g_flat(down(b)) 542.34/241.42 down(g(c)) -> g_flat(down(c)) 542.34/241.42 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.42 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.42 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.42 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.42 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.42 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.42 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.42 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.42 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.42 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.42 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.42 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.42 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.42 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.42 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.42 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.42 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.42 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.42 542.34/241.42 The set Q consists of the following terms: 542.34/241.42 542.34/241.42 down(a) 542.34/241.42 down(b) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.42 down(f(a)) 542.34/241.42 down(f(b)) 542.34/241.42 down(f(g(x0))) 542.34/241.42 down(f(c)) 542.34/241.42 down(f(fresh_constant)) 542.34/241.42 down(g(a)) 542.34/241.42 down(g(f(x0))) 542.34/241.42 down(g(b)) 542.34/241.42 down(g(c)) 542.34/241.42 down(g(fresh_constant)) 542.34/241.42 down(f(f(a))) 542.34/241.42 down(f(f(b))) 542.34/241.42 down(f(f(g(x0)))) 542.34/241.42 down(f(f(c))) 542.34/241.42 down(f(f(fresh_constant))) 542.34/241.42 down(g(g(a))) 542.34/241.42 down(g(g(f(x0)))) 542.34/241.42 down(g(g(b))) 542.34/241.42 down(g(g(c))) 542.34/241.42 down(g(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) 542.34/241.42 down(f(f(f(g(x0))))) 542.34/241.42 down(f(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) 542.34/241.42 down(g(g(g(f(x0))))) 542.34/241.42 down(g(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(x0)))))) 542.34/241.42 down(f(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(x0)))))) 542.34/241.42 down(g(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(x0))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(x0))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 f_flat(up(x0)) 542.34/241.42 g_flat(up(x0)) 542.34/241.42 542.34/241.42 We have to consider all minimal (P,Q,R)-chains. 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (211) TransformationProof (EQUIVALENT) 542.34/241.42 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(b))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.42 542.34/241.42 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 542.34/241.42 542.34/241.42 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (212) 542.34/241.42 Obligation: 542.34/241.42 Q DP problem: 542.34/241.42 The TRS P consists of the following rules: 542.34/241.42 542.34/241.42 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.42 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.42 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.42 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.42 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.42 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.42 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.42 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.42 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.42 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.42 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.42 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.42 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.42 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.42 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.42 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.42 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.42 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.42 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.42 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.42 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.42 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.42 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.42 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.42 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.42 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.42 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.42 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.42 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.42 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.42 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.42 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.42 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.42 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.42 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.42 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.42 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.42 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.42 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.42 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.42 542.34/241.42 The TRS R consists of the following rules: 542.34/241.42 542.34/241.42 down(a) -> up(f(a)) 542.34/241.42 down(b) -> up(g(b)) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.42 down(f(a)) -> f_flat(down(a)) 542.34/241.42 down(f(b)) -> f_flat(down(b)) 542.34/241.42 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.42 down(f(c)) -> f_flat(down(c)) 542.34/241.42 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.42 down(g(a)) -> g_flat(down(a)) 542.34/241.42 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.42 down(g(b)) -> g_flat(down(b)) 542.34/241.42 down(g(c)) -> g_flat(down(c)) 542.34/241.42 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.42 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.42 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.42 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.42 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.42 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.42 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.42 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.42 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.42 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.42 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.42 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.42 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.42 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.42 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.42 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.42 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.42 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.42 542.34/241.42 The set Q consists of the following terms: 542.34/241.42 542.34/241.42 down(a) 542.34/241.42 down(b) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.42 down(f(a)) 542.34/241.42 down(f(b)) 542.34/241.42 down(f(g(x0))) 542.34/241.42 down(f(c)) 542.34/241.42 down(f(fresh_constant)) 542.34/241.42 down(g(a)) 542.34/241.42 down(g(f(x0))) 542.34/241.42 down(g(b)) 542.34/241.42 down(g(c)) 542.34/241.42 down(g(fresh_constant)) 542.34/241.42 down(f(f(a))) 542.34/241.42 down(f(f(b))) 542.34/241.42 down(f(f(g(x0)))) 542.34/241.42 down(f(f(c))) 542.34/241.42 down(f(f(fresh_constant))) 542.34/241.42 down(g(g(a))) 542.34/241.42 down(g(g(f(x0)))) 542.34/241.42 down(g(g(b))) 542.34/241.42 down(g(g(c))) 542.34/241.42 down(g(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) 542.34/241.42 down(f(f(f(g(x0))))) 542.34/241.42 down(f(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) 542.34/241.42 down(g(g(g(f(x0))))) 542.34/241.42 down(g(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(x0)))))) 542.34/241.42 down(f(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(x0)))))) 542.34/241.42 down(g(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(x0))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(x0))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 f_flat(up(x0)) 542.34/241.42 g_flat(up(x0)) 542.34/241.42 542.34/241.42 We have to consider all minimal (P,Q,R)-chains. 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (213) TransformationProof (EQUIVALENT) 542.34/241.42 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(c))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.42 542.34/241.42 (TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))),TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 542.34/241.42 542.34/241.42 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (214) 542.34/241.42 Obligation: 542.34/241.42 Q DP problem: 542.34/241.42 The TRS P consists of the following rules: 542.34/241.42 542.34/241.42 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.42 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.42 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.42 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.42 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.42 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.42 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.42 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.42 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.42 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.42 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.42 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.42 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.42 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.42 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.42 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.42 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.42 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.42 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.42 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.42 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.42 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.42 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.42 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.42 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.42 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.42 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.42 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.42 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.42 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.42 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.42 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.42 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.42 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.42 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.42 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.42 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.42 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.42 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.42 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.42 542.34/241.42 The TRS R consists of the following rules: 542.34/241.42 542.34/241.42 down(a) -> up(f(a)) 542.34/241.42 down(b) -> up(g(b)) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.42 down(f(a)) -> f_flat(down(a)) 542.34/241.42 down(f(b)) -> f_flat(down(b)) 542.34/241.42 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.42 down(f(c)) -> f_flat(down(c)) 542.34/241.42 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.42 down(g(a)) -> g_flat(down(a)) 542.34/241.42 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.42 down(g(b)) -> g_flat(down(b)) 542.34/241.42 down(g(c)) -> g_flat(down(c)) 542.34/241.42 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.42 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.42 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.42 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.42 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.42 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.42 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.42 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.42 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.42 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.42 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.42 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.42 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.42 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.42 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.42 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.42 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.42 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.42 542.34/241.42 The set Q consists of the following terms: 542.34/241.42 542.34/241.42 down(a) 542.34/241.42 down(b) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.42 down(f(a)) 542.34/241.42 down(f(b)) 542.34/241.42 down(f(g(x0))) 542.34/241.42 down(f(c)) 542.34/241.42 down(f(fresh_constant)) 542.34/241.42 down(g(a)) 542.34/241.42 down(g(f(x0))) 542.34/241.42 down(g(b)) 542.34/241.42 down(g(c)) 542.34/241.42 down(g(fresh_constant)) 542.34/241.42 down(f(f(a))) 542.34/241.42 down(f(f(b))) 542.34/241.42 down(f(f(g(x0)))) 542.34/241.42 down(f(f(c))) 542.34/241.42 down(f(f(fresh_constant))) 542.34/241.42 down(g(g(a))) 542.34/241.42 down(g(g(f(x0)))) 542.34/241.42 down(g(g(b))) 542.34/241.42 down(g(g(c))) 542.34/241.42 down(g(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) 542.34/241.42 down(f(f(f(g(x0))))) 542.34/241.42 down(f(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) 542.34/241.42 down(g(g(g(f(x0))))) 542.34/241.42 down(g(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(x0)))))) 542.34/241.42 down(f(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(x0)))))) 542.34/241.42 down(g(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(x0))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(x0))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 f_flat(up(x0)) 542.34/241.42 g_flat(up(x0)) 542.34/241.42 542.34/241.42 We have to consider all minimal (P,Q,R)-chains. 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (215) TransformationProof (EQUIVALENT) 542.34/241.42 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.42 542.34/241.42 (TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))),TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 542.34/241.42 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (216) 542.34/241.42 Obligation: 542.34/241.42 Q DP problem: 542.34/241.42 The TRS P consists of the following rules: 542.34/241.42 542.34/241.42 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.42 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.42 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.42 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.42 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.42 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.42 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.42 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.42 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.42 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.42 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.42 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.42 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.42 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.42 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.42 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.42 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.42 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.42 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.42 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.42 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.42 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.42 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.42 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.42 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.42 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.42 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.42 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.42 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.42 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.42 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.42 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.42 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.42 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.42 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.42 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.42 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.42 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.42 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.42 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 542.34/241.42 The TRS R consists of the following rules: 542.34/241.42 542.34/241.42 down(a) -> up(f(a)) 542.34/241.42 down(b) -> up(g(b)) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.42 down(f(a)) -> f_flat(down(a)) 542.34/241.42 down(f(b)) -> f_flat(down(b)) 542.34/241.42 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.42 down(f(c)) -> f_flat(down(c)) 542.34/241.42 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.42 down(g(a)) -> g_flat(down(a)) 542.34/241.42 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.42 down(g(b)) -> g_flat(down(b)) 542.34/241.42 down(g(c)) -> g_flat(down(c)) 542.34/241.42 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.42 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.42 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.42 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.42 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.42 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.42 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.42 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.42 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.42 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.42 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.42 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.42 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.42 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.42 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.42 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.42 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.42 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.42 542.34/241.42 The set Q consists of the following terms: 542.34/241.42 542.34/241.42 down(a) 542.34/241.42 down(b) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.42 down(f(a)) 542.34/241.42 down(f(b)) 542.34/241.42 down(f(g(x0))) 542.34/241.42 down(f(c)) 542.34/241.42 down(f(fresh_constant)) 542.34/241.42 down(g(a)) 542.34/241.42 down(g(f(x0))) 542.34/241.42 down(g(b)) 542.34/241.42 down(g(c)) 542.34/241.42 down(g(fresh_constant)) 542.34/241.42 down(f(f(a))) 542.34/241.42 down(f(f(b))) 542.34/241.42 down(f(f(g(x0)))) 542.34/241.42 down(f(f(c))) 542.34/241.42 down(f(f(fresh_constant))) 542.34/241.42 down(g(g(a))) 542.34/241.42 down(g(g(f(x0)))) 542.34/241.42 down(g(g(b))) 542.34/241.42 down(g(g(c))) 542.34/241.42 down(g(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) 542.34/241.42 down(f(f(f(g(x0))))) 542.34/241.42 down(f(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) 542.34/241.42 down(g(g(g(f(x0))))) 542.34/241.42 down(g(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(x0)))))) 542.34/241.42 down(f(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(x0)))))) 542.34/241.42 down(g(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(x0))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(x0))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 f_flat(up(x0)) 542.34/241.42 g_flat(up(x0)) 542.34/241.42 542.34/241.42 We have to consider all minimal (P,Q,R)-chains. 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (217) TransformationProof (EQUIVALENT) 542.34/241.42 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(a)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.42 542.34/241.42 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 542.34/241.42 542.34/241.42 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (218) 542.34/241.42 Obligation: 542.34/241.42 Q DP problem: 542.34/241.42 The TRS P consists of the following rules: 542.34/241.42 542.34/241.42 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.42 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.42 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.42 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.42 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.42 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.42 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.42 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.42 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.42 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.42 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.42 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.42 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.42 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.42 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.42 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.42 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.42 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.42 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.42 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.42 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.42 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.42 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.42 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.42 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.42 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.42 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.42 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.42 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.42 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.42 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.42 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.42 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.42 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.42 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.42 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.42 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.42 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.42 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.42 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.42 542.34/241.42 The TRS R consists of the following rules: 542.34/241.42 542.34/241.42 down(a) -> up(f(a)) 542.34/241.42 down(b) -> up(g(b)) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.42 down(f(a)) -> f_flat(down(a)) 542.34/241.42 down(f(b)) -> f_flat(down(b)) 542.34/241.42 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.42 down(f(c)) -> f_flat(down(c)) 542.34/241.42 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.42 down(g(a)) -> g_flat(down(a)) 542.34/241.42 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.42 down(g(b)) -> g_flat(down(b)) 542.34/241.42 down(g(c)) -> g_flat(down(c)) 542.34/241.42 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.42 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.42 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.42 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.42 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.42 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.42 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.42 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.42 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.42 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.42 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.42 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.42 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.42 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.42 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.42 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.42 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.42 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.42 542.34/241.42 The set Q consists of the following terms: 542.34/241.42 542.34/241.42 down(a) 542.34/241.42 down(b) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.42 down(f(a)) 542.34/241.42 down(f(b)) 542.34/241.42 down(f(g(x0))) 542.34/241.42 down(f(c)) 542.34/241.42 down(f(fresh_constant)) 542.34/241.42 down(g(a)) 542.34/241.42 down(g(f(x0))) 542.34/241.42 down(g(b)) 542.34/241.42 down(g(c)) 542.34/241.42 down(g(fresh_constant)) 542.34/241.42 down(f(f(a))) 542.34/241.42 down(f(f(b))) 542.34/241.42 down(f(f(g(x0)))) 542.34/241.42 down(f(f(c))) 542.34/241.42 down(f(f(fresh_constant))) 542.34/241.42 down(g(g(a))) 542.34/241.42 down(g(g(f(x0)))) 542.34/241.42 down(g(g(b))) 542.34/241.42 down(g(g(c))) 542.34/241.42 down(g(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) 542.34/241.42 down(f(f(f(g(x0))))) 542.34/241.42 down(f(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) 542.34/241.42 down(g(g(g(f(x0))))) 542.34/241.42 down(g(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(x0)))))) 542.34/241.42 down(f(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(x0)))))) 542.34/241.42 down(g(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(x0))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(x0))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 f_flat(up(x0)) 542.34/241.42 g_flat(up(x0)) 542.34/241.42 542.34/241.42 We have to consider all minimal (P,Q,R)-chains. 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (219) TransformationProof (EQUIVALENT) 542.34/241.42 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.42 542.34/241.42 (TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))),TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.42 542.34/241.42 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (220) 542.34/241.42 Obligation: 542.34/241.42 Q DP problem: 542.34/241.42 The TRS P consists of the following rules: 542.34/241.42 542.34/241.42 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.42 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.42 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.42 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.42 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.42 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.42 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.42 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.42 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.42 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.42 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.42 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.42 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.42 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.42 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.42 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.42 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.42 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.42 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.42 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.42 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.42 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.42 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.42 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.42 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.42 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.42 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.42 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.42 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.42 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.42 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.42 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.42 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.42 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.42 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.42 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.42 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.42 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.42 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.42 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.42 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.42 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 542.34/241.42 The TRS R consists of the following rules: 542.34/241.42 542.34/241.42 down(a) -> up(f(a)) 542.34/241.42 down(b) -> up(g(b)) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.42 down(f(a)) -> f_flat(down(a)) 542.34/241.42 down(f(b)) -> f_flat(down(b)) 542.34/241.42 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.42 down(f(c)) -> f_flat(down(c)) 542.34/241.42 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.42 down(g(a)) -> g_flat(down(a)) 542.34/241.42 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.42 down(g(b)) -> g_flat(down(b)) 542.34/241.42 down(g(c)) -> g_flat(down(c)) 542.34/241.42 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.42 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.42 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.42 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.42 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.42 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.42 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.42 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.42 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.42 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.42 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.42 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.42 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.42 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.42 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.42 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.42 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.42 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.42 542.34/241.42 The set Q consists of the following terms: 542.34/241.42 542.34/241.42 down(a) 542.34/241.42 down(b) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.42 down(f(a)) 542.34/241.42 down(f(b)) 542.34/241.42 down(f(g(x0))) 542.34/241.42 down(f(c)) 542.34/241.42 down(f(fresh_constant)) 542.34/241.42 down(g(a)) 542.34/241.42 down(g(f(x0))) 542.34/241.42 down(g(b)) 542.34/241.42 down(g(c)) 542.34/241.42 down(g(fresh_constant)) 542.34/241.42 down(f(f(a))) 542.34/241.42 down(f(f(b))) 542.34/241.42 down(f(f(g(x0)))) 542.34/241.42 down(f(f(c))) 542.34/241.42 down(f(f(fresh_constant))) 542.34/241.42 down(g(g(a))) 542.34/241.42 down(g(g(f(x0)))) 542.34/241.42 down(g(g(b))) 542.34/241.42 down(g(g(c))) 542.34/241.42 down(g(g(fresh_constant))) 542.34/241.42 down(f(f(f(a)))) 542.34/241.42 down(f(f(f(b)))) 542.34/241.42 down(f(f(f(g(x0))))) 542.34/241.42 down(f(f(f(c)))) 542.34/241.42 down(f(f(f(fresh_constant)))) 542.34/241.42 down(g(g(g(a)))) 542.34/241.42 down(g(g(g(f(x0))))) 542.34/241.42 down(g(g(g(b)))) 542.34/241.42 down(g(g(g(c)))) 542.34/241.42 down(g(g(g(fresh_constant)))) 542.34/241.42 down(f(f(f(f(a))))) 542.34/241.42 down(f(f(f(f(b))))) 542.34/241.42 down(f(f(f(f(g(x0)))))) 542.34/241.42 down(f(f(f(f(c))))) 542.34/241.42 down(f(f(f(f(fresh_constant))))) 542.34/241.42 down(g(g(g(g(a))))) 542.34/241.42 down(g(g(g(g(f(x0)))))) 542.34/241.42 down(g(g(g(g(b))))) 542.34/241.42 down(g(g(g(g(c))))) 542.34/241.42 down(g(g(g(g(fresh_constant))))) 542.34/241.42 down(f(f(f(f(f(a)))))) 542.34/241.42 down(f(f(f(f(f(b)))))) 542.34/241.42 down(f(f(f(f(f(g(x0))))))) 542.34/241.42 down(f(f(f(f(f(c)))))) 542.34/241.42 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.42 down(g(g(g(g(g(a)))))) 542.34/241.42 down(g(g(g(g(g(f(x0))))))) 542.34/241.42 down(g(g(g(g(g(b)))))) 542.34/241.42 down(g(g(g(g(g(c)))))) 542.34/241.42 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.42 down(f(f(f(f(f(f(a))))))) 542.34/241.42 down(f(f(f(f(f(f(b))))))) 542.34/241.42 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.42 down(f(f(f(f(f(f(c))))))) 542.34/241.42 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.42 down(g(g(g(g(g(g(a))))))) 542.34/241.42 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.42 down(g(g(g(g(g(g(b))))))) 542.34/241.42 down(g(g(g(g(g(g(c))))))) 542.34/241.42 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.42 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.42 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.42 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.42 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.42 f_flat(up(x0)) 542.34/241.42 g_flat(up(x0)) 542.34/241.42 542.34/241.42 We have to consider all minimal (P,Q,R)-chains. 542.34/241.42 ---------------------------------------- 542.34/241.42 542.34/241.42 (221) TransformationProof (EQUIVALENT) 542.34/241.42 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(c)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.43 542.34/241.43 (TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))),TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 542.34/241.43 542.34/241.43 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (222) 542.34/241.43 Obligation: 542.34/241.43 Q DP problem: 542.34/241.43 The TRS P consists of the following rules: 542.34/241.43 542.34/241.43 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.43 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.43 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.43 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.43 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.43 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.43 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.43 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.43 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.43 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.43 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.43 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.43 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.43 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.43 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.43 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.43 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.43 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.43 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.43 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.43 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.43 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.43 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.43 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.43 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.43 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.43 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.43 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.43 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.43 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.43 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.43 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.43 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.43 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.43 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.43 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.43 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.43 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.43 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.43 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.43 542.34/241.43 The TRS R consists of the following rules: 542.34/241.43 542.34/241.43 down(a) -> up(f(a)) 542.34/241.43 down(b) -> up(g(b)) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.43 down(f(a)) -> f_flat(down(a)) 542.34/241.43 down(f(b)) -> f_flat(down(b)) 542.34/241.43 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.43 down(f(c)) -> f_flat(down(c)) 542.34/241.43 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.43 down(g(a)) -> g_flat(down(a)) 542.34/241.43 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.43 down(g(b)) -> g_flat(down(b)) 542.34/241.43 down(g(c)) -> g_flat(down(c)) 542.34/241.43 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.43 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.43 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.43 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.43 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.43 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.43 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.43 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.43 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.43 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.43 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.43 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.43 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.43 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.43 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.43 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.43 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.43 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.43 542.34/241.43 The set Q consists of the following terms: 542.34/241.43 542.34/241.43 down(a) 542.34/241.43 down(b) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.43 down(f(a)) 542.34/241.43 down(f(b)) 542.34/241.43 down(f(g(x0))) 542.34/241.43 down(f(c)) 542.34/241.43 down(f(fresh_constant)) 542.34/241.43 down(g(a)) 542.34/241.43 down(g(f(x0))) 542.34/241.43 down(g(b)) 542.34/241.43 down(g(c)) 542.34/241.43 down(g(fresh_constant)) 542.34/241.43 down(f(f(a))) 542.34/241.43 down(f(f(b))) 542.34/241.43 down(f(f(g(x0)))) 542.34/241.43 down(f(f(c))) 542.34/241.43 down(f(f(fresh_constant))) 542.34/241.43 down(g(g(a))) 542.34/241.43 down(g(g(f(x0)))) 542.34/241.43 down(g(g(b))) 542.34/241.43 down(g(g(c))) 542.34/241.43 down(g(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) 542.34/241.43 down(f(f(f(g(x0))))) 542.34/241.43 down(f(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) 542.34/241.43 down(g(g(g(f(x0))))) 542.34/241.43 down(g(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(x0)))))) 542.34/241.43 down(f(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(x0)))))) 542.34/241.43 down(g(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(x0))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(x0))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 f_flat(up(x0)) 542.34/241.43 g_flat(up(x0)) 542.34/241.43 542.34/241.43 We have to consider all minimal (P,Q,R)-chains. 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (223) TransformationProof (EQUIVALENT) 542.34/241.43 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.43 542.34/241.43 (TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))),TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.43 542.34/241.43 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (224) 542.34/241.43 Obligation: 542.34/241.43 Q DP problem: 542.34/241.43 The TRS P consists of the following rules: 542.34/241.43 542.34/241.43 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.43 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.43 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.43 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.43 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.43 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.43 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.43 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.43 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.43 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.43 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.43 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.43 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.43 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.43 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.43 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.43 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.43 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.43 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.43 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.43 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.43 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.43 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.43 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.43 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.43 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.43 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.43 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.43 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.43 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.43 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.43 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.43 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.43 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.43 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.43 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.43 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.43 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.43 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.43 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 542.34/241.43 The TRS R consists of the following rules: 542.34/241.43 542.34/241.43 down(a) -> up(f(a)) 542.34/241.43 down(b) -> up(g(b)) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.43 down(f(a)) -> f_flat(down(a)) 542.34/241.43 down(f(b)) -> f_flat(down(b)) 542.34/241.43 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.43 down(f(c)) -> f_flat(down(c)) 542.34/241.43 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.43 down(g(a)) -> g_flat(down(a)) 542.34/241.43 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.43 down(g(b)) -> g_flat(down(b)) 542.34/241.43 down(g(c)) -> g_flat(down(c)) 542.34/241.43 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.43 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.43 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.43 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.43 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.43 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.43 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.43 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.43 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.43 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.43 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.43 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.43 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.43 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.43 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.43 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.43 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.43 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.43 542.34/241.43 The set Q consists of the following terms: 542.34/241.43 542.34/241.43 down(a) 542.34/241.43 down(b) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.43 down(f(a)) 542.34/241.43 down(f(b)) 542.34/241.43 down(f(g(x0))) 542.34/241.43 down(f(c)) 542.34/241.43 down(f(fresh_constant)) 542.34/241.43 down(g(a)) 542.34/241.43 down(g(f(x0))) 542.34/241.43 down(g(b)) 542.34/241.43 down(g(c)) 542.34/241.43 down(g(fresh_constant)) 542.34/241.43 down(f(f(a))) 542.34/241.43 down(f(f(b))) 542.34/241.43 down(f(f(g(x0)))) 542.34/241.43 down(f(f(c))) 542.34/241.43 down(f(f(fresh_constant))) 542.34/241.43 down(g(g(a))) 542.34/241.43 down(g(g(f(x0)))) 542.34/241.43 down(g(g(b))) 542.34/241.43 down(g(g(c))) 542.34/241.43 down(g(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) 542.34/241.43 down(f(f(f(g(x0))))) 542.34/241.43 down(f(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) 542.34/241.43 down(g(g(g(f(x0))))) 542.34/241.43 down(g(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(x0)))))) 542.34/241.43 down(f(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(x0)))))) 542.34/241.43 down(g(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(x0))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(x0))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 f_flat(up(x0)) 542.34/241.43 g_flat(up(x0)) 542.34/241.43 542.34/241.43 We have to consider all minimal (P,Q,R)-chains. 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (225) TransformationProof (EQUIVALENT) 542.34/241.43 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(a))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.43 542.34/241.43 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a)))))))))))) 542.34/241.43 542.34/241.43 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (226) 542.34/241.43 Obligation: 542.34/241.43 Q DP problem: 542.34/241.43 The TRS P consists of the following rules: 542.34/241.43 542.34/241.43 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.43 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.43 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.43 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.43 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.43 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.43 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.43 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.43 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.43 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.43 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.43 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.43 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.43 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.43 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.43 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.43 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.43 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.43 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.43 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.43 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.43 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.43 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.43 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.43 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.43 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.43 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.43 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.43 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.43 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.43 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.43 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.43 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.43 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.43 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.43 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.43 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.43 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.43 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.43 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.43 542.34/241.43 The TRS R consists of the following rules: 542.34/241.43 542.34/241.43 down(a) -> up(f(a)) 542.34/241.43 down(b) -> up(g(b)) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.43 down(f(a)) -> f_flat(down(a)) 542.34/241.43 down(f(b)) -> f_flat(down(b)) 542.34/241.43 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.43 down(f(c)) -> f_flat(down(c)) 542.34/241.43 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.43 down(g(a)) -> g_flat(down(a)) 542.34/241.43 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.43 down(g(b)) -> g_flat(down(b)) 542.34/241.43 down(g(c)) -> g_flat(down(c)) 542.34/241.43 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.43 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.43 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.43 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.43 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.43 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.43 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.43 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.43 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.43 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.43 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.43 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.43 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.43 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.43 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.43 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.43 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.43 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.43 542.34/241.43 The set Q consists of the following terms: 542.34/241.43 542.34/241.43 down(a) 542.34/241.43 down(b) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.43 down(f(a)) 542.34/241.43 down(f(b)) 542.34/241.43 down(f(g(x0))) 542.34/241.43 down(f(c)) 542.34/241.43 down(f(fresh_constant)) 542.34/241.43 down(g(a)) 542.34/241.43 down(g(f(x0))) 542.34/241.43 down(g(b)) 542.34/241.43 down(g(c)) 542.34/241.43 down(g(fresh_constant)) 542.34/241.43 down(f(f(a))) 542.34/241.43 down(f(f(b))) 542.34/241.43 down(f(f(g(x0)))) 542.34/241.43 down(f(f(c))) 542.34/241.43 down(f(f(fresh_constant))) 542.34/241.43 down(g(g(a))) 542.34/241.43 down(g(g(f(x0)))) 542.34/241.43 down(g(g(b))) 542.34/241.43 down(g(g(c))) 542.34/241.43 down(g(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) 542.34/241.43 down(f(f(f(g(x0))))) 542.34/241.43 down(f(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) 542.34/241.43 down(g(g(g(f(x0))))) 542.34/241.43 down(g(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(x0)))))) 542.34/241.43 down(f(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(x0)))))) 542.34/241.43 down(g(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(x0))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(x0))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 f_flat(up(x0)) 542.34/241.43 g_flat(up(x0)) 542.34/241.43 542.34/241.43 We have to consider all minimal (P,Q,R)-chains. 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (227) TransformationProof (EQUIVALENT) 542.34/241.43 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(b))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.43 542.34/241.43 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b)))))))))))) 542.34/241.43 542.34/241.43 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (228) 542.34/241.43 Obligation: 542.34/241.43 Q DP problem: 542.34/241.43 The TRS P consists of the following rules: 542.34/241.43 542.34/241.43 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.43 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.43 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.43 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.43 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.43 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.43 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.43 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.43 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.43 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.43 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.43 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.43 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.43 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.43 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.43 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.43 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.43 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.43 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.43 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.43 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.43 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.43 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.43 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.43 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.43 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.43 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.43 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.43 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.43 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.43 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.43 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.43 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.43 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.43 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.43 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.43 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.43 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.43 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.43 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.43 542.34/241.43 The TRS R consists of the following rules: 542.34/241.43 542.34/241.43 down(a) -> up(f(a)) 542.34/241.43 down(b) -> up(g(b)) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.43 down(f(a)) -> f_flat(down(a)) 542.34/241.43 down(f(b)) -> f_flat(down(b)) 542.34/241.43 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.43 down(f(c)) -> f_flat(down(c)) 542.34/241.43 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.43 down(g(a)) -> g_flat(down(a)) 542.34/241.43 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.43 down(g(b)) -> g_flat(down(b)) 542.34/241.43 down(g(c)) -> g_flat(down(c)) 542.34/241.43 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.43 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.43 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.43 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.43 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.43 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.43 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.43 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.43 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.43 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.43 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.43 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.43 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.43 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.43 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.43 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.43 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.43 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.43 542.34/241.43 The set Q consists of the following terms: 542.34/241.43 542.34/241.43 down(a) 542.34/241.43 down(b) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.43 down(f(a)) 542.34/241.43 down(f(b)) 542.34/241.43 down(f(g(x0))) 542.34/241.43 down(f(c)) 542.34/241.43 down(f(fresh_constant)) 542.34/241.43 down(g(a)) 542.34/241.43 down(g(f(x0))) 542.34/241.43 down(g(b)) 542.34/241.43 down(g(c)) 542.34/241.43 down(g(fresh_constant)) 542.34/241.43 down(f(f(a))) 542.34/241.43 down(f(f(b))) 542.34/241.43 down(f(f(g(x0)))) 542.34/241.43 down(f(f(c))) 542.34/241.43 down(f(f(fresh_constant))) 542.34/241.43 down(g(g(a))) 542.34/241.43 down(g(g(f(x0)))) 542.34/241.43 down(g(g(b))) 542.34/241.43 down(g(g(c))) 542.34/241.43 down(g(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) 542.34/241.43 down(f(f(f(g(x0))))) 542.34/241.43 down(f(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) 542.34/241.43 down(g(g(g(f(x0))))) 542.34/241.43 down(g(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(x0)))))) 542.34/241.43 down(f(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(x0)))))) 542.34/241.43 down(g(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(x0))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(x0))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 f_flat(up(x0)) 542.34/241.43 g_flat(up(x0)) 542.34/241.43 542.34/241.43 We have to consider all minimal (P,Q,R)-chains. 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (229) TransformationProof (EQUIVALENT) 542.34/241.43 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(g(x0)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.43 542.34/241.43 (TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0))))))))))))) 542.34/241.43 542.34/241.43 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (230) 542.34/241.43 Obligation: 542.34/241.43 Q DP problem: 542.34/241.43 The TRS P consists of the following rules: 542.34/241.43 542.34/241.43 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.43 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.43 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.43 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.43 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.43 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.43 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.43 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.43 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.43 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.43 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.43 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.43 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.43 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.43 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.43 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.43 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.43 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.43 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.43 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.43 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.43 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.43 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.43 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.43 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.43 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.43 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.43 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.43 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.43 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.43 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.43 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.43 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.43 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.43 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.43 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.43 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.43 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.43 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.43 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.43 542.34/241.43 The TRS R consists of the following rules: 542.34/241.43 542.34/241.43 down(a) -> up(f(a)) 542.34/241.43 down(b) -> up(g(b)) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.43 down(f(a)) -> f_flat(down(a)) 542.34/241.43 down(f(b)) -> f_flat(down(b)) 542.34/241.43 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.43 down(f(c)) -> f_flat(down(c)) 542.34/241.43 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.43 down(g(a)) -> g_flat(down(a)) 542.34/241.43 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.43 down(g(b)) -> g_flat(down(b)) 542.34/241.43 down(g(c)) -> g_flat(down(c)) 542.34/241.43 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.43 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.43 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.43 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.43 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.43 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.43 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.43 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.43 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.43 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.43 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.43 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.43 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.43 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.43 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.43 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.43 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.43 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.43 542.34/241.43 The set Q consists of the following terms: 542.34/241.43 542.34/241.43 down(a) 542.34/241.43 down(b) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.43 down(f(a)) 542.34/241.43 down(f(b)) 542.34/241.43 down(f(g(x0))) 542.34/241.43 down(f(c)) 542.34/241.43 down(f(fresh_constant)) 542.34/241.43 down(g(a)) 542.34/241.43 down(g(f(x0))) 542.34/241.43 down(g(b)) 542.34/241.43 down(g(c)) 542.34/241.43 down(g(fresh_constant)) 542.34/241.43 down(f(f(a))) 542.34/241.43 down(f(f(b))) 542.34/241.43 down(f(f(g(x0)))) 542.34/241.43 down(f(f(c))) 542.34/241.43 down(f(f(fresh_constant))) 542.34/241.43 down(g(g(a))) 542.34/241.43 down(g(g(f(x0)))) 542.34/241.43 down(g(g(b))) 542.34/241.43 down(g(g(c))) 542.34/241.43 down(g(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) 542.34/241.43 down(f(f(f(g(x0))))) 542.34/241.43 down(f(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) 542.34/241.43 down(g(g(g(f(x0))))) 542.34/241.43 down(g(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(x0)))))) 542.34/241.43 down(f(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(x0)))))) 542.34/241.43 down(g(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(x0))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(x0))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 f_flat(up(x0)) 542.34/241.43 g_flat(up(x0)) 542.34/241.43 542.34/241.43 We have to consider all minimal (P,Q,R)-chains. 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (231) TransformationProof (EQUIVALENT) 542.34/241.43 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(b)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.43 542.34/241.43 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 542.34/241.43 542.34/241.43 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (232) 542.34/241.43 Obligation: 542.34/241.43 Q DP problem: 542.34/241.43 The TRS P consists of the following rules: 542.34/241.43 542.34/241.43 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.43 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.43 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.43 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.43 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.43 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.43 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.43 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.43 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.43 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.43 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.43 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.43 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.43 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.43 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.43 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.43 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.43 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.43 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.43 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.43 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.43 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.43 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.43 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.43 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.43 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.43 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.43 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.43 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.43 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.43 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.43 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.43 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.43 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.43 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.43 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.43 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.43 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.43 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.43 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.43 542.34/241.43 The TRS R consists of the following rules: 542.34/241.43 542.34/241.43 down(a) -> up(f(a)) 542.34/241.43 down(b) -> up(g(b)) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.43 down(f(a)) -> f_flat(down(a)) 542.34/241.43 down(f(b)) -> f_flat(down(b)) 542.34/241.43 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.43 down(f(c)) -> f_flat(down(c)) 542.34/241.43 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.43 down(g(a)) -> g_flat(down(a)) 542.34/241.43 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.43 down(g(b)) -> g_flat(down(b)) 542.34/241.43 down(g(c)) -> g_flat(down(c)) 542.34/241.43 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.43 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.43 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.43 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.43 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.43 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.43 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.43 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.43 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.43 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.43 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.43 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.43 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.43 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.43 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.43 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.43 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.43 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.43 542.34/241.43 The set Q consists of the following terms: 542.34/241.43 542.34/241.43 down(a) 542.34/241.43 down(b) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.43 down(f(a)) 542.34/241.43 down(f(b)) 542.34/241.43 down(f(g(x0))) 542.34/241.43 down(f(c)) 542.34/241.43 down(f(fresh_constant)) 542.34/241.43 down(g(a)) 542.34/241.43 down(g(f(x0))) 542.34/241.43 down(g(b)) 542.34/241.43 down(g(c)) 542.34/241.43 down(g(fresh_constant)) 542.34/241.43 down(f(f(a))) 542.34/241.43 down(f(f(b))) 542.34/241.43 down(f(f(g(x0)))) 542.34/241.43 down(f(f(c))) 542.34/241.43 down(f(f(fresh_constant))) 542.34/241.43 down(g(g(a))) 542.34/241.43 down(g(g(f(x0)))) 542.34/241.43 down(g(g(b))) 542.34/241.43 down(g(g(c))) 542.34/241.43 down(g(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) 542.34/241.43 down(f(f(f(g(x0))))) 542.34/241.43 down(f(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) 542.34/241.43 down(g(g(g(f(x0))))) 542.34/241.43 down(g(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(x0)))))) 542.34/241.43 down(f(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(x0)))))) 542.34/241.43 down(g(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(x0))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(x0))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 f_flat(up(x0)) 542.34/241.43 g_flat(up(x0)) 542.34/241.43 542.34/241.43 We have to consider all minimal (P,Q,R)-chains. 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (233) TransformationProof (EQUIVALENT) 542.34/241.43 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(c)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.43 542.34/241.43 (TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))),TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 542.34/241.43 542.34/241.43 542.34/241.43 ---------------------------------------- 542.34/241.43 542.34/241.43 (234) 542.34/241.43 Obligation: 542.34/241.43 Q DP problem: 542.34/241.43 The TRS P consists of the following rules: 542.34/241.43 542.34/241.43 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.43 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.43 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.43 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.43 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.43 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.43 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.43 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.43 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.43 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.43 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.43 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.43 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.43 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.43 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.43 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.43 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.43 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.43 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.43 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.43 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.43 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.43 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.43 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.43 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.43 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.43 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.43 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.43 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.43 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.43 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.43 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.43 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.43 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.43 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.43 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.43 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.43 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.43 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.43 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.43 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.43 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.43 542.34/241.43 The TRS R consists of the following rules: 542.34/241.43 542.34/241.43 down(a) -> up(f(a)) 542.34/241.43 down(b) -> up(g(b)) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.43 down(f(a)) -> f_flat(down(a)) 542.34/241.43 down(f(b)) -> f_flat(down(b)) 542.34/241.43 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.43 down(f(c)) -> f_flat(down(c)) 542.34/241.43 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.43 down(g(a)) -> g_flat(down(a)) 542.34/241.43 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.43 down(g(b)) -> g_flat(down(b)) 542.34/241.43 down(g(c)) -> g_flat(down(c)) 542.34/241.43 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.43 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.43 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.43 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.43 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.43 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.43 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.43 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.43 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.43 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.43 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.43 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.43 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.43 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.43 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.43 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.43 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.43 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.43 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.43 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.43 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.43 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.43 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.43 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.43 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.43 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.43 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.43 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.43 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.43 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.43 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.43 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.43 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.43 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.43 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.43 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.43 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.43 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.43 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.43 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.43 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.43 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.43 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.43 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.43 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.43 542.34/241.43 The set Q consists of the following terms: 542.34/241.43 542.34/241.43 down(a) 542.34/241.43 down(b) 542.34/241.43 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.43 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.43 down(f(a)) 542.34/241.43 down(f(b)) 542.34/241.43 down(f(g(x0))) 542.34/241.43 down(f(c)) 542.34/241.43 down(f(fresh_constant)) 542.34/241.43 down(g(a)) 542.34/241.43 down(g(f(x0))) 542.34/241.43 down(g(b)) 542.34/241.43 down(g(c)) 542.34/241.43 down(g(fresh_constant)) 542.34/241.43 down(f(f(a))) 542.34/241.43 down(f(f(b))) 542.34/241.43 down(f(f(g(x0)))) 542.34/241.43 down(f(f(c))) 542.34/241.43 down(f(f(fresh_constant))) 542.34/241.43 down(g(g(a))) 542.34/241.43 down(g(g(f(x0)))) 542.34/241.43 down(g(g(b))) 542.34/241.43 down(g(g(c))) 542.34/241.43 down(g(g(fresh_constant))) 542.34/241.43 down(f(f(f(a)))) 542.34/241.43 down(f(f(f(b)))) 542.34/241.43 down(f(f(f(g(x0))))) 542.34/241.43 down(f(f(f(c)))) 542.34/241.43 down(f(f(f(fresh_constant)))) 542.34/241.43 down(g(g(g(a)))) 542.34/241.43 down(g(g(g(f(x0))))) 542.34/241.43 down(g(g(g(b)))) 542.34/241.43 down(g(g(g(c)))) 542.34/241.43 down(g(g(g(fresh_constant)))) 542.34/241.43 down(f(f(f(f(a))))) 542.34/241.43 down(f(f(f(f(b))))) 542.34/241.43 down(f(f(f(f(g(x0)))))) 542.34/241.43 down(f(f(f(f(c))))) 542.34/241.43 down(f(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(x0)))))) 542.34/241.44 down(g(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(x0))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(x0))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 f_flat(up(x0)) 542.34/241.44 g_flat(up(x0)) 542.34/241.44 542.34/241.44 We have to consider all minimal (P,Q,R)-chains. 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (235) TransformationProof (EQUIVALENT) 542.34/241.44 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.44 542.34/241.44 (TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))),TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.44 542.34/241.44 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (236) 542.34/241.44 Obligation: 542.34/241.44 Q DP problem: 542.34/241.44 The TRS P consists of the following rules: 542.34/241.44 542.34/241.44 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.44 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.44 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.44 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.44 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.44 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.44 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.44 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.44 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.44 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.44 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.44 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.44 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.44 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.44 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.44 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.44 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.44 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.44 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.44 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.44 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.44 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.44 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.44 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.44 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.44 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.44 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.44 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.44 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.44 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.44 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.44 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.44 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.44 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.44 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.44 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.44 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.44 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.44 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.44 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 542.34/241.44 The TRS R consists of the following rules: 542.34/241.44 542.34/241.44 down(a) -> up(f(a)) 542.34/241.44 down(b) -> up(g(b)) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.44 down(f(a)) -> f_flat(down(a)) 542.34/241.44 down(f(b)) -> f_flat(down(b)) 542.34/241.44 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.44 down(f(c)) -> f_flat(down(c)) 542.34/241.44 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.44 down(g(a)) -> g_flat(down(a)) 542.34/241.44 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.44 down(g(b)) -> g_flat(down(b)) 542.34/241.44 down(g(c)) -> g_flat(down(c)) 542.34/241.44 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.44 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.44 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.44 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.44 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.44 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.44 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.44 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.44 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.44 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.44 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.44 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.44 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.44 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.44 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.44 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.44 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.44 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.44 542.34/241.44 The set Q consists of the following terms: 542.34/241.44 542.34/241.44 down(a) 542.34/241.44 down(b) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.44 down(f(a)) 542.34/241.44 down(f(b)) 542.34/241.44 down(f(g(x0))) 542.34/241.44 down(f(c)) 542.34/241.44 down(f(fresh_constant)) 542.34/241.44 down(g(a)) 542.34/241.44 down(g(f(x0))) 542.34/241.44 down(g(b)) 542.34/241.44 down(g(c)) 542.34/241.44 down(g(fresh_constant)) 542.34/241.44 down(f(f(a))) 542.34/241.44 down(f(f(b))) 542.34/241.44 down(f(f(g(x0)))) 542.34/241.44 down(f(f(c))) 542.34/241.44 down(f(f(fresh_constant))) 542.34/241.44 down(g(g(a))) 542.34/241.44 down(g(g(f(x0)))) 542.34/241.44 down(g(g(b))) 542.34/241.44 down(g(g(c))) 542.34/241.44 down(g(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) 542.34/241.44 down(f(f(f(g(x0))))) 542.34/241.44 down(f(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) 542.34/241.44 down(g(g(g(f(x0))))) 542.34/241.44 down(g(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(x0)))))) 542.34/241.44 down(f(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(x0)))))) 542.34/241.44 down(g(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(x0))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(x0))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 f_flat(up(x0)) 542.34/241.44 g_flat(up(x0)) 542.34/241.44 542.34/241.44 We have to consider all minimal (P,Q,R)-chains. 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (237) TransformationProof (EQUIVALENT) 542.34/241.44 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(a))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.44 542.34/241.44 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a)))))))))))) 542.34/241.44 542.34/241.44 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (238) 542.34/241.44 Obligation: 542.34/241.44 Q DP problem: 542.34/241.44 The TRS P consists of the following rules: 542.34/241.44 542.34/241.44 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.44 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.44 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.44 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.44 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.44 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.44 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.44 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.44 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.44 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.44 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.44 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.44 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.44 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.44 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.44 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.44 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.44 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.44 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.44 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.44 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.44 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.44 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.44 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.44 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.44 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.44 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.44 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.44 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.44 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.44 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.44 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.44 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.44 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.44 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.44 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.44 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.44 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.44 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.44 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.44 542.34/241.44 The TRS R consists of the following rules: 542.34/241.44 542.34/241.44 down(a) -> up(f(a)) 542.34/241.44 down(b) -> up(g(b)) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.44 down(f(a)) -> f_flat(down(a)) 542.34/241.44 down(f(b)) -> f_flat(down(b)) 542.34/241.44 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.44 down(f(c)) -> f_flat(down(c)) 542.34/241.44 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.44 down(g(a)) -> g_flat(down(a)) 542.34/241.44 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.44 down(g(b)) -> g_flat(down(b)) 542.34/241.44 down(g(c)) -> g_flat(down(c)) 542.34/241.44 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.44 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.44 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.44 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.44 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.44 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.44 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.44 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.44 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.44 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.44 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.44 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.44 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.44 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.44 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.44 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.44 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.44 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.44 542.34/241.44 The set Q consists of the following terms: 542.34/241.44 542.34/241.44 down(a) 542.34/241.44 down(b) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.44 down(f(a)) 542.34/241.44 down(f(b)) 542.34/241.44 down(f(g(x0))) 542.34/241.44 down(f(c)) 542.34/241.44 down(f(fresh_constant)) 542.34/241.44 down(g(a)) 542.34/241.44 down(g(f(x0))) 542.34/241.44 down(g(b)) 542.34/241.44 down(g(c)) 542.34/241.44 down(g(fresh_constant)) 542.34/241.44 down(f(f(a))) 542.34/241.44 down(f(f(b))) 542.34/241.44 down(f(f(g(x0)))) 542.34/241.44 down(f(f(c))) 542.34/241.44 down(f(f(fresh_constant))) 542.34/241.44 down(g(g(a))) 542.34/241.44 down(g(g(f(x0)))) 542.34/241.44 down(g(g(b))) 542.34/241.44 down(g(g(c))) 542.34/241.44 down(g(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) 542.34/241.44 down(f(f(f(g(x0))))) 542.34/241.44 down(f(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) 542.34/241.44 down(g(g(g(f(x0))))) 542.34/241.44 down(g(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(x0)))))) 542.34/241.44 down(f(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(x0)))))) 542.34/241.44 down(g(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(x0))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(x0))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 f_flat(up(x0)) 542.34/241.44 g_flat(up(x0)) 542.34/241.44 542.34/241.44 We have to consider all minimal (P,Q,R)-chains. 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (239) TransformationProof (EQUIVALENT) 542.34/241.44 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(f(x0)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.44 542.34/241.44 (TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0))))))))))))) 542.34/241.44 542.34/241.44 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (240) 542.34/241.44 Obligation: 542.34/241.44 Q DP problem: 542.34/241.44 The TRS P consists of the following rules: 542.34/241.44 542.34/241.44 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.44 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.44 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.44 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.44 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.44 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.44 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.44 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.44 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.44 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.44 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.44 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.44 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.44 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.44 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.44 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.44 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.44 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.44 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.44 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.44 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.44 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.44 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.44 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.44 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.44 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.44 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.44 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.44 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.44 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.44 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.44 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.44 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.44 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.44 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.44 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.44 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.44 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.44 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.44 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.44 542.34/241.44 The TRS R consists of the following rules: 542.34/241.44 542.34/241.44 down(a) -> up(f(a)) 542.34/241.44 down(b) -> up(g(b)) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.44 down(f(a)) -> f_flat(down(a)) 542.34/241.44 down(f(b)) -> f_flat(down(b)) 542.34/241.44 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.44 down(f(c)) -> f_flat(down(c)) 542.34/241.44 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.44 down(g(a)) -> g_flat(down(a)) 542.34/241.44 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.44 down(g(b)) -> g_flat(down(b)) 542.34/241.44 down(g(c)) -> g_flat(down(c)) 542.34/241.44 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.44 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.44 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.44 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.44 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.44 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.44 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.44 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.44 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.44 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.44 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.44 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.44 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.44 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.44 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.44 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.44 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.44 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.44 542.34/241.44 The set Q consists of the following terms: 542.34/241.44 542.34/241.44 down(a) 542.34/241.44 down(b) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.44 down(f(a)) 542.34/241.44 down(f(b)) 542.34/241.44 down(f(g(x0))) 542.34/241.44 down(f(c)) 542.34/241.44 down(f(fresh_constant)) 542.34/241.44 down(g(a)) 542.34/241.44 down(g(f(x0))) 542.34/241.44 down(g(b)) 542.34/241.44 down(g(c)) 542.34/241.44 down(g(fresh_constant)) 542.34/241.44 down(f(f(a))) 542.34/241.44 down(f(f(b))) 542.34/241.44 down(f(f(g(x0)))) 542.34/241.44 down(f(f(c))) 542.34/241.44 down(f(f(fresh_constant))) 542.34/241.44 down(g(g(a))) 542.34/241.44 down(g(g(f(x0)))) 542.34/241.44 down(g(g(b))) 542.34/241.44 down(g(g(c))) 542.34/241.44 down(g(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) 542.34/241.44 down(f(f(f(g(x0))))) 542.34/241.44 down(f(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) 542.34/241.44 down(g(g(g(f(x0))))) 542.34/241.44 down(g(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(x0)))))) 542.34/241.44 down(f(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(x0)))))) 542.34/241.44 down(g(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(x0))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(x0))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 f_flat(up(x0)) 542.34/241.44 g_flat(up(x0)) 542.34/241.44 542.34/241.44 We have to consider all minimal (P,Q,R)-chains. 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (241) TransformationProof (EQUIVALENT) 542.34/241.44 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(c))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.44 542.34/241.44 (TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c)))))))))))) 542.34/241.44 542.34/241.44 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (242) 542.34/241.44 Obligation: 542.34/241.44 Q DP problem: 542.34/241.44 The TRS P consists of the following rules: 542.34/241.44 542.34/241.44 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.44 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.44 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.44 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.44 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.44 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.44 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.44 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.44 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.44 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.44 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.44 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.44 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.44 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.44 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.44 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.44 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.44 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.44 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.44 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.44 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.44 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.44 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.44 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.44 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.44 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.44 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.44 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.44 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.44 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.44 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.44 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.44 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.44 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.44 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.44 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.44 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.44 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.44 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.44 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.34/241.44 542.34/241.44 The TRS R consists of the following rules: 542.34/241.44 542.34/241.44 down(a) -> up(f(a)) 542.34/241.44 down(b) -> up(g(b)) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.44 down(f(a)) -> f_flat(down(a)) 542.34/241.44 down(f(b)) -> f_flat(down(b)) 542.34/241.44 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.44 down(f(c)) -> f_flat(down(c)) 542.34/241.44 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.44 down(g(a)) -> g_flat(down(a)) 542.34/241.44 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.44 down(g(b)) -> g_flat(down(b)) 542.34/241.44 down(g(c)) -> g_flat(down(c)) 542.34/241.44 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.44 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.44 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.44 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.44 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.44 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.44 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.44 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.44 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.44 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.44 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.44 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.44 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.44 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.44 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.44 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.44 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.44 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.44 542.34/241.44 The set Q consists of the following terms: 542.34/241.44 542.34/241.44 down(a) 542.34/241.44 down(b) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.44 down(f(a)) 542.34/241.44 down(f(b)) 542.34/241.44 down(f(g(x0))) 542.34/241.44 down(f(c)) 542.34/241.44 down(f(fresh_constant)) 542.34/241.44 down(g(a)) 542.34/241.44 down(g(f(x0))) 542.34/241.44 down(g(b)) 542.34/241.44 down(g(c)) 542.34/241.44 down(g(fresh_constant)) 542.34/241.44 down(f(f(a))) 542.34/241.44 down(f(f(b))) 542.34/241.44 down(f(f(g(x0)))) 542.34/241.44 down(f(f(c))) 542.34/241.44 down(f(f(fresh_constant))) 542.34/241.44 down(g(g(a))) 542.34/241.44 down(g(g(f(x0)))) 542.34/241.44 down(g(g(b))) 542.34/241.44 down(g(g(c))) 542.34/241.44 down(g(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) 542.34/241.44 down(f(f(f(g(x0))))) 542.34/241.44 down(f(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) 542.34/241.44 down(g(g(g(f(x0))))) 542.34/241.44 down(g(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(x0)))))) 542.34/241.44 down(f(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(x0)))))) 542.34/241.44 down(g(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(x0))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(x0))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 f_flat(up(x0)) 542.34/241.44 g_flat(up(x0)) 542.34/241.44 542.34/241.44 We have to consider all minimal (P,Q,R)-chains. 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (243) TransformationProof (EQUIVALENT) 542.34/241.44 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(down(f(f(f(f(f(f(f(f(fresh_constant))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.44 542.34/241.44 (TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant)))))))))))) 542.34/241.44 542.34/241.44 542.34/241.44 ---------------------------------------- 542.34/241.44 542.34/241.44 (244) 542.34/241.44 Obligation: 542.34/241.44 Q DP problem: 542.34/241.44 The TRS P consists of the following rules: 542.34/241.44 542.34/241.44 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.44 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.44 TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) 542.34/241.44 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.44 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.44 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.44 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.44 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.44 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.44 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.44 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.44 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.44 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.44 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.44 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.44 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.44 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.44 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.44 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.44 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.44 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.44 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.44 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.44 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.44 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.44 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.44 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.44 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.44 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.44 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.44 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.44 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.44 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.44 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.44 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.44 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.44 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.44 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.44 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.44 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.44 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.34/241.44 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.44 542.34/241.44 The TRS R consists of the following rules: 542.34/241.44 542.34/241.44 down(a) -> up(f(a)) 542.34/241.44 down(b) -> up(g(b)) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.44 down(f(a)) -> f_flat(down(a)) 542.34/241.44 down(f(b)) -> f_flat(down(b)) 542.34/241.44 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.44 down(f(c)) -> f_flat(down(c)) 542.34/241.44 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.44 down(g(a)) -> g_flat(down(a)) 542.34/241.44 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.44 down(g(b)) -> g_flat(down(b)) 542.34/241.44 down(g(c)) -> g_flat(down(c)) 542.34/241.44 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.44 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.44 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.44 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.44 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.44 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.44 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.44 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.44 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.44 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.44 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.44 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.44 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.44 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.44 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.44 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.44 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.44 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.44 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.44 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.44 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.44 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.44 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.44 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.44 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.44 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.44 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.44 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.44 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.44 542.34/241.44 The set Q consists of the following terms: 542.34/241.44 542.34/241.44 down(a) 542.34/241.44 down(b) 542.34/241.44 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.44 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.44 down(f(a)) 542.34/241.44 down(f(b)) 542.34/241.44 down(f(g(x0))) 542.34/241.44 down(f(c)) 542.34/241.44 down(f(fresh_constant)) 542.34/241.44 down(g(a)) 542.34/241.44 down(g(f(x0))) 542.34/241.44 down(g(b)) 542.34/241.44 down(g(c)) 542.34/241.44 down(g(fresh_constant)) 542.34/241.44 down(f(f(a))) 542.34/241.44 down(f(f(b))) 542.34/241.44 down(f(f(g(x0)))) 542.34/241.44 down(f(f(c))) 542.34/241.44 down(f(f(fresh_constant))) 542.34/241.44 down(g(g(a))) 542.34/241.44 down(g(g(f(x0)))) 542.34/241.44 down(g(g(b))) 542.34/241.44 down(g(g(c))) 542.34/241.44 down(g(g(fresh_constant))) 542.34/241.44 down(f(f(f(a)))) 542.34/241.44 down(f(f(f(b)))) 542.34/241.44 down(f(f(f(g(x0))))) 542.34/241.44 down(f(f(f(c)))) 542.34/241.44 down(f(f(f(fresh_constant)))) 542.34/241.44 down(g(g(g(a)))) 542.34/241.44 down(g(g(g(f(x0))))) 542.34/241.44 down(g(g(g(b)))) 542.34/241.44 down(g(g(g(c)))) 542.34/241.44 down(g(g(g(fresh_constant)))) 542.34/241.44 down(f(f(f(f(a))))) 542.34/241.44 down(f(f(f(f(b))))) 542.34/241.44 down(f(f(f(f(g(x0)))))) 542.34/241.44 down(f(f(f(f(c))))) 542.34/241.44 down(f(f(f(f(fresh_constant))))) 542.34/241.44 down(g(g(g(g(a))))) 542.34/241.44 down(g(g(g(g(f(x0)))))) 542.34/241.44 down(g(g(g(g(b))))) 542.34/241.44 down(g(g(g(g(c))))) 542.34/241.44 down(g(g(g(g(fresh_constant))))) 542.34/241.44 down(f(f(f(f(f(a)))))) 542.34/241.44 down(f(f(f(f(f(b)))))) 542.34/241.44 down(f(f(f(f(f(g(x0))))))) 542.34/241.44 down(f(f(f(f(f(c)))))) 542.34/241.44 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.44 down(g(g(g(g(g(a)))))) 542.34/241.44 down(g(g(g(g(g(f(x0))))))) 542.34/241.44 down(g(g(g(g(g(b)))))) 542.34/241.44 down(g(g(g(g(g(c)))))) 542.34/241.44 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.44 down(f(f(f(f(f(f(a))))))) 542.34/241.44 down(f(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 f_flat(up(x0)) 542.34/241.45 g_flat(up(x0)) 542.34/241.45 542.34/241.45 We have to consider all minimal (P,Q,R)-chains. 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (245) TransformationProof (EQUIVALENT) 542.34/241.45 By rewriting [LPAR04] the rule TOP(up(f(a))) -> TOP(f_flat(up(f(a)))) at position [0] we obtained the following new rules [LPAR04]: 542.34/241.45 542.34/241.45 (TOP(up(f(a))) -> TOP(up(f(f(a)))),TOP(up(f(a))) -> TOP(up(f(f(a))))) 542.34/241.45 542.34/241.45 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (246) 542.34/241.45 Obligation: 542.34/241.45 Q DP problem: 542.34/241.45 The TRS P consists of the following rules: 542.34/241.45 542.34/241.45 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.45 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.45 TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) 542.34/241.45 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.45 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.45 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.45 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.45 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.45 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.45 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.45 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.45 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.45 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.45 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.45 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.45 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.45 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.45 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.45 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.45 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.45 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.45 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.45 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.45 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.45 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.45 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.45 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.45 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.45 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.45 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.45 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.45 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.45 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.45 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.45 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.45 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.45 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.45 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.45 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.45 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.34/241.45 542.34/241.45 The TRS R consists of the following rules: 542.34/241.45 542.34/241.45 down(a) -> up(f(a)) 542.34/241.45 down(b) -> up(g(b)) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.45 down(f(a)) -> f_flat(down(a)) 542.34/241.45 down(f(b)) -> f_flat(down(b)) 542.34/241.45 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.45 down(f(c)) -> f_flat(down(c)) 542.34/241.45 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.45 down(g(a)) -> g_flat(down(a)) 542.34/241.45 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.45 down(g(b)) -> g_flat(down(b)) 542.34/241.45 down(g(c)) -> g_flat(down(c)) 542.34/241.45 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.45 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.45 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.45 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.45 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.45 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.45 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.45 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.45 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.45 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.45 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.45 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.45 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.45 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.45 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.45 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.45 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.45 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.45 542.34/241.45 The set Q consists of the following terms: 542.34/241.45 542.34/241.45 down(a) 542.34/241.45 down(b) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.45 down(f(a)) 542.34/241.45 down(f(b)) 542.34/241.45 down(f(g(x0))) 542.34/241.45 down(f(c)) 542.34/241.45 down(f(fresh_constant)) 542.34/241.45 down(g(a)) 542.34/241.45 down(g(f(x0))) 542.34/241.45 down(g(b)) 542.34/241.45 down(g(c)) 542.34/241.45 down(g(fresh_constant)) 542.34/241.45 down(f(f(a))) 542.34/241.45 down(f(f(b))) 542.34/241.45 down(f(f(g(x0)))) 542.34/241.45 down(f(f(c))) 542.34/241.45 down(f(f(fresh_constant))) 542.34/241.45 down(g(g(a))) 542.34/241.45 down(g(g(f(x0)))) 542.34/241.45 down(g(g(b))) 542.34/241.45 down(g(g(c))) 542.34/241.45 down(g(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) 542.34/241.45 down(f(f(f(g(x0))))) 542.34/241.45 down(f(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) 542.34/241.45 down(g(g(g(f(x0))))) 542.34/241.45 down(g(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(x0)))))) 542.34/241.45 down(f(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(x0)))))) 542.34/241.45 down(g(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(x0))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(x0))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 f_flat(up(x0)) 542.34/241.45 g_flat(up(x0)) 542.34/241.45 542.34/241.45 We have to consider all minimal (P,Q,R)-chains. 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (247) TransformationProof (EQUIVALENT) 542.34/241.45 By rewriting [LPAR04] the rule TOP(up(f(b))) -> TOP(f_flat(up(g(b)))) at position [0] we obtained the following new rules [LPAR04]: 542.34/241.45 542.34/241.45 (TOP(up(f(b))) -> TOP(up(f(g(b)))),TOP(up(f(b))) -> TOP(up(f(g(b))))) 542.34/241.45 542.34/241.45 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (248) 542.34/241.45 Obligation: 542.34/241.45 Q DP problem: 542.34/241.45 The TRS P consists of the following rules: 542.34/241.45 542.34/241.45 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.45 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.45 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) 542.34/241.45 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.45 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.45 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.45 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.45 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.45 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.45 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.45 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.45 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.45 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.45 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.45 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.45 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.45 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.45 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.45 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.45 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.45 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.45 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.45 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.45 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.45 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.45 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.45 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.45 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.45 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.45 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.45 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.45 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.45 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.45 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.45 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.45 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.45 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.45 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.45 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.34/241.45 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.34/241.45 542.34/241.45 The TRS R consists of the following rules: 542.34/241.45 542.34/241.45 down(a) -> up(f(a)) 542.34/241.45 down(b) -> up(g(b)) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.45 down(f(a)) -> f_flat(down(a)) 542.34/241.45 down(f(b)) -> f_flat(down(b)) 542.34/241.45 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.45 down(f(c)) -> f_flat(down(c)) 542.34/241.45 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.45 down(g(a)) -> g_flat(down(a)) 542.34/241.45 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.45 down(g(b)) -> g_flat(down(b)) 542.34/241.45 down(g(c)) -> g_flat(down(c)) 542.34/241.45 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.45 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.45 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.45 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.45 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.45 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.45 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.45 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.45 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.45 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.45 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.45 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.45 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.45 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.45 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.45 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.45 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.45 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.45 542.34/241.45 The set Q consists of the following terms: 542.34/241.45 542.34/241.45 down(a) 542.34/241.45 down(b) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.45 down(f(a)) 542.34/241.45 down(f(b)) 542.34/241.45 down(f(g(x0))) 542.34/241.45 down(f(c)) 542.34/241.45 down(f(fresh_constant)) 542.34/241.45 down(g(a)) 542.34/241.45 down(g(f(x0))) 542.34/241.45 down(g(b)) 542.34/241.45 down(g(c)) 542.34/241.45 down(g(fresh_constant)) 542.34/241.45 down(f(f(a))) 542.34/241.45 down(f(f(b))) 542.34/241.45 down(f(f(g(x0)))) 542.34/241.45 down(f(f(c))) 542.34/241.45 down(f(f(fresh_constant))) 542.34/241.45 down(g(g(a))) 542.34/241.45 down(g(g(f(x0)))) 542.34/241.45 down(g(g(b))) 542.34/241.45 down(g(g(c))) 542.34/241.45 down(g(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) 542.34/241.45 down(f(f(f(g(x0))))) 542.34/241.45 down(f(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) 542.34/241.45 down(g(g(g(f(x0))))) 542.34/241.45 down(g(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(x0)))))) 542.34/241.45 down(f(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(x0)))))) 542.34/241.45 down(g(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(x0))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(x0))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 f_flat(up(x0)) 542.34/241.45 g_flat(up(x0)) 542.34/241.45 542.34/241.45 We have to consider all minimal (P,Q,R)-chains. 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (249) TransformationProof (EQUIVALENT) 542.34/241.45 By rewriting [LPAR04] the rule TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(down(a)))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.34/241.45 542.34/241.45 (TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))),TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a)))))) 542.34/241.45 542.34/241.45 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (250) 542.34/241.45 Obligation: 542.34/241.45 Q DP problem: 542.34/241.45 The TRS P consists of the following rules: 542.34/241.45 542.34/241.45 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.45 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.45 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) 542.34/241.45 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.45 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.45 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.45 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.45 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.45 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.45 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.45 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.45 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.45 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.45 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.45 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.45 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.45 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.45 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.45 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.45 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.45 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.45 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.45 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.45 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.45 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.45 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.45 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.45 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.45 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.45 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.45 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.45 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.45 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.45 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.45 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.45 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.45 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.45 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.34/241.45 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.34/241.45 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.34/241.45 542.34/241.45 The TRS R consists of the following rules: 542.34/241.45 542.34/241.45 down(a) -> up(f(a)) 542.34/241.45 down(b) -> up(g(b)) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.45 down(f(a)) -> f_flat(down(a)) 542.34/241.45 down(f(b)) -> f_flat(down(b)) 542.34/241.45 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.45 down(f(c)) -> f_flat(down(c)) 542.34/241.45 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.45 down(g(a)) -> g_flat(down(a)) 542.34/241.45 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.45 down(g(b)) -> g_flat(down(b)) 542.34/241.45 down(g(c)) -> g_flat(down(c)) 542.34/241.45 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.45 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.45 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.45 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.45 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.45 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.45 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.45 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.45 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.45 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.45 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.45 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.45 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.45 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.45 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.45 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.45 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.45 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.45 542.34/241.45 The set Q consists of the following terms: 542.34/241.45 542.34/241.45 down(a) 542.34/241.45 down(b) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.45 down(f(a)) 542.34/241.45 down(f(b)) 542.34/241.45 down(f(g(x0))) 542.34/241.45 down(f(c)) 542.34/241.45 down(f(fresh_constant)) 542.34/241.45 down(g(a)) 542.34/241.45 down(g(f(x0))) 542.34/241.45 down(g(b)) 542.34/241.45 down(g(c)) 542.34/241.45 down(g(fresh_constant)) 542.34/241.45 down(f(f(a))) 542.34/241.45 down(f(f(b))) 542.34/241.45 down(f(f(g(x0)))) 542.34/241.45 down(f(f(c))) 542.34/241.45 down(f(f(fresh_constant))) 542.34/241.45 down(g(g(a))) 542.34/241.45 down(g(g(f(x0)))) 542.34/241.45 down(g(g(b))) 542.34/241.45 down(g(g(c))) 542.34/241.45 down(g(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) 542.34/241.45 down(f(f(f(g(x0))))) 542.34/241.45 down(f(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) 542.34/241.45 down(g(g(g(f(x0))))) 542.34/241.45 down(g(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(x0)))))) 542.34/241.45 down(f(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(x0)))))) 542.34/241.45 down(g(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(x0))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(x0))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 f_flat(up(x0)) 542.34/241.45 g_flat(up(x0)) 542.34/241.45 542.34/241.45 We have to consider all minimal (P,Q,R)-chains. 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (251) TransformationProof (EQUIVALENT) 542.34/241.45 By rewriting [LPAR04] the rule TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(down(b)))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.34/241.45 542.34/241.45 (TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))),TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b)))))) 542.34/241.45 542.34/241.45 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (252) 542.34/241.45 Obligation: 542.34/241.45 Q DP problem: 542.34/241.45 The TRS P consists of the following rules: 542.34/241.45 542.34/241.45 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.45 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.45 TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.45 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.45 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.45 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.45 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.45 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.45 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.45 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.45 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.45 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.45 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.45 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.45 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.45 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.45 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.45 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.45 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.45 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.45 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.45 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.45 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.45 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.45 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.45 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.45 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.45 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.45 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.45 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.45 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.45 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.45 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.45 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.45 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.45 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.45 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.34/241.45 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.34/241.45 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.34/241.45 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.34/241.45 542.34/241.45 The TRS R consists of the following rules: 542.34/241.45 542.34/241.45 down(a) -> up(f(a)) 542.34/241.45 down(b) -> up(g(b)) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.45 down(f(a)) -> f_flat(down(a)) 542.34/241.45 down(f(b)) -> f_flat(down(b)) 542.34/241.45 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.45 down(f(c)) -> f_flat(down(c)) 542.34/241.45 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.45 down(g(a)) -> g_flat(down(a)) 542.34/241.45 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.45 down(g(b)) -> g_flat(down(b)) 542.34/241.45 down(g(c)) -> g_flat(down(c)) 542.34/241.45 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.45 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.45 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.45 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.45 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.45 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.45 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.45 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.45 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.45 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.45 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.45 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.45 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.45 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.45 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.45 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.45 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.45 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.45 542.34/241.45 The set Q consists of the following terms: 542.34/241.45 542.34/241.45 down(a) 542.34/241.45 down(b) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.45 down(f(a)) 542.34/241.45 down(f(b)) 542.34/241.45 down(f(g(x0))) 542.34/241.45 down(f(c)) 542.34/241.45 down(f(fresh_constant)) 542.34/241.45 down(g(a)) 542.34/241.45 down(g(f(x0))) 542.34/241.45 down(g(b)) 542.34/241.45 down(g(c)) 542.34/241.45 down(g(fresh_constant)) 542.34/241.45 down(f(f(a))) 542.34/241.45 down(f(f(b))) 542.34/241.45 down(f(f(g(x0)))) 542.34/241.45 down(f(f(c))) 542.34/241.45 down(f(f(fresh_constant))) 542.34/241.45 down(g(g(a))) 542.34/241.45 down(g(g(f(x0)))) 542.34/241.45 down(g(g(b))) 542.34/241.45 down(g(g(c))) 542.34/241.45 down(g(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) 542.34/241.45 down(f(f(f(g(x0))))) 542.34/241.45 down(f(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) 542.34/241.45 down(g(g(g(f(x0))))) 542.34/241.45 down(g(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(x0)))))) 542.34/241.45 down(f(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(x0)))))) 542.34/241.45 down(g(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(x0))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(x0))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 f_flat(up(x0)) 542.34/241.45 g_flat(up(x0)) 542.34/241.45 542.34/241.45 We have to consider all minimal (P,Q,R)-chains. 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (253) TransformationProof (EQUIVALENT) 542.34/241.45 By rewriting [LPAR04] the rule TOP(up(g(b))) -> TOP(g_flat(up(g(b)))) at position [0] we obtained the following new rules [LPAR04]: 542.34/241.45 542.34/241.45 (TOP(up(g(b))) -> TOP(up(g(g(b)))),TOP(up(g(b))) -> TOP(up(g(g(b))))) 542.34/241.45 542.34/241.45 542.34/241.45 ---------------------------------------- 542.34/241.45 542.34/241.45 (254) 542.34/241.45 Obligation: 542.34/241.45 Q DP problem: 542.34/241.45 The TRS P consists of the following rules: 542.34/241.45 542.34/241.45 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.45 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.45 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.45 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.45 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.45 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.45 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.45 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.45 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.45 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.45 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.45 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.45 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.45 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.45 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.45 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.45 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.45 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.45 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.45 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.45 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.45 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.45 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.45 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.45 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.45 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.45 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.45 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.45 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.45 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.45 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.45 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.45 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.45 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.45 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.45 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.34/241.45 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.45 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.34/241.45 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.34/241.45 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.34/241.45 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.34/241.45 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.34/241.45 542.34/241.45 The TRS R consists of the following rules: 542.34/241.45 542.34/241.45 down(a) -> up(f(a)) 542.34/241.45 down(b) -> up(g(b)) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.45 down(f(a)) -> f_flat(down(a)) 542.34/241.45 down(f(b)) -> f_flat(down(b)) 542.34/241.45 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.45 down(f(c)) -> f_flat(down(c)) 542.34/241.45 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.45 down(g(a)) -> g_flat(down(a)) 542.34/241.45 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.45 down(g(b)) -> g_flat(down(b)) 542.34/241.45 down(g(c)) -> g_flat(down(c)) 542.34/241.45 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.45 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.45 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.45 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.45 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.45 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.45 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.45 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.45 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.45 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.45 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.45 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.45 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.45 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.45 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.45 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.45 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.45 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.45 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.45 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.45 542.34/241.45 The set Q consists of the following terms: 542.34/241.45 542.34/241.45 down(a) 542.34/241.45 down(b) 542.34/241.45 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.45 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.45 down(f(a)) 542.34/241.45 down(f(b)) 542.34/241.45 down(f(g(x0))) 542.34/241.45 down(f(c)) 542.34/241.45 down(f(fresh_constant)) 542.34/241.45 down(g(a)) 542.34/241.45 down(g(f(x0))) 542.34/241.45 down(g(b)) 542.34/241.45 down(g(c)) 542.34/241.45 down(g(fresh_constant)) 542.34/241.45 down(f(f(a))) 542.34/241.45 down(f(f(b))) 542.34/241.45 down(f(f(g(x0)))) 542.34/241.45 down(f(f(c))) 542.34/241.45 down(f(f(fresh_constant))) 542.34/241.45 down(g(g(a))) 542.34/241.45 down(g(g(f(x0)))) 542.34/241.45 down(g(g(b))) 542.34/241.45 down(g(g(c))) 542.34/241.45 down(g(g(fresh_constant))) 542.34/241.45 down(f(f(f(a)))) 542.34/241.45 down(f(f(f(b)))) 542.34/241.45 down(f(f(f(g(x0))))) 542.34/241.45 down(f(f(f(c)))) 542.34/241.45 down(f(f(f(fresh_constant)))) 542.34/241.45 down(g(g(g(a)))) 542.34/241.45 down(g(g(g(f(x0))))) 542.34/241.45 down(g(g(g(b)))) 542.34/241.45 down(g(g(g(c)))) 542.34/241.45 down(g(g(g(fresh_constant)))) 542.34/241.45 down(f(f(f(f(a))))) 542.34/241.45 down(f(f(f(f(b))))) 542.34/241.45 down(f(f(f(f(g(x0)))))) 542.34/241.45 down(f(f(f(f(c))))) 542.34/241.45 down(f(f(f(f(fresh_constant))))) 542.34/241.45 down(g(g(g(g(a))))) 542.34/241.45 down(g(g(g(g(f(x0)))))) 542.34/241.45 down(g(g(g(g(b))))) 542.34/241.45 down(g(g(g(g(c))))) 542.34/241.45 down(g(g(g(g(fresh_constant))))) 542.34/241.45 down(f(f(f(f(f(a)))))) 542.34/241.45 down(f(f(f(f(f(b)))))) 542.34/241.45 down(f(f(f(f(f(g(x0))))))) 542.34/241.45 down(f(f(f(f(f(c)))))) 542.34/241.45 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.45 down(g(g(g(g(g(a)))))) 542.34/241.45 down(g(g(g(g(g(f(x0))))))) 542.34/241.45 down(g(g(g(g(g(b)))))) 542.34/241.45 down(g(g(g(g(g(c)))))) 542.34/241.45 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.45 down(f(f(f(f(f(f(a))))))) 542.34/241.45 down(f(f(f(f(f(f(b))))))) 542.34/241.45 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.45 down(f(f(f(f(f(f(c))))))) 542.34/241.45 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.45 down(g(g(g(g(g(g(a))))))) 542.34/241.45 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.45 down(g(g(g(g(g(g(b))))))) 542.34/241.45 down(g(g(g(g(g(g(c))))))) 542.34/241.45 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.45 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.45 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.46 f_flat(up(x0)) 542.34/241.46 g_flat(up(x0)) 542.34/241.46 542.34/241.46 We have to consider all minimal (P,Q,R)-chains. 542.34/241.46 ---------------------------------------- 542.34/241.46 542.34/241.46 (255) TransformationProof (EQUIVALENT) 542.34/241.46 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(b))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.46 542.34/241.46 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b)))))))))))) 542.34/241.46 542.34/241.46 542.34/241.46 ---------------------------------------- 542.34/241.46 542.34/241.46 (256) 542.34/241.46 Obligation: 542.34/241.46 Q DP problem: 542.34/241.46 The TRS P consists of the following rules: 542.34/241.46 542.34/241.46 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.46 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.46 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.46 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.46 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.46 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.46 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.46 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.46 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.46 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.46 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.46 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.46 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.46 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.46 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.46 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.46 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.46 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.46 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.46 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.46 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.46 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.46 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.46 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.46 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.46 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.46 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.46 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.46 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.46 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.46 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.46 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.46 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.46 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.46 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.46 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.34/241.46 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.34/241.46 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.34/241.46 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.34/241.46 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.34/241.46 542.34/241.46 The TRS R consists of the following rules: 542.34/241.46 542.34/241.46 down(a) -> up(f(a)) 542.34/241.46 down(b) -> up(g(b)) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.46 down(f(a)) -> f_flat(down(a)) 542.34/241.46 down(f(b)) -> f_flat(down(b)) 542.34/241.46 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.46 down(f(c)) -> f_flat(down(c)) 542.34/241.46 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.46 down(g(a)) -> g_flat(down(a)) 542.34/241.46 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.46 down(g(b)) -> g_flat(down(b)) 542.34/241.46 down(g(c)) -> g_flat(down(c)) 542.34/241.46 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.46 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.46 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.46 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.46 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.46 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.46 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.46 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.46 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.46 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.46 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.46 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.46 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.46 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.46 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.46 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.46 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.46 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.46 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.46 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.46 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.46 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.46 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.46 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.46 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.46 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.46 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.46 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.46 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.46 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.46 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.46 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.46 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.46 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.46 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.46 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.46 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.46 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.46 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.46 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.46 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.46 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.46 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.46 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.46 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.46 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.46 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.46 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.46 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.46 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.46 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.46 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.46 g_flat(up(x_1)) -> up(g(x_1)) 542.34/241.46 f_flat(up(x_1)) -> up(f(x_1)) 542.34/241.46 542.34/241.46 The set Q consists of the following terms: 542.34/241.46 542.34/241.46 down(a) 542.34/241.46 down(b) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.34/241.46 down(f(a)) 542.34/241.46 down(f(b)) 542.34/241.46 down(f(g(x0))) 542.34/241.46 down(f(c)) 542.34/241.46 down(f(fresh_constant)) 542.34/241.46 down(g(a)) 542.34/241.46 down(g(f(x0))) 542.34/241.46 down(g(b)) 542.34/241.46 down(g(c)) 542.34/241.46 down(g(fresh_constant)) 542.34/241.46 down(f(f(a))) 542.34/241.46 down(f(f(b))) 542.34/241.46 down(f(f(g(x0)))) 542.34/241.46 down(f(f(c))) 542.34/241.46 down(f(f(fresh_constant))) 542.34/241.46 down(g(g(a))) 542.34/241.46 down(g(g(f(x0)))) 542.34/241.46 down(g(g(b))) 542.34/241.46 down(g(g(c))) 542.34/241.46 down(g(g(fresh_constant))) 542.34/241.46 down(f(f(f(a)))) 542.34/241.46 down(f(f(f(b)))) 542.34/241.46 down(f(f(f(g(x0))))) 542.34/241.46 down(f(f(f(c)))) 542.34/241.46 down(f(f(f(fresh_constant)))) 542.34/241.46 down(g(g(g(a)))) 542.34/241.46 down(g(g(g(f(x0))))) 542.34/241.46 down(g(g(g(b)))) 542.34/241.46 down(g(g(g(c)))) 542.34/241.46 down(g(g(g(fresh_constant)))) 542.34/241.46 down(f(f(f(f(a))))) 542.34/241.46 down(f(f(f(f(b))))) 542.34/241.46 down(f(f(f(f(g(x0)))))) 542.34/241.46 down(f(f(f(f(c))))) 542.34/241.46 down(f(f(f(f(fresh_constant))))) 542.34/241.46 down(g(g(g(g(a))))) 542.34/241.46 down(g(g(g(g(f(x0)))))) 542.34/241.46 down(g(g(g(g(b))))) 542.34/241.46 down(g(g(g(g(c))))) 542.34/241.46 down(g(g(g(g(fresh_constant))))) 542.34/241.46 down(f(f(f(f(f(a)))))) 542.34/241.46 down(f(f(f(f(f(b)))))) 542.34/241.46 down(f(f(f(f(f(g(x0))))))) 542.34/241.46 down(f(f(f(f(f(c)))))) 542.34/241.46 down(f(f(f(f(f(fresh_constant)))))) 542.34/241.46 down(g(g(g(g(g(a)))))) 542.34/241.46 down(g(g(g(g(g(f(x0))))))) 542.34/241.46 down(g(g(g(g(g(b)))))) 542.34/241.46 down(g(g(g(g(g(c)))))) 542.34/241.46 down(g(g(g(g(g(fresh_constant)))))) 542.34/241.46 down(f(f(f(f(f(f(a))))))) 542.34/241.46 down(f(f(f(f(f(f(b))))))) 542.34/241.46 down(f(f(f(f(f(f(g(x0)))))))) 542.34/241.46 down(f(f(f(f(f(f(c))))))) 542.34/241.46 down(f(f(f(f(f(f(fresh_constant))))))) 542.34/241.46 down(g(g(g(g(g(g(a))))))) 542.34/241.46 down(g(g(g(g(g(g(f(x0)))))))) 542.34/241.46 down(g(g(g(g(g(g(b))))))) 542.34/241.46 down(g(g(g(g(g(g(c))))))) 542.34/241.46 down(g(g(g(g(g(g(fresh_constant))))))) 542.34/241.46 down(f(f(f(f(f(f(f(a)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(b)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(g(x0))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(c)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(a)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(f(x0))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(b)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(c)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(a))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(b))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(c))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(a))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(b))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(c))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.46 f_flat(up(x0)) 542.34/241.46 g_flat(up(x0)) 542.34/241.46 542.34/241.46 We have to consider all minimal (P,Q,R)-chains. 542.34/241.46 ---------------------------------------- 542.34/241.46 542.34/241.46 (257) TransformationProof (EQUIVALENT) 542.34/241.46 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(c))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.34/241.46 542.34/241.46 (TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c)))))))))))) 542.34/241.46 542.34/241.46 542.34/241.46 ---------------------------------------- 542.34/241.46 542.34/241.46 (258) 542.34/241.46 Obligation: 542.34/241.46 Q DP problem: 542.34/241.46 The TRS P consists of the following rules: 542.34/241.46 542.34/241.46 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.34/241.46 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.34/241.46 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.34/241.46 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.34/241.46 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.34/241.46 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.34/241.46 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.34/241.46 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.34/241.46 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.34/241.46 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.34/241.46 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.34/241.46 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.34/241.46 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.34/241.46 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.34/241.46 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.34/241.46 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.34/241.46 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.34/241.46 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.34/241.46 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.34/241.46 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.34/241.46 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.34/241.46 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.34/241.46 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.34/241.46 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.34/241.46 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.34/241.46 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.34/241.46 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.34/241.46 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.34/241.46 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.34/241.46 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.34/241.46 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.34/241.46 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.34/241.46 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.34/241.46 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.34/241.46 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.34/241.46 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.34/241.46 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.34/241.46 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.34/241.46 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.34/241.46 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.34/241.46 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.34/241.46 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.34/241.46 542.34/241.46 The TRS R consists of the following rules: 542.34/241.46 542.34/241.46 down(a) -> up(f(a)) 542.34/241.46 down(b) -> up(g(b)) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.34/241.46 down(f(a)) -> f_flat(down(a)) 542.34/241.46 down(f(b)) -> f_flat(down(b)) 542.34/241.46 down(f(g(y4))) -> f_flat(down(g(y4))) 542.34/241.46 down(f(c)) -> f_flat(down(c)) 542.34/241.46 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.34/241.46 down(g(a)) -> g_flat(down(a)) 542.34/241.46 down(g(f(y6))) -> g_flat(down(f(y6))) 542.34/241.46 down(g(b)) -> g_flat(down(b)) 542.34/241.46 down(g(c)) -> g_flat(down(c)) 542.34/241.46 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.34/241.46 down(f(f(a))) -> f_flat(down(f(a))) 542.34/241.46 down(f(f(b))) -> f_flat(down(f(b))) 542.34/241.46 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.34/241.46 down(f(f(c))) -> f_flat(down(f(c))) 542.34/241.46 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.34/241.46 down(g(g(a))) -> g_flat(down(g(a))) 542.34/241.46 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.34/241.46 down(g(g(b))) -> g_flat(down(g(b))) 542.34/241.46 down(g(g(c))) -> g_flat(down(g(c))) 542.34/241.46 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.34/241.46 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.34/241.46 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.34/241.46 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.34/241.46 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.34/241.46 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.34/241.46 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.34/241.46 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.34/241.46 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.34/241.46 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.34/241.46 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.34/241.46 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.34/241.46 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.34/241.46 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.34/241.46 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.34/241.46 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.34/241.46 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.34/241.46 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.34/241.46 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.34/241.46 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.34/241.46 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.34/241.46 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.34/241.46 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.34/241.46 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.34/241.46 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.34/241.46 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.34/241.46 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.34/241.46 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.34/241.46 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.34/241.46 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.34/241.46 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.34/241.46 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.34/241.46 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.34/241.46 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.34/241.46 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.34/241.46 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.34/241.46 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.34/241.46 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.34/241.46 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.34/241.46 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.34/241.46 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.34/241.46 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.34/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.34/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.34/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.46 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.46 542.63/241.46 The set Q consists of the following terms: 542.63/241.46 542.63/241.46 down(a) 542.63/241.46 down(b) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.46 down(f(a)) 542.63/241.46 down(f(b)) 542.63/241.46 down(f(g(x0))) 542.63/241.46 down(f(c)) 542.63/241.46 down(f(fresh_constant)) 542.63/241.46 down(g(a)) 542.63/241.46 down(g(f(x0))) 542.63/241.46 down(g(b)) 542.63/241.46 down(g(c)) 542.63/241.46 down(g(fresh_constant)) 542.63/241.46 down(f(f(a))) 542.63/241.46 down(f(f(b))) 542.63/241.46 down(f(f(g(x0)))) 542.63/241.46 down(f(f(c))) 542.63/241.46 down(f(f(fresh_constant))) 542.63/241.46 down(g(g(a))) 542.63/241.46 down(g(g(f(x0)))) 542.63/241.46 down(g(g(b))) 542.63/241.46 down(g(g(c))) 542.63/241.46 down(g(g(fresh_constant))) 542.63/241.46 down(f(f(f(a)))) 542.63/241.46 down(f(f(f(b)))) 542.63/241.46 down(f(f(f(g(x0))))) 542.63/241.46 down(f(f(f(c)))) 542.63/241.46 down(f(f(f(fresh_constant)))) 542.63/241.46 down(g(g(g(a)))) 542.63/241.46 down(g(g(g(f(x0))))) 542.63/241.46 down(g(g(g(b)))) 542.63/241.46 down(g(g(g(c)))) 542.63/241.46 down(g(g(g(fresh_constant)))) 542.63/241.46 down(f(f(f(f(a))))) 542.63/241.46 down(f(f(f(f(b))))) 542.63/241.46 down(f(f(f(f(g(x0)))))) 542.63/241.46 down(f(f(f(f(c))))) 542.63/241.46 down(f(f(f(f(fresh_constant))))) 542.63/241.46 down(g(g(g(g(a))))) 542.63/241.46 down(g(g(g(g(f(x0)))))) 542.63/241.46 down(g(g(g(g(b))))) 542.63/241.46 down(g(g(g(g(c))))) 542.63/241.46 down(g(g(g(g(fresh_constant))))) 542.63/241.46 down(f(f(f(f(f(a)))))) 542.63/241.46 down(f(f(f(f(f(b)))))) 542.63/241.46 down(f(f(f(f(f(g(x0))))))) 542.63/241.46 down(f(f(f(f(f(c)))))) 542.63/241.46 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.46 down(g(g(g(g(g(a)))))) 542.63/241.46 down(g(g(g(g(g(f(x0))))))) 542.63/241.46 down(g(g(g(g(g(b)))))) 542.63/241.46 down(g(g(g(g(g(c)))))) 542.63/241.46 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.46 down(f(f(f(f(f(f(a))))))) 542.63/241.46 down(f(f(f(f(f(f(b))))))) 542.63/241.46 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.46 down(f(f(f(f(f(f(c))))))) 542.63/241.46 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.46 down(g(g(g(g(g(g(a))))))) 542.63/241.46 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.46 down(g(g(g(g(g(g(b))))))) 542.63/241.46 down(g(g(g(g(g(g(c))))))) 542.63/241.46 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.46 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 f_flat(up(x0)) 542.63/241.46 g_flat(up(x0)) 542.63/241.46 542.63/241.46 We have to consider all minimal (P,Q,R)-chains. 542.63/241.46 ---------------------------------------- 542.63/241.46 542.63/241.46 (259) TransformationProof (EQUIVALENT) 542.63/241.46 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(down(g(g(g(g(g(g(g(g(fresh_constant))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 542.63/241.46 542.63/241.46 (TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant)))))))))))) 542.63/241.46 542.63/241.46 542.63/241.46 ---------------------------------------- 542.63/241.46 542.63/241.46 (260) 542.63/241.46 Obligation: 542.63/241.46 Q DP problem: 542.63/241.46 The TRS P consists of the following rules: 542.63/241.46 542.63/241.46 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.46 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.46 TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) 542.63/241.46 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.63/241.46 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.46 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.46 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.63/241.46 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.63/241.46 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.63/241.46 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.63/241.46 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.63/241.46 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.63/241.46 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.46 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.46 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.46 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.46 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.46 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.46 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.46 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.46 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.46 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.46 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.46 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.46 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.46 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.46 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.46 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.46 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.46 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.46 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.46 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.46 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.46 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.46 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.46 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.46 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.46 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.46 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.46 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.46 542.63/241.46 The TRS R consists of the following rules: 542.63/241.46 542.63/241.46 down(a) -> up(f(a)) 542.63/241.46 down(b) -> up(g(b)) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.46 down(f(a)) -> f_flat(down(a)) 542.63/241.46 down(f(b)) -> f_flat(down(b)) 542.63/241.46 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.46 down(f(c)) -> f_flat(down(c)) 542.63/241.46 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.46 down(g(a)) -> g_flat(down(a)) 542.63/241.46 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.46 down(g(b)) -> g_flat(down(b)) 542.63/241.46 down(g(c)) -> g_flat(down(c)) 542.63/241.46 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.46 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.46 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.46 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.46 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.46 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.46 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.46 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.46 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.46 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.46 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.46 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.46 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.46 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.46 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.46 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.46 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.46 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.46 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.46 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.46 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.46 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.46 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.46 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.46 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.46 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.46 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.46 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.46 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.46 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.46 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.46 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.46 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.46 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.46 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.46 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.46 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.46 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.46 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.46 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.46 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.46 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.46 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.46 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.46 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.46 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.46 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.46 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.46 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.46 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.46 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.46 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.46 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.46 542.63/241.46 The set Q consists of the following terms: 542.63/241.46 542.63/241.46 down(a) 542.63/241.46 down(b) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.46 down(f(a)) 542.63/241.46 down(f(b)) 542.63/241.46 down(f(g(x0))) 542.63/241.46 down(f(c)) 542.63/241.46 down(f(fresh_constant)) 542.63/241.46 down(g(a)) 542.63/241.46 down(g(f(x0))) 542.63/241.46 down(g(b)) 542.63/241.46 down(g(c)) 542.63/241.46 down(g(fresh_constant)) 542.63/241.46 down(f(f(a))) 542.63/241.46 down(f(f(b))) 542.63/241.46 down(f(f(g(x0)))) 542.63/241.46 down(f(f(c))) 542.63/241.46 down(f(f(fresh_constant))) 542.63/241.46 down(g(g(a))) 542.63/241.46 down(g(g(f(x0)))) 542.63/241.46 down(g(g(b))) 542.63/241.46 down(g(g(c))) 542.63/241.46 down(g(g(fresh_constant))) 542.63/241.46 down(f(f(f(a)))) 542.63/241.46 down(f(f(f(b)))) 542.63/241.46 down(f(f(f(g(x0))))) 542.63/241.46 down(f(f(f(c)))) 542.63/241.46 down(f(f(f(fresh_constant)))) 542.63/241.46 down(g(g(g(a)))) 542.63/241.46 down(g(g(g(f(x0))))) 542.63/241.46 down(g(g(g(b)))) 542.63/241.46 down(g(g(g(c)))) 542.63/241.46 down(g(g(g(fresh_constant)))) 542.63/241.46 down(f(f(f(f(a))))) 542.63/241.46 down(f(f(f(f(b))))) 542.63/241.46 down(f(f(f(f(g(x0)))))) 542.63/241.46 down(f(f(f(f(c))))) 542.63/241.46 down(f(f(f(f(fresh_constant))))) 542.63/241.46 down(g(g(g(g(a))))) 542.63/241.46 down(g(g(g(g(f(x0)))))) 542.63/241.46 down(g(g(g(g(b))))) 542.63/241.46 down(g(g(g(g(c))))) 542.63/241.46 down(g(g(g(g(fresh_constant))))) 542.63/241.46 down(f(f(f(f(f(a)))))) 542.63/241.46 down(f(f(f(f(f(b)))))) 542.63/241.46 down(f(f(f(f(f(g(x0))))))) 542.63/241.46 down(f(f(f(f(f(c)))))) 542.63/241.46 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.46 down(g(g(g(g(g(a)))))) 542.63/241.46 down(g(g(g(g(g(f(x0))))))) 542.63/241.46 down(g(g(g(g(g(b)))))) 542.63/241.46 down(g(g(g(g(g(c)))))) 542.63/241.46 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.46 down(f(f(f(f(f(f(a))))))) 542.63/241.46 down(f(f(f(f(f(f(b))))))) 542.63/241.46 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.46 down(f(f(f(f(f(f(c))))))) 542.63/241.46 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.46 down(g(g(g(g(g(g(a))))))) 542.63/241.46 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.46 down(g(g(g(g(g(g(b))))))) 542.63/241.46 down(g(g(g(g(g(g(c))))))) 542.63/241.46 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.46 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 f_flat(up(x0)) 542.63/241.46 g_flat(up(x0)) 542.63/241.46 542.63/241.46 We have to consider all minimal (P,Q,R)-chains. 542.63/241.46 ---------------------------------------- 542.63/241.46 542.63/241.46 (261) TransformationProof (EQUIVALENT) 542.63/241.46 By rewriting [LPAR04] the rule TOP(up(g(a))) -> TOP(g_flat(up(f(a)))) at position [0] we obtained the following new rules [LPAR04]: 542.63/241.46 542.63/241.46 (TOP(up(g(a))) -> TOP(up(g(f(a)))),TOP(up(g(a))) -> TOP(up(g(f(a))))) 542.63/241.46 542.63/241.46 542.63/241.46 ---------------------------------------- 542.63/241.46 542.63/241.46 (262) 542.63/241.46 Obligation: 542.63/241.46 Q DP problem: 542.63/241.46 The TRS P consists of the following rules: 542.63/241.46 542.63/241.46 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.46 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.46 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) 542.63/241.46 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.46 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.46 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.63/241.46 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.63/241.46 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.63/241.46 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.63/241.46 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.63/241.46 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.63/241.46 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.46 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.46 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.46 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.46 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.46 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.46 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.46 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.46 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.46 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.46 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.46 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.46 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.46 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.46 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.46 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.46 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.46 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.46 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.46 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.46 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.46 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.46 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.46 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.46 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.46 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.46 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.46 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.46 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.46 542.63/241.46 The TRS R consists of the following rules: 542.63/241.46 542.63/241.46 down(a) -> up(f(a)) 542.63/241.46 down(b) -> up(g(b)) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.46 down(f(a)) -> f_flat(down(a)) 542.63/241.46 down(f(b)) -> f_flat(down(b)) 542.63/241.46 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.46 down(f(c)) -> f_flat(down(c)) 542.63/241.46 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.46 down(g(a)) -> g_flat(down(a)) 542.63/241.46 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.46 down(g(b)) -> g_flat(down(b)) 542.63/241.46 down(g(c)) -> g_flat(down(c)) 542.63/241.46 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.46 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.46 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.46 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.46 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.46 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.46 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.46 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.46 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.46 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.46 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.46 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.46 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.46 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.46 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.46 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.46 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.46 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.46 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.46 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.46 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.46 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.46 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.46 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.46 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.46 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.46 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.46 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.46 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.46 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.46 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.46 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.46 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.46 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.46 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.46 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.46 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.46 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.46 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.46 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.46 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.46 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.46 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.46 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.46 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.46 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.46 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.46 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.46 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.46 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.46 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.46 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.46 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.46 542.63/241.46 The set Q consists of the following terms: 542.63/241.46 542.63/241.46 down(a) 542.63/241.46 down(b) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.46 down(f(a)) 542.63/241.46 down(f(b)) 542.63/241.46 down(f(g(x0))) 542.63/241.46 down(f(c)) 542.63/241.46 down(f(fresh_constant)) 542.63/241.46 down(g(a)) 542.63/241.46 down(g(f(x0))) 542.63/241.46 down(g(b)) 542.63/241.46 down(g(c)) 542.63/241.46 down(g(fresh_constant)) 542.63/241.46 down(f(f(a))) 542.63/241.46 down(f(f(b))) 542.63/241.46 down(f(f(g(x0)))) 542.63/241.46 down(f(f(c))) 542.63/241.46 down(f(f(fresh_constant))) 542.63/241.46 down(g(g(a))) 542.63/241.46 down(g(g(f(x0)))) 542.63/241.46 down(g(g(b))) 542.63/241.46 down(g(g(c))) 542.63/241.46 down(g(g(fresh_constant))) 542.63/241.46 down(f(f(f(a)))) 542.63/241.46 down(f(f(f(b)))) 542.63/241.46 down(f(f(f(g(x0))))) 542.63/241.46 down(f(f(f(c)))) 542.63/241.46 down(f(f(f(fresh_constant)))) 542.63/241.46 down(g(g(g(a)))) 542.63/241.46 down(g(g(g(f(x0))))) 542.63/241.46 down(g(g(g(b)))) 542.63/241.46 down(g(g(g(c)))) 542.63/241.46 down(g(g(g(fresh_constant)))) 542.63/241.46 down(f(f(f(f(a))))) 542.63/241.46 down(f(f(f(f(b))))) 542.63/241.46 down(f(f(f(f(g(x0)))))) 542.63/241.46 down(f(f(f(f(c))))) 542.63/241.46 down(f(f(f(f(fresh_constant))))) 542.63/241.46 down(g(g(g(g(a))))) 542.63/241.46 down(g(g(g(g(f(x0)))))) 542.63/241.46 down(g(g(g(g(b))))) 542.63/241.46 down(g(g(g(g(c))))) 542.63/241.46 down(g(g(g(g(fresh_constant))))) 542.63/241.46 down(f(f(f(f(f(a)))))) 542.63/241.46 down(f(f(f(f(f(b)))))) 542.63/241.46 down(f(f(f(f(f(g(x0))))))) 542.63/241.46 down(f(f(f(f(f(c)))))) 542.63/241.46 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.46 down(g(g(g(g(g(a)))))) 542.63/241.46 down(g(g(g(g(g(f(x0))))))) 542.63/241.46 down(g(g(g(g(g(b)))))) 542.63/241.46 down(g(g(g(g(g(c)))))) 542.63/241.46 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.46 down(f(f(f(f(f(f(a))))))) 542.63/241.46 down(f(f(f(f(f(f(b))))))) 542.63/241.46 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.46 down(f(f(f(f(f(f(c))))))) 542.63/241.46 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.46 down(g(g(g(g(g(g(a))))))) 542.63/241.46 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.46 down(g(g(g(g(g(g(b))))))) 542.63/241.46 down(g(g(g(g(g(g(c))))))) 542.63/241.46 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.46 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 f_flat(up(x0)) 542.63/241.46 g_flat(up(x0)) 542.63/241.46 542.63/241.46 We have to consider all minimal (P,Q,R)-chains. 542.63/241.46 ---------------------------------------- 542.63/241.46 542.63/241.46 (263) TransformationProof (EQUIVALENT) 542.63/241.46 By rewriting [LPAR04] the rule TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(down(a)))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.46 542.63/241.46 (TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))),TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a)))))) 542.63/241.46 542.63/241.46 542.63/241.46 ---------------------------------------- 542.63/241.46 542.63/241.46 (264) 542.63/241.46 Obligation: 542.63/241.46 Q DP problem: 542.63/241.46 The TRS P consists of the following rules: 542.63/241.46 542.63/241.46 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.46 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.46 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.46 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.46 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) 542.63/241.46 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.63/241.46 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.63/241.46 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.63/241.46 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.63/241.46 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.63/241.46 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.46 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.46 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.46 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.46 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.46 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.46 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.46 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.46 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.46 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.46 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.46 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.46 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.46 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.46 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.46 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.46 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.46 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.46 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.46 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.46 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.46 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.46 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.46 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.46 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.46 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.46 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.46 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.46 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.46 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.46 542.63/241.46 The TRS R consists of the following rules: 542.63/241.46 542.63/241.46 down(a) -> up(f(a)) 542.63/241.46 down(b) -> up(g(b)) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.46 down(f(a)) -> f_flat(down(a)) 542.63/241.46 down(f(b)) -> f_flat(down(b)) 542.63/241.46 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.46 down(f(c)) -> f_flat(down(c)) 542.63/241.46 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.46 down(g(a)) -> g_flat(down(a)) 542.63/241.46 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.46 down(g(b)) -> g_flat(down(b)) 542.63/241.46 down(g(c)) -> g_flat(down(c)) 542.63/241.46 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.46 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.46 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.46 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.46 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.46 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.46 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.46 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.46 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.46 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.46 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.46 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.46 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.46 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.46 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.46 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.46 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.46 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.46 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.46 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.46 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.46 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.46 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.46 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.46 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.46 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.46 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.46 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.46 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.46 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.46 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.46 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.46 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.46 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.46 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.46 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.46 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.46 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.46 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.46 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.46 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.46 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.46 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.46 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.46 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.46 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.46 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.46 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.46 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.46 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.46 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.46 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.46 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.46 542.63/241.46 The set Q consists of the following terms: 542.63/241.46 542.63/241.46 down(a) 542.63/241.46 down(b) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.46 down(f(a)) 542.63/241.46 down(f(b)) 542.63/241.46 down(f(g(x0))) 542.63/241.46 down(f(c)) 542.63/241.46 down(f(fresh_constant)) 542.63/241.46 down(g(a)) 542.63/241.46 down(g(f(x0))) 542.63/241.46 down(g(b)) 542.63/241.46 down(g(c)) 542.63/241.46 down(g(fresh_constant)) 542.63/241.46 down(f(f(a))) 542.63/241.46 down(f(f(b))) 542.63/241.46 down(f(f(g(x0)))) 542.63/241.46 down(f(f(c))) 542.63/241.46 down(f(f(fresh_constant))) 542.63/241.46 down(g(g(a))) 542.63/241.46 down(g(g(f(x0)))) 542.63/241.46 down(g(g(b))) 542.63/241.46 down(g(g(c))) 542.63/241.46 down(g(g(fresh_constant))) 542.63/241.46 down(f(f(f(a)))) 542.63/241.46 down(f(f(f(b)))) 542.63/241.46 down(f(f(f(g(x0))))) 542.63/241.46 down(f(f(f(c)))) 542.63/241.46 down(f(f(f(fresh_constant)))) 542.63/241.46 down(g(g(g(a)))) 542.63/241.46 down(g(g(g(f(x0))))) 542.63/241.46 down(g(g(g(b)))) 542.63/241.46 down(g(g(g(c)))) 542.63/241.46 down(g(g(g(fresh_constant)))) 542.63/241.46 down(f(f(f(f(a))))) 542.63/241.46 down(f(f(f(f(b))))) 542.63/241.46 down(f(f(f(f(g(x0)))))) 542.63/241.46 down(f(f(f(f(c))))) 542.63/241.46 down(f(f(f(f(fresh_constant))))) 542.63/241.46 down(g(g(g(g(a))))) 542.63/241.46 down(g(g(g(g(f(x0)))))) 542.63/241.46 down(g(g(g(g(b))))) 542.63/241.46 down(g(g(g(g(c))))) 542.63/241.46 down(g(g(g(g(fresh_constant))))) 542.63/241.46 down(f(f(f(f(f(a)))))) 542.63/241.46 down(f(f(f(f(f(b)))))) 542.63/241.46 down(f(f(f(f(f(g(x0))))))) 542.63/241.46 down(f(f(f(f(f(c)))))) 542.63/241.46 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.46 down(g(g(g(g(g(a)))))) 542.63/241.46 down(g(g(g(g(g(f(x0))))))) 542.63/241.46 down(g(g(g(g(g(b)))))) 542.63/241.46 down(g(g(g(g(g(c)))))) 542.63/241.46 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.46 down(f(f(f(f(f(f(a))))))) 542.63/241.46 down(f(f(f(f(f(f(b))))))) 542.63/241.46 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.46 down(f(f(f(f(f(f(c))))))) 542.63/241.46 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.46 down(g(g(g(g(g(g(a))))))) 542.63/241.46 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.46 down(g(g(g(g(g(g(b))))))) 542.63/241.46 down(g(g(g(g(g(g(c))))))) 542.63/241.46 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.46 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.46 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.46 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.46 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 f_flat(up(x0)) 542.63/241.46 g_flat(up(x0)) 542.63/241.46 542.63/241.46 We have to consider all minimal (P,Q,R)-chains. 542.63/241.46 ---------------------------------------- 542.63/241.46 542.63/241.46 (265) TransformationProof (EQUIVALENT) 542.63/241.46 By rewriting [LPAR04] the rule TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(down(b)))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.46 542.63/241.46 (TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))),TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b)))))) 542.63/241.46 542.63/241.46 542.63/241.46 ---------------------------------------- 542.63/241.46 542.63/241.46 (266) 542.63/241.46 Obligation: 542.63/241.46 Q DP problem: 542.63/241.46 The TRS P consists of the following rules: 542.63/241.46 542.63/241.46 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.46 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.46 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.46 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.46 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) 542.63/241.46 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.63/241.46 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.63/241.46 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.63/241.46 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.63/241.46 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.46 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.46 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.46 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.46 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.46 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.46 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.46 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.46 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.46 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.46 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.46 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.46 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.46 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.46 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.46 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.46 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.46 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.46 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.46 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.46 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.46 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.46 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.46 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.46 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.46 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.46 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.46 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.46 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.46 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.46 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.46 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.46 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.47 542.63/241.47 The TRS R consists of the following rules: 542.63/241.47 542.63/241.47 down(a) -> up(f(a)) 542.63/241.47 down(b) -> up(g(b)) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.47 down(f(a)) -> f_flat(down(a)) 542.63/241.47 down(f(b)) -> f_flat(down(b)) 542.63/241.47 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.47 down(f(c)) -> f_flat(down(c)) 542.63/241.47 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.47 down(g(a)) -> g_flat(down(a)) 542.63/241.47 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.47 down(g(b)) -> g_flat(down(b)) 542.63/241.47 down(g(c)) -> g_flat(down(c)) 542.63/241.47 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.47 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.47 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.47 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.47 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.47 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.47 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.47 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.47 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.47 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.47 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.47 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.47 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.47 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.47 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.47 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.47 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.47 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.47 542.63/241.47 The set Q consists of the following terms: 542.63/241.47 542.63/241.47 down(a) 542.63/241.47 down(b) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.47 down(f(a)) 542.63/241.47 down(f(b)) 542.63/241.47 down(f(g(x0))) 542.63/241.47 down(f(c)) 542.63/241.47 down(f(fresh_constant)) 542.63/241.47 down(g(a)) 542.63/241.47 down(g(f(x0))) 542.63/241.47 down(g(b)) 542.63/241.47 down(g(c)) 542.63/241.47 down(g(fresh_constant)) 542.63/241.47 down(f(f(a))) 542.63/241.47 down(f(f(b))) 542.63/241.47 down(f(f(g(x0)))) 542.63/241.47 down(f(f(c))) 542.63/241.47 down(f(f(fresh_constant))) 542.63/241.47 down(g(g(a))) 542.63/241.47 down(g(g(f(x0)))) 542.63/241.47 down(g(g(b))) 542.63/241.47 down(g(g(c))) 542.63/241.47 down(g(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) 542.63/241.47 down(f(f(f(g(x0))))) 542.63/241.47 down(f(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) 542.63/241.47 down(g(g(g(f(x0))))) 542.63/241.47 down(g(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(x0)))))) 542.63/241.47 down(f(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(x0)))))) 542.63/241.47 down(g(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(x0))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(x0))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 f_flat(up(x0)) 542.63/241.47 g_flat(up(x0)) 542.63/241.47 542.63/241.47 We have to consider all minimal (P,Q,R)-chains. 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (267) TransformationProof (EQUIVALENT) 542.63/241.47 By rewriting [LPAR04] the rule TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(down(f(a))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.47 542.63/241.47 (TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))),TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a)))))) 542.63/241.47 542.63/241.47 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (268) 542.63/241.47 Obligation: 542.63/241.47 Q DP problem: 542.63/241.47 The TRS P consists of the following rules: 542.63/241.47 542.63/241.47 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.47 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.47 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.47 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.47 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) 542.63/241.47 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.63/241.47 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.63/241.47 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.63/241.47 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.47 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.47 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.47 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.47 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.47 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.47 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.47 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.47 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.47 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.47 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.47 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.47 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.47 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.47 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.47 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.47 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.47 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.47 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.47 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.47 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.47 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.47 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.47 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.47 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.47 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.47 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.47 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.47 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.47 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.47 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.47 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.47 542.63/241.47 The TRS R consists of the following rules: 542.63/241.47 542.63/241.47 down(a) -> up(f(a)) 542.63/241.47 down(b) -> up(g(b)) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.47 down(f(a)) -> f_flat(down(a)) 542.63/241.47 down(f(b)) -> f_flat(down(b)) 542.63/241.47 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.47 down(f(c)) -> f_flat(down(c)) 542.63/241.47 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.47 down(g(a)) -> g_flat(down(a)) 542.63/241.47 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.47 down(g(b)) -> g_flat(down(b)) 542.63/241.47 down(g(c)) -> g_flat(down(c)) 542.63/241.47 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.47 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.47 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.47 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.47 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.47 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.47 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.47 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.47 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.47 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.47 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.47 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.47 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.47 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.47 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.47 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.47 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.47 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.47 542.63/241.47 The set Q consists of the following terms: 542.63/241.47 542.63/241.47 down(a) 542.63/241.47 down(b) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.47 down(f(a)) 542.63/241.47 down(f(b)) 542.63/241.47 down(f(g(x0))) 542.63/241.47 down(f(c)) 542.63/241.47 down(f(fresh_constant)) 542.63/241.47 down(g(a)) 542.63/241.47 down(g(f(x0))) 542.63/241.47 down(g(b)) 542.63/241.47 down(g(c)) 542.63/241.47 down(g(fresh_constant)) 542.63/241.47 down(f(f(a))) 542.63/241.47 down(f(f(b))) 542.63/241.47 down(f(f(g(x0)))) 542.63/241.47 down(f(f(c))) 542.63/241.47 down(f(f(fresh_constant))) 542.63/241.47 down(g(g(a))) 542.63/241.47 down(g(g(f(x0)))) 542.63/241.47 down(g(g(b))) 542.63/241.47 down(g(g(c))) 542.63/241.47 down(g(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) 542.63/241.47 down(f(f(f(g(x0))))) 542.63/241.47 down(f(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) 542.63/241.47 down(g(g(g(f(x0))))) 542.63/241.47 down(g(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(x0)))))) 542.63/241.47 down(f(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(x0)))))) 542.63/241.47 down(g(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(x0))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(x0))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 f_flat(up(x0)) 542.63/241.47 g_flat(up(x0)) 542.63/241.47 542.63/241.47 We have to consider all minimal (P,Q,R)-chains. 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (269) TransformationProof (EQUIVALENT) 542.63/241.47 By rewriting [LPAR04] the rule TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(down(f(b))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.47 542.63/241.47 (TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))),TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b)))))) 542.63/241.47 542.63/241.47 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (270) 542.63/241.47 Obligation: 542.63/241.47 Q DP problem: 542.63/241.47 The TRS P consists of the following rules: 542.63/241.47 542.63/241.47 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.47 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.47 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.47 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.47 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) 542.63/241.47 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.63/241.47 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.63/241.47 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.47 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.47 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.47 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.47 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.47 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.47 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.47 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.47 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.47 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.47 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.47 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.47 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.47 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.47 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.47 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.47 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.47 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.47 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.47 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.47 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.47 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.47 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.47 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.47 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.47 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.47 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.47 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.47 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.47 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.47 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.47 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.47 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.47 542.63/241.47 The TRS R consists of the following rules: 542.63/241.47 542.63/241.47 down(a) -> up(f(a)) 542.63/241.47 down(b) -> up(g(b)) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.47 down(f(a)) -> f_flat(down(a)) 542.63/241.47 down(f(b)) -> f_flat(down(b)) 542.63/241.47 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.47 down(f(c)) -> f_flat(down(c)) 542.63/241.47 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.47 down(g(a)) -> g_flat(down(a)) 542.63/241.47 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.47 down(g(b)) -> g_flat(down(b)) 542.63/241.47 down(g(c)) -> g_flat(down(c)) 542.63/241.47 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.47 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.47 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.47 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.47 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.47 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.47 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.47 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.47 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.47 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.47 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.47 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.47 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.47 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.47 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.47 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.47 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.47 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.47 542.63/241.47 The set Q consists of the following terms: 542.63/241.47 542.63/241.47 down(a) 542.63/241.47 down(b) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.47 down(f(a)) 542.63/241.47 down(f(b)) 542.63/241.47 down(f(g(x0))) 542.63/241.47 down(f(c)) 542.63/241.47 down(f(fresh_constant)) 542.63/241.47 down(g(a)) 542.63/241.47 down(g(f(x0))) 542.63/241.47 down(g(b)) 542.63/241.47 down(g(c)) 542.63/241.47 down(g(fresh_constant)) 542.63/241.47 down(f(f(a))) 542.63/241.47 down(f(f(b))) 542.63/241.47 down(f(f(g(x0)))) 542.63/241.47 down(f(f(c))) 542.63/241.47 down(f(f(fresh_constant))) 542.63/241.47 down(g(g(a))) 542.63/241.47 down(g(g(f(x0)))) 542.63/241.47 down(g(g(b))) 542.63/241.47 down(g(g(c))) 542.63/241.47 down(g(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) 542.63/241.47 down(f(f(f(g(x0))))) 542.63/241.47 down(f(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) 542.63/241.47 down(g(g(g(f(x0))))) 542.63/241.47 down(g(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(x0)))))) 542.63/241.47 down(f(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(x0)))))) 542.63/241.47 down(g(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(x0))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(x0))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 f_flat(up(x0)) 542.63/241.47 g_flat(up(x0)) 542.63/241.47 542.63/241.47 We have to consider all minimal (P,Q,R)-chains. 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (271) TransformationProof (EQUIVALENT) 542.63/241.47 By rewriting [LPAR04] the rule TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(down(f(g(x0)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.47 542.63/241.47 (TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))),TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0))))))) 542.63/241.47 542.63/241.47 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (272) 542.63/241.47 Obligation: 542.63/241.47 Q DP problem: 542.63/241.47 The TRS P consists of the following rules: 542.63/241.47 542.63/241.47 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.47 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.47 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.47 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.47 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) 542.63/241.47 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.63/241.47 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.47 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.47 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.47 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.47 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.47 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.47 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.47 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.47 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.47 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.47 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.47 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.47 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.47 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.47 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.47 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.47 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.47 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.47 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.47 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.47 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.47 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.47 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.47 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.47 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.47 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.47 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.47 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.47 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.47 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.47 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.47 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.47 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.47 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.47 542.63/241.47 The TRS R consists of the following rules: 542.63/241.47 542.63/241.47 down(a) -> up(f(a)) 542.63/241.47 down(b) -> up(g(b)) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.47 down(f(a)) -> f_flat(down(a)) 542.63/241.47 down(f(b)) -> f_flat(down(b)) 542.63/241.47 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.47 down(f(c)) -> f_flat(down(c)) 542.63/241.47 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.47 down(g(a)) -> g_flat(down(a)) 542.63/241.47 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.47 down(g(b)) -> g_flat(down(b)) 542.63/241.47 down(g(c)) -> g_flat(down(c)) 542.63/241.47 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.47 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.47 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.47 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.47 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.47 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.47 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.47 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.47 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.47 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.47 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.47 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.47 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.47 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.47 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.47 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.47 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.47 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.47 542.63/241.47 The set Q consists of the following terms: 542.63/241.47 542.63/241.47 down(a) 542.63/241.47 down(b) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.47 down(f(a)) 542.63/241.47 down(f(b)) 542.63/241.47 down(f(g(x0))) 542.63/241.47 down(f(c)) 542.63/241.47 down(f(fresh_constant)) 542.63/241.47 down(g(a)) 542.63/241.47 down(g(f(x0))) 542.63/241.47 down(g(b)) 542.63/241.47 down(g(c)) 542.63/241.47 down(g(fresh_constant)) 542.63/241.47 down(f(f(a))) 542.63/241.47 down(f(f(b))) 542.63/241.47 down(f(f(g(x0)))) 542.63/241.47 down(f(f(c))) 542.63/241.47 down(f(f(fresh_constant))) 542.63/241.47 down(g(g(a))) 542.63/241.47 down(g(g(f(x0)))) 542.63/241.47 down(g(g(b))) 542.63/241.47 down(g(g(c))) 542.63/241.47 down(g(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) 542.63/241.47 down(f(f(f(g(x0))))) 542.63/241.47 down(f(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) 542.63/241.47 down(g(g(g(f(x0))))) 542.63/241.47 down(g(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(x0)))))) 542.63/241.47 down(f(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(x0)))))) 542.63/241.47 down(g(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(x0))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(x0))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 f_flat(up(x0)) 542.63/241.47 g_flat(up(x0)) 542.63/241.47 542.63/241.47 We have to consider all minimal (P,Q,R)-chains. 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (273) TransformationProof (EQUIVALENT) 542.63/241.47 By rewriting [LPAR04] the rule TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(down(f(c))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.47 542.63/241.47 (TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(f_flat(down(c))))),TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(f_flat(down(c)))))) 542.63/241.47 542.63/241.47 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (274) 542.63/241.47 Obligation: 542.63/241.47 Q DP problem: 542.63/241.47 The TRS P consists of the following rules: 542.63/241.47 542.63/241.47 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.47 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.47 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.47 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.47 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.63/241.47 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.47 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.47 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.47 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.47 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.47 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.47 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.47 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.47 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.47 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.47 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.47 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.47 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.47 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.47 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.47 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.47 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.47 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.47 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.47 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.47 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.47 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.47 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.47 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.47 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.47 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.47 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.47 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.47 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.47 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.47 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.47 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.47 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.47 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.47 TOP(up(f(f(f(c))))) -> TOP(f_flat(f_flat(f_flat(down(c))))) 542.63/241.47 542.63/241.47 The TRS R consists of the following rules: 542.63/241.47 542.63/241.47 down(a) -> up(f(a)) 542.63/241.47 down(b) -> up(g(b)) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.47 down(f(a)) -> f_flat(down(a)) 542.63/241.47 down(f(b)) -> f_flat(down(b)) 542.63/241.47 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.47 down(f(c)) -> f_flat(down(c)) 542.63/241.47 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.47 down(g(a)) -> g_flat(down(a)) 542.63/241.47 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.47 down(g(b)) -> g_flat(down(b)) 542.63/241.47 down(g(c)) -> g_flat(down(c)) 542.63/241.47 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.47 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.47 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.47 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.47 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.47 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.47 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.47 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.47 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.47 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.47 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.47 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.47 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.47 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.47 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.47 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.47 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.47 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.47 542.63/241.47 The set Q consists of the following terms: 542.63/241.47 542.63/241.47 down(a) 542.63/241.47 down(b) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.47 down(f(a)) 542.63/241.47 down(f(b)) 542.63/241.47 down(f(g(x0))) 542.63/241.47 down(f(c)) 542.63/241.47 down(f(fresh_constant)) 542.63/241.47 down(g(a)) 542.63/241.47 down(g(f(x0))) 542.63/241.47 down(g(b)) 542.63/241.47 down(g(c)) 542.63/241.47 down(g(fresh_constant)) 542.63/241.47 down(f(f(a))) 542.63/241.47 down(f(f(b))) 542.63/241.47 down(f(f(g(x0)))) 542.63/241.47 down(f(f(c))) 542.63/241.47 down(f(f(fresh_constant))) 542.63/241.47 down(g(g(a))) 542.63/241.47 down(g(g(f(x0)))) 542.63/241.47 down(g(g(b))) 542.63/241.47 down(g(g(c))) 542.63/241.47 down(g(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) 542.63/241.47 down(f(f(f(g(x0))))) 542.63/241.47 down(f(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) 542.63/241.47 down(g(g(g(f(x0))))) 542.63/241.47 down(g(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(x0)))))) 542.63/241.47 down(f(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(x0)))))) 542.63/241.47 down(g(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(x0))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(x0))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 f_flat(up(x0)) 542.63/241.47 g_flat(up(x0)) 542.63/241.47 542.63/241.47 We have to consider all minimal (P,Q,R)-chains. 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (275) DependencyGraphProof (EQUIVALENT) 542.63/241.47 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (276) 542.63/241.47 Obligation: 542.63/241.47 Q DP problem: 542.63/241.47 The TRS P consists of the following rules: 542.63/241.47 542.63/241.47 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.47 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.47 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.47 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.47 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) 542.63/241.47 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.47 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.47 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.47 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.47 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.47 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.47 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.47 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.47 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.47 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.47 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.47 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.47 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.47 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.47 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.47 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.47 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.47 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.47 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.47 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.47 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.47 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.47 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.47 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.47 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.47 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.47 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.47 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.47 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.47 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.47 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.47 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.47 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.47 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.47 542.63/241.47 The TRS R consists of the following rules: 542.63/241.47 542.63/241.47 down(a) -> up(f(a)) 542.63/241.47 down(b) -> up(g(b)) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.47 down(f(a)) -> f_flat(down(a)) 542.63/241.47 down(f(b)) -> f_flat(down(b)) 542.63/241.47 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.47 down(f(c)) -> f_flat(down(c)) 542.63/241.47 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.47 down(g(a)) -> g_flat(down(a)) 542.63/241.47 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.47 down(g(b)) -> g_flat(down(b)) 542.63/241.47 down(g(c)) -> g_flat(down(c)) 542.63/241.47 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.47 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.47 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.47 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.47 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.47 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.47 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.47 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.47 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.47 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.47 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.47 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.47 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.47 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.47 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.47 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.47 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.47 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.47 542.63/241.47 The set Q consists of the following terms: 542.63/241.47 542.63/241.47 down(a) 542.63/241.47 down(b) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.47 down(f(a)) 542.63/241.47 down(f(b)) 542.63/241.47 down(f(g(x0))) 542.63/241.47 down(f(c)) 542.63/241.47 down(f(fresh_constant)) 542.63/241.47 down(g(a)) 542.63/241.47 down(g(f(x0))) 542.63/241.47 down(g(b)) 542.63/241.47 down(g(c)) 542.63/241.47 down(g(fresh_constant)) 542.63/241.47 down(f(f(a))) 542.63/241.47 down(f(f(b))) 542.63/241.47 down(f(f(g(x0)))) 542.63/241.47 down(f(f(c))) 542.63/241.47 down(f(f(fresh_constant))) 542.63/241.47 down(g(g(a))) 542.63/241.47 down(g(g(f(x0)))) 542.63/241.47 down(g(g(b))) 542.63/241.47 down(g(g(c))) 542.63/241.47 down(g(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) 542.63/241.47 down(f(f(f(g(x0))))) 542.63/241.47 down(f(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) 542.63/241.47 down(g(g(g(f(x0))))) 542.63/241.47 down(g(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(x0)))))) 542.63/241.47 down(f(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(x0)))))) 542.63/241.47 down(g(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(x0))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(x0))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 f_flat(up(x0)) 542.63/241.47 g_flat(up(x0)) 542.63/241.47 542.63/241.47 We have to consider all minimal (P,Q,R)-chains. 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (277) TransformationProof (EQUIVALENT) 542.63/241.47 By rewriting [LPAR04] the rule TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(down(f(fresh_constant))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.47 542.63/241.47 (TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(f_flat(down(fresh_constant))))),TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(f_flat(down(fresh_constant)))))) 542.63/241.47 542.63/241.47 542.63/241.47 ---------------------------------------- 542.63/241.47 542.63/241.47 (278) 542.63/241.47 Obligation: 542.63/241.47 Q DP problem: 542.63/241.47 The TRS P consists of the following rules: 542.63/241.47 542.63/241.47 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.47 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.47 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.47 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.47 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.47 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.47 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.47 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.47 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.47 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.47 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.47 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.47 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.47 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.47 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.47 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.47 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.47 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.47 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.47 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.47 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.47 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.47 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.47 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.47 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.47 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.47 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.47 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.47 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.47 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.47 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.47 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.47 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.47 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.47 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.47 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.47 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.47 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.47 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.47 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.47 TOP(up(f(f(f(fresh_constant))))) -> TOP(f_flat(f_flat(f_flat(down(fresh_constant))))) 542.63/241.47 542.63/241.47 The TRS R consists of the following rules: 542.63/241.47 542.63/241.47 down(a) -> up(f(a)) 542.63/241.47 down(b) -> up(g(b)) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.47 down(f(a)) -> f_flat(down(a)) 542.63/241.47 down(f(b)) -> f_flat(down(b)) 542.63/241.47 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.47 down(f(c)) -> f_flat(down(c)) 542.63/241.47 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.47 down(g(a)) -> g_flat(down(a)) 542.63/241.47 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.47 down(g(b)) -> g_flat(down(b)) 542.63/241.47 down(g(c)) -> g_flat(down(c)) 542.63/241.47 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.47 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.47 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.47 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.47 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.47 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.47 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.47 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.47 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.47 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.47 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.47 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.47 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.47 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.47 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.47 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.47 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.47 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.47 542.63/241.47 The set Q consists of the following terms: 542.63/241.47 542.63/241.47 down(a) 542.63/241.47 down(b) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.47 down(f(a)) 542.63/241.47 down(f(b)) 542.63/241.47 down(f(g(x0))) 542.63/241.47 down(f(c)) 542.63/241.47 down(f(fresh_constant)) 542.63/241.47 down(g(a)) 542.63/241.47 down(g(f(x0))) 542.63/241.47 down(g(b)) 542.63/241.47 down(g(c)) 542.63/241.47 down(g(fresh_constant)) 542.63/241.47 down(f(f(a))) 542.63/241.47 down(f(f(b))) 542.63/241.47 down(f(f(g(x0)))) 542.63/241.47 down(f(f(c))) 542.63/241.47 down(f(f(fresh_constant))) 542.63/241.47 down(g(g(a))) 542.63/241.47 down(g(g(f(x0)))) 542.63/241.47 down(g(g(b))) 542.63/241.47 down(g(g(c))) 542.63/241.47 down(g(g(fresh_constant))) 542.63/241.47 down(f(f(f(a)))) 542.63/241.47 down(f(f(f(b)))) 542.63/241.47 down(f(f(f(g(x0))))) 542.63/241.47 down(f(f(f(c)))) 542.63/241.47 down(f(f(f(fresh_constant)))) 542.63/241.47 down(g(g(g(a)))) 542.63/241.47 down(g(g(g(f(x0))))) 542.63/241.47 down(g(g(g(b)))) 542.63/241.47 down(g(g(g(c)))) 542.63/241.47 down(g(g(g(fresh_constant)))) 542.63/241.47 down(f(f(f(f(a))))) 542.63/241.47 down(f(f(f(f(b))))) 542.63/241.47 down(f(f(f(f(g(x0)))))) 542.63/241.47 down(f(f(f(f(c))))) 542.63/241.47 down(f(f(f(f(fresh_constant))))) 542.63/241.47 down(g(g(g(g(a))))) 542.63/241.47 down(g(g(g(g(f(x0)))))) 542.63/241.47 down(g(g(g(g(b))))) 542.63/241.47 down(g(g(g(g(c))))) 542.63/241.47 down(g(g(g(g(fresh_constant))))) 542.63/241.47 down(f(f(f(f(f(a)))))) 542.63/241.47 down(f(f(f(f(f(b)))))) 542.63/241.47 down(f(f(f(f(f(g(x0))))))) 542.63/241.47 down(f(f(f(f(f(c)))))) 542.63/241.47 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.47 down(g(g(g(g(g(a)))))) 542.63/241.47 down(g(g(g(g(g(f(x0))))))) 542.63/241.47 down(g(g(g(g(g(b)))))) 542.63/241.47 down(g(g(g(g(g(c)))))) 542.63/241.47 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.47 down(f(f(f(f(f(f(a))))))) 542.63/241.47 down(f(f(f(f(f(f(b))))))) 542.63/241.47 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.47 down(f(f(f(f(f(f(c))))))) 542.63/241.47 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.47 down(g(g(g(g(g(g(a))))))) 542.63/241.47 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.47 down(g(g(g(g(g(g(b))))))) 542.63/241.47 down(g(g(g(g(g(g(c))))))) 542.63/241.47 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.47 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.47 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.47 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.47 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.47 f_flat(up(x0)) 542.63/241.47 g_flat(up(x0)) 542.63/241.47 542.63/241.47 We have to consider all minimal (P,Q,R)-chains. 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (279) DependencyGraphProof (EQUIVALENT) 542.63/241.48 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (280) 542.63/241.48 Obligation: 542.63/241.48 Q DP problem: 542.63/241.48 The TRS P consists of the following rules: 542.63/241.48 542.63/241.48 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.48 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.48 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.48 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.48 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) 542.63/241.48 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.48 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.48 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.48 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.48 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.48 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.48 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.48 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.48 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.48 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.48 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.48 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.48 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.48 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.48 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.48 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.48 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.48 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.48 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.48 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.48 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.48 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.48 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.48 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.48 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.48 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.48 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.48 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.48 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.48 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.48 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.48 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.48 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.48 542.63/241.48 The TRS R consists of the following rules: 542.63/241.48 542.63/241.48 down(a) -> up(f(a)) 542.63/241.48 down(b) -> up(g(b)) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.48 down(f(a)) -> f_flat(down(a)) 542.63/241.48 down(f(b)) -> f_flat(down(b)) 542.63/241.48 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.48 down(f(c)) -> f_flat(down(c)) 542.63/241.48 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.48 down(g(a)) -> g_flat(down(a)) 542.63/241.48 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.48 down(g(b)) -> g_flat(down(b)) 542.63/241.48 down(g(c)) -> g_flat(down(c)) 542.63/241.48 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.48 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.48 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.48 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.48 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.48 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.48 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.48 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.48 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.48 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.48 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.48 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.48 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.48 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.48 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.48 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.48 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.48 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.48 542.63/241.48 The set Q consists of the following terms: 542.63/241.48 542.63/241.48 down(a) 542.63/241.48 down(b) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.48 down(f(a)) 542.63/241.48 down(f(b)) 542.63/241.48 down(f(g(x0))) 542.63/241.48 down(f(c)) 542.63/241.48 down(f(fresh_constant)) 542.63/241.48 down(g(a)) 542.63/241.48 down(g(f(x0))) 542.63/241.48 down(g(b)) 542.63/241.48 down(g(c)) 542.63/241.48 down(g(fresh_constant)) 542.63/241.48 down(f(f(a))) 542.63/241.48 down(f(f(b))) 542.63/241.48 down(f(f(g(x0)))) 542.63/241.48 down(f(f(c))) 542.63/241.48 down(f(f(fresh_constant))) 542.63/241.48 down(g(g(a))) 542.63/241.48 down(g(g(f(x0)))) 542.63/241.48 down(g(g(b))) 542.63/241.48 down(g(g(c))) 542.63/241.48 down(g(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) 542.63/241.48 down(f(f(f(g(x0))))) 542.63/241.48 down(f(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) 542.63/241.48 down(g(g(g(f(x0))))) 542.63/241.48 down(g(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(x0)))))) 542.63/241.48 down(f(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(x0)))))) 542.63/241.48 down(g(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(x0))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(x0))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 f_flat(up(x0)) 542.63/241.48 g_flat(up(x0)) 542.63/241.48 542.63/241.48 We have to consider all minimal (P,Q,R)-chains. 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (281) TransformationProof (EQUIVALENT) 542.63/241.48 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(down(f(f(a)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.48 542.63/241.48 (TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))),TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a))))))) 542.63/241.48 542.63/241.48 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (282) 542.63/241.48 Obligation: 542.63/241.48 Q DP problem: 542.63/241.48 The TRS P consists of the following rules: 542.63/241.48 542.63/241.48 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.48 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.48 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.48 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.48 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) 542.63/241.48 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.48 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.48 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.48 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.48 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.48 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.48 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.48 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.48 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.48 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.48 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.48 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.48 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.48 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.48 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.48 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.48 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.48 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.48 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.48 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.48 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.48 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.48 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.48 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.48 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.48 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.48 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.48 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.48 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.48 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.48 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.48 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.48 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.63/241.48 542.63/241.48 The TRS R consists of the following rules: 542.63/241.48 542.63/241.48 down(a) -> up(f(a)) 542.63/241.48 down(b) -> up(g(b)) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.48 down(f(a)) -> f_flat(down(a)) 542.63/241.48 down(f(b)) -> f_flat(down(b)) 542.63/241.48 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.48 down(f(c)) -> f_flat(down(c)) 542.63/241.48 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.48 down(g(a)) -> g_flat(down(a)) 542.63/241.48 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.48 down(g(b)) -> g_flat(down(b)) 542.63/241.48 down(g(c)) -> g_flat(down(c)) 542.63/241.48 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.48 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.48 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.48 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.48 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.48 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.48 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.48 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.48 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.48 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.48 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.48 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.48 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.48 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.48 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.48 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.48 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.48 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.48 542.63/241.48 The set Q consists of the following terms: 542.63/241.48 542.63/241.48 down(a) 542.63/241.48 down(b) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.48 down(f(a)) 542.63/241.48 down(f(b)) 542.63/241.48 down(f(g(x0))) 542.63/241.48 down(f(c)) 542.63/241.48 down(f(fresh_constant)) 542.63/241.48 down(g(a)) 542.63/241.48 down(g(f(x0))) 542.63/241.48 down(g(b)) 542.63/241.48 down(g(c)) 542.63/241.48 down(g(fresh_constant)) 542.63/241.48 down(f(f(a))) 542.63/241.48 down(f(f(b))) 542.63/241.48 down(f(f(g(x0)))) 542.63/241.48 down(f(f(c))) 542.63/241.48 down(f(f(fresh_constant))) 542.63/241.48 down(g(g(a))) 542.63/241.48 down(g(g(f(x0)))) 542.63/241.48 down(g(g(b))) 542.63/241.48 down(g(g(c))) 542.63/241.48 down(g(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) 542.63/241.48 down(f(f(f(g(x0))))) 542.63/241.48 down(f(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) 542.63/241.48 down(g(g(g(f(x0))))) 542.63/241.48 down(g(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(x0)))))) 542.63/241.48 down(f(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(x0)))))) 542.63/241.48 down(g(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(x0))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(x0))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 f_flat(up(x0)) 542.63/241.48 g_flat(up(x0)) 542.63/241.48 542.63/241.48 We have to consider all minimal (P,Q,R)-chains. 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (283) TransformationProof (EQUIVALENT) 542.63/241.48 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(down(f(f(b)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.48 542.63/241.48 (TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))),TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b))))))) 542.63/241.48 542.63/241.48 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (284) 542.63/241.48 Obligation: 542.63/241.48 Q DP problem: 542.63/241.48 The TRS P consists of the following rules: 542.63/241.48 542.63/241.48 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.48 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.48 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.48 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.48 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) 542.63/241.48 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.48 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.48 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.48 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.48 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.48 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.48 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.48 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.48 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.48 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.48 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.48 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.48 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.48 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.48 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.48 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.48 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.48 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.48 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.48 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.48 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.48 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.48 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.48 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.48 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.48 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.48 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.48 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.48 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.48 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.48 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.48 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.63/241.48 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.63/241.48 542.63/241.48 The TRS R consists of the following rules: 542.63/241.48 542.63/241.48 down(a) -> up(f(a)) 542.63/241.48 down(b) -> up(g(b)) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.48 down(f(a)) -> f_flat(down(a)) 542.63/241.48 down(f(b)) -> f_flat(down(b)) 542.63/241.48 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.48 down(f(c)) -> f_flat(down(c)) 542.63/241.48 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.48 down(g(a)) -> g_flat(down(a)) 542.63/241.48 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.48 down(g(b)) -> g_flat(down(b)) 542.63/241.48 down(g(c)) -> g_flat(down(c)) 542.63/241.48 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.48 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.48 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.48 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.48 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.48 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.48 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.48 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.48 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.48 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.48 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.48 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.48 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.48 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.48 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.48 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.48 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.48 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.48 542.63/241.48 The set Q consists of the following terms: 542.63/241.48 542.63/241.48 down(a) 542.63/241.48 down(b) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.48 down(f(a)) 542.63/241.48 down(f(b)) 542.63/241.48 down(f(g(x0))) 542.63/241.48 down(f(c)) 542.63/241.48 down(f(fresh_constant)) 542.63/241.48 down(g(a)) 542.63/241.48 down(g(f(x0))) 542.63/241.48 down(g(b)) 542.63/241.48 down(g(c)) 542.63/241.48 down(g(fresh_constant)) 542.63/241.48 down(f(f(a))) 542.63/241.48 down(f(f(b))) 542.63/241.48 down(f(f(g(x0)))) 542.63/241.48 down(f(f(c))) 542.63/241.48 down(f(f(fresh_constant))) 542.63/241.48 down(g(g(a))) 542.63/241.48 down(g(g(f(x0)))) 542.63/241.48 down(g(g(b))) 542.63/241.48 down(g(g(c))) 542.63/241.48 down(g(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) 542.63/241.48 down(f(f(f(g(x0))))) 542.63/241.48 down(f(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) 542.63/241.48 down(g(g(g(f(x0))))) 542.63/241.48 down(g(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(x0)))))) 542.63/241.48 down(f(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(x0)))))) 542.63/241.48 down(g(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(x0))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(x0))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 f_flat(up(x0)) 542.63/241.48 g_flat(up(x0)) 542.63/241.48 542.63/241.48 We have to consider all minimal (P,Q,R)-chains. 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (285) TransformationProof (EQUIVALENT) 542.63/241.48 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(down(f(f(g(x0))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.48 542.63/241.48 (TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))),TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 542.63/241.48 542.63/241.48 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (286) 542.63/241.48 Obligation: 542.63/241.48 Q DP problem: 542.63/241.48 The TRS P consists of the following rules: 542.63/241.48 542.63/241.48 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.48 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.48 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.48 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.48 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) 542.63/241.48 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.48 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.48 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.48 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.48 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.48 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.48 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.48 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.48 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.48 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.48 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.48 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.48 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.48 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.48 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.48 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.48 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.48 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.48 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.48 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.48 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.48 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.48 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.48 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.48 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.48 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.48 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.48 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.48 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.48 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.48 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.63/241.48 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.63/241.48 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.63/241.48 542.63/241.48 The TRS R consists of the following rules: 542.63/241.48 542.63/241.48 down(a) -> up(f(a)) 542.63/241.48 down(b) -> up(g(b)) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.48 down(f(a)) -> f_flat(down(a)) 542.63/241.48 down(f(b)) -> f_flat(down(b)) 542.63/241.48 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.48 down(f(c)) -> f_flat(down(c)) 542.63/241.48 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.48 down(g(a)) -> g_flat(down(a)) 542.63/241.48 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.48 down(g(b)) -> g_flat(down(b)) 542.63/241.48 down(g(c)) -> g_flat(down(c)) 542.63/241.48 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.48 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.48 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.48 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.48 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.48 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.48 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.48 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.48 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.48 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.48 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.48 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.48 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.48 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.48 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.48 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.48 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.48 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.48 542.63/241.48 The set Q consists of the following terms: 542.63/241.48 542.63/241.48 down(a) 542.63/241.48 down(b) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.48 down(f(a)) 542.63/241.48 down(f(b)) 542.63/241.48 down(f(g(x0))) 542.63/241.48 down(f(c)) 542.63/241.48 down(f(fresh_constant)) 542.63/241.48 down(g(a)) 542.63/241.48 down(g(f(x0))) 542.63/241.48 down(g(b)) 542.63/241.48 down(g(c)) 542.63/241.48 down(g(fresh_constant)) 542.63/241.48 down(f(f(a))) 542.63/241.48 down(f(f(b))) 542.63/241.48 down(f(f(g(x0)))) 542.63/241.48 down(f(f(c))) 542.63/241.48 down(f(f(fresh_constant))) 542.63/241.48 down(g(g(a))) 542.63/241.48 down(g(g(f(x0)))) 542.63/241.48 down(g(g(b))) 542.63/241.48 down(g(g(c))) 542.63/241.48 down(g(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) 542.63/241.48 down(f(f(f(g(x0))))) 542.63/241.48 down(f(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) 542.63/241.48 down(g(g(g(f(x0))))) 542.63/241.48 down(g(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(x0)))))) 542.63/241.48 down(f(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(x0)))))) 542.63/241.48 down(g(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(x0))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(x0))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 f_flat(up(x0)) 542.63/241.48 g_flat(up(x0)) 542.63/241.48 542.63/241.48 We have to consider all minimal (P,Q,R)-chains. 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (287) TransformationProof (EQUIVALENT) 542.63/241.48 By rewriting [LPAR04] the rule TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(down(g(a))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.48 542.63/241.48 (TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))),TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a)))))) 542.63/241.48 542.63/241.48 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (288) 542.63/241.48 Obligation: 542.63/241.48 Q DP problem: 542.63/241.48 The TRS P consists of the following rules: 542.63/241.48 542.63/241.48 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.48 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.48 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.48 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.48 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) 542.63/241.48 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.48 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.48 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.48 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.48 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.48 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.48 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.48 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.48 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.48 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.48 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.48 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.48 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.48 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.48 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.48 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.48 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.48 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.48 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.48 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.48 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.48 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.48 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.48 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.48 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.48 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.48 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.48 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.48 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.48 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.63/241.48 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.63/241.48 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.63/241.48 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.63/241.48 542.63/241.48 The TRS R consists of the following rules: 542.63/241.48 542.63/241.48 down(a) -> up(f(a)) 542.63/241.48 down(b) -> up(g(b)) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.48 down(f(a)) -> f_flat(down(a)) 542.63/241.48 down(f(b)) -> f_flat(down(b)) 542.63/241.48 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.48 down(f(c)) -> f_flat(down(c)) 542.63/241.48 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.48 down(g(a)) -> g_flat(down(a)) 542.63/241.48 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.48 down(g(b)) -> g_flat(down(b)) 542.63/241.48 down(g(c)) -> g_flat(down(c)) 542.63/241.48 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.48 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.48 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.48 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.48 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.48 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.48 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.48 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.48 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.48 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.48 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.48 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.48 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.48 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.48 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.48 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.48 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.48 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.48 542.63/241.48 The set Q consists of the following terms: 542.63/241.48 542.63/241.48 down(a) 542.63/241.48 down(b) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.48 down(f(a)) 542.63/241.48 down(f(b)) 542.63/241.48 down(f(g(x0))) 542.63/241.48 down(f(c)) 542.63/241.48 down(f(fresh_constant)) 542.63/241.48 down(g(a)) 542.63/241.48 down(g(f(x0))) 542.63/241.48 down(g(b)) 542.63/241.48 down(g(c)) 542.63/241.48 down(g(fresh_constant)) 542.63/241.48 down(f(f(a))) 542.63/241.48 down(f(f(b))) 542.63/241.48 down(f(f(g(x0)))) 542.63/241.48 down(f(f(c))) 542.63/241.48 down(f(f(fresh_constant))) 542.63/241.48 down(g(g(a))) 542.63/241.48 down(g(g(f(x0)))) 542.63/241.48 down(g(g(b))) 542.63/241.48 down(g(g(c))) 542.63/241.48 down(g(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) 542.63/241.48 down(f(f(f(g(x0))))) 542.63/241.48 down(f(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) 542.63/241.48 down(g(g(g(f(x0))))) 542.63/241.48 down(g(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(x0)))))) 542.63/241.48 down(f(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(x0)))))) 542.63/241.48 down(g(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(x0))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(x0))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 f_flat(up(x0)) 542.63/241.48 g_flat(up(x0)) 542.63/241.48 542.63/241.48 We have to consider all minimal (P,Q,R)-chains. 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (289) TransformationProof (EQUIVALENT) 542.63/241.48 By rewriting [LPAR04] the rule TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(down(g(f(x0)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.48 542.63/241.48 (TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))),TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0))))))) 542.63/241.48 542.63/241.48 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (290) 542.63/241.48 Obligation: 542.63/241.48 Q DP problem: 542.63/241.48 The TRS P consists of the following rules: 542.63/241.48 542.63/241.48 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.48 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.48 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.48 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.48 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) 542.63/241.48 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.48 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.48 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.48 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.48 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.48 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.48 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.48 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.48 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.48 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.48 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.48 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.48 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.48 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.48 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.48 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.48 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.48 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.48 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.48 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.48 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.48 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.48 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.48 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.48 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.48 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.48 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.48 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.48 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.63/241.48 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.63/241.48 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.63/241.48 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.63/241.48 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.63/241.48 542.63/241.48 The TRS R consists of the following rules: 542.63/241.48 542.63/241.48 down(a) -> up(f(a)) 542.63/241.48 down(b) -> up(g(b)) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.48 down(f(a)) -> f_flat(down(a)) 542.63/241.48 down(f(b)) -> f_flat(down(b)) 542.63/241.48 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.48 down(f(c)) -> f_flat(down(c)) 542.63/241.48 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.48 down(g(a)) -> g_flat(down(a)) 542.63/241.48 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.48 down(g(b)) -> g_flat(down(b)) 542.63/241.48 down(g(c)) -> g_flat(down(c)) 542.63/241.48 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.48 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.48 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.48 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.48 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.48 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.48 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.48 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.48 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.48 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.48 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.48 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.48 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.48 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.48 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.48 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.48 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.48 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.48 542.63/241.48 The set Q consists of the following terms: 542.63/241.48 542.63/241.48 down(a) 542.63/241.48 down(b) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.48 down(f(a)) 542.63/241.48 down(f(b)) 542.63/241.48 down(f(g(x0))) 542.63/241.48 down(f(c)) 542.63/241.48 down(f(fresh_constant)) 542.63/241.48 down(g(a)) 542.63/241.48 down(g(f(x0))) 542.63/241.48 down(g(b)) 542.63/241.48 down(g(c)) 542.63/241.48 down(g(fresh_constant)) 542.63/241.48 down(f(f(a))) 542.63/241.48 down(f(f(b))) 542.63/241.48 down(f(f(g(x0)))) 542.63/241.48 down(f(f(c))) 542.63/241.48 down(f(f(fresh_constant))) 542.63/241.48 down(g(g(a))) 542.63/241.48 down(g(g(f(x0)))) 542.63/241.48 down(g(g(b))) 542.63/241.48 down(g(g(c))) 542.63/241.48 down(g(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) 542.63/241.48 down(f(f(f(g(x0))))) 542.63/241.48 down(f(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) 542.63/241.48 down(g(g(g(f(x0))))) 542.63/241.48 down(g(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(x0)))))) 542.63/241.48 down(f(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(x0)))))) 542.63/241.48 down(g(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(x0))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(x0))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 f_flat(up(x0)) 542.63/241.48 g_flat(up(x0)) 542.63/241.48 542.63/241.48 We have to consider all minimal (P,Q,R)-chains. 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (291) TransformationProof (EQUIVALENT) 542.63/241.48 By rewriting [LPAR04] the rule TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(down(g(b))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.48 542.63/241.48 (TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))),TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b)))))) 542.63/241.48 542.63/241.48 542.63/241.48 ---------------------------------------- 542.63/241.48 542.63/241.48 (292) 542.63/241.48 Obligation: 542.63/241.48 Q DP problem: 542.63/241.48 The TRS P consists of the following rules: 542.63/241.48 542.63/241.48 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.48 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.48 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.48 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.48 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) 542.63/241.48 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.48 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.48 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.48 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.48 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.48 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.48 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.48 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.48 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.48 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.48 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.48 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.48 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.48 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.48 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.48 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.48 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.48 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.48 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.48 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.48 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.48 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.48 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.48 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.48 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.48 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.48 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.48 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.48 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.48 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.63/241.48 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.63/241.48 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.63/241.48 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.63/241.48 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.63/241.48 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.63/241.48 542.63/241.48 The TRS R consists of the following rules: 542.63/241.48 542.63/241.48 down(a) -> up(f(a)) 542.63/241.48 down(b) -> up(g(b)) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.48 down(f(a)) -> f_flat(down(a)) 542.63/241.48 down(f(b)) -> f_flat(down(b)) 542.63/241.48 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.48 down(f(c)) -> f_flat(down(c)) 542.63/241.48 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.48 down(g(a)) -> g_flat(down(a)) 542.63/241.48 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.48 down(g(b)) -> g_flat(down(b)) 542.63/241.48 down(g(c)) -> g_flat(down(c)) 542.63/241.48 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.48 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.48 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.48 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.48 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.48 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.48 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.48 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.48 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.48 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.48 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.48 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.48 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.48 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.48 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.48 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.48 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.48 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.48 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.48 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.48 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.48 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.48 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.48 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.48 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.48 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.48 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.48 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.48 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.48 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.48 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.48 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.48 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.48 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.48 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.48 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.48 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.48 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.48 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.48 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.48 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.48 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.48 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.48 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.48 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.48 542.63/241.48 The set Q consists of the following terms: 542.63/241.48 542.63/241.48 down(a) 542.63/241.48 down(b) 542.63/241.48 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.48 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.48 down(f(a)) 542.63/241.48 down(f(b)) 542.63/241.48 down(f(g(x0))) 542.63/241.48 down(f(c)) 542.63/241.48 down(f(fresh_constant)) 542.63/241.48 down(g(a)) 542.63/241.48 down(g(f(x0))) 542.63/241.48 down(g(b)) 542.63/241.48 down(g(c)) 542.63/241.48 down(g(fresh_constant)) 542.63/241.48 down(f(f(a))) 542.63/241.48 down(f(f(b))) 542.63/241.48 down(f(f(g(x0)))) 542.63/241.48 down(f(f(c))) 542.63/241.48 down(f(f(fresh_constant))) 542.63/241.48 down(g(g(a))) 542.63/241.48 down(g(g(f(x0)))) 542.63/241.48 down(g(g(b))) 542.63/241.48 down(g(g(c))) 542.63/241.48 down(g(g(fresh_constant))) 542.63/241.48 down(f(f(f(a)))) 542.63/241.48 down(f(f(f(b)))) 542.63/241.48 down(f(f(f(g(x0))))) 542.63/241.48 down(f(f(f(c)))) 542.63/241.48 down(f(f(f(fresh_constant)))) 542.63/241.48 down(g(g(g(a)))) 542.63/241.48 down(g(g(g(f(x0))))) 542.63/241.48 down(g(g(g(b)))) 542.63/241.48 down(g(g(g(c)))) 542.63/241.48 down(g(g(g(fresh_constant)))) 542.63/241.48 down(f(f(f(f(a))))) 542.63/241.48 down(f(f(f(f(b))))) 542.63/241.48 down(f(f(f(f(g(x0)))))) 542.63/241.48 down(f(f(f(f(c))))) 542.63/241.48 down(f(f(f(f(fresh_constant))))) 542.63/241.49 down(g(g(g(g(a))))) 542.63/241.49 down(g(g(g(g(f(x0)))))) 542.63/241.49 down(g(g(g(g(b))))) 542.63/241.49 down(g(g(g(g(c))))) 542.63/241.49 down(g(g(g(g(fresh_constant))))) 542.63/241.49 down(f(f(f(f(f(a)))))) 542.63/241.49 down(f(f(f(f(f(b)))))) 542.63/241.49 down(f(f(f(f(f(g(x0))))))) 542.63/241.49 down(f(f(f(f(f(c)))))) 542.63/241.49 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.49 down(g(g(g(g(g(a)))))) 542.63/241.49 down(g(g(g(g(g(f(x0))))))) 542.63/241.49 down(g(g(g(g(g(b)))))) 542.63/241.49 down(g(g(g(g(g(c)))))) 542.63/241.49 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.49 down(f(f(f(f(f(f(a))))))) 542.63/241.49 down(f(f(f(f(f(f(b))))))) 542.63/241.49 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.49 down(f(f(f(f(f(f(c))))))) 542.63/241.49 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.49 down(g(g(g(g(g(g(a))))))) 542.63/241.49 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.49 down(g(g(g(g(g(g(b))))))) 542.63/241.49 down(g(g(g(g(g(g(c))))))) 542.63/241.49 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.49 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.49 f_flat(up(x0)) 542.63/241.49 g_flat(up(x0)) 542.63/241.49 542.63/241.49 We have to consider all minimal (P,Q,R)-chains. 542.63/241.49 ---------------------------------------- 542.63/241.49 542.63/241.49 (293) TransformationProof (EQUIVALENT) 542.63/241.49 By rewriting [LPAR04] the rule TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(down(g(c))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.49 542.63/241.49 (TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(g_flat(down(c))))),TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(g_flat(down(c)))))) 542.63/241.49 542.63/241.49 542.63/241.49 ---------------------------------------- 542.63/241.49 542.63/241.49 (294) 542.63/241.49 Obligation: 542.63/241.49 Q DP problem: 542.63/241.49 The TRS P consists of the following rules: 542.63/241.49 542.63/241.49 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.49 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.49 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.49 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.49 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.49 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.49 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.49 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.49 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.49 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.49 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.49 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.49 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.49 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.49 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.49 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.49 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.49 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.49 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.49 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.49 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.49 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.49 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.49 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.49 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.49 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.49 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.49 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.49 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.49 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.49 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.49 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.63/241.49 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.63/241.49 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.63/241.49 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.63/241.49 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.63/241.49 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.63/241.49 TOP(up(g(g(g(c))))) -> TOP(g_flat(g_flat(g_flat(down(c))))) 542.63/241.49 542.63/241.49 The TRS R consists of the following rules: 542.63/241.49 542.63/241.49 down(a) -> up(f(a)) 542.63/241.49 down(b) -> up(g(b)) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.49 down(f(a)) -> f_flat(down(a)) 542.63/241.49 down(f(b)) -> f_flat(down(b)) 542.63/241.49 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.49 down(f(c)) -> f_flat(down(c)) 542.63/241.49 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.49 down(g(a)) -> g_flat(down(a)) 542.63/241.49 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.49 down(g(b)) -> g_flat(down(b)) 542.63/241.49 down(g(c)) -> g_flat(down(c)) 542.63/241.49 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.49 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.49 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.49 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.49 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.49 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.49 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.49 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.49 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.49 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.49 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.49 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.49 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.49 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.49 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.49 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.49 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.49 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.49 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.49 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.49 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.49 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.49 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.49 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.49 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.49 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.49 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.49 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.49 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.49 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.49 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.49 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.49 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.49 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.49 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.49 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.49 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.49 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.49 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.49 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.49 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.49 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.49 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.49 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.49 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.49 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.49 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.49 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.49 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.49 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.49 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.49 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.49 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.49 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.49 542.63/241.49 The set Q consists of the following terms: 542.63/241.49 542.63/241.49 down(a) 542.63/241.49 down(b) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.49 down(f(a)) 542.63/241.49 down(f(b)) 542.63/241.49 down(f(g(x0))) 542.63/241.49 down(f(c)) 542.63/241.49 down(f(fresh_constant)) 542.63/241.49 down(g(a)) 542.63/241.49 down(g(f(x0))) 542.63/241.49 down(g(b)) 542.63/241.49 down(g(c)) 542.63/241.49 down(g(fresh_constant)) 542.63/241.49 down(f(f(a))) 542.63/241.49 down(f(f(b))) 542.63/241.49 down(f(f(g(x0)))) 542.63/241.49 down(f(f(c))) 542.63/241.49 down(f(f(fresh_constant))) 542.63/241.49 down(g(g(a))) 542.63/241.49 down(g(g(f(x0)))) 542.63/241.49 down(g(g(b))) 542.63/241.49 down(g(g(c))) 542.63/241.49 down(g(g(fresh_constant))) 542.63/241.49 down(f(f(f(a)))) 542.63/241.49 down(f(f(f(b)))) 542.63/241.49 down(f(f(f(g(x0))))) 542.63/241.49 down(f(f(f(c)))) 542.63/241.49 down(f(f(f(fresh_constant)))) 542.63/241.49 down(g(g(g(a)))) 542.63/241.49 down(g(g(g(f(x0))))) 542.63/241.49 down(g(g(g(b)))) 542.63/241.49 down(g(g(g(c)))) 542.63/241.49 down(g(g(g(fresh_constant)))) 542.63/241.49 down(f(f(f(f(a))))) 542.63/241.49 down(f(f(f(f(b))))) 542.63/241.49 down(f(f(f(f(g(x0)))))) 542.63/241.49 down(f(f(f(f(c))))) 542.63/241.49 down(f(f(f(f(fresh_constant))))) 542.63/241.49 down(g(g(g(g(a))))) 542.63/241.49 down(g(g(g(g(f(x0)))))) 542.63/241.49 down(g(g(g(g(b))))) 542.63/241.49 down(g(g(g(g(c))))) 542.63/241.49 down(g(g(g(g(fresh_constant))))) 542.63/241.49 down(f(f(f(f(f(a)))))) 542.63/241.49 down(f(f(f(f(f(b)))))) 542.63/241.49 down(f(f(f(f(f(g(x0))))))) 542.63/241.49 down(f(f(f(f(f(c)))))) 542.63/241.49 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.49 down(g(g(g(g(g(a)))))) 542.63/241.49 down(g(g(g(g(g(f(x0))))))) 542.63/241.49 down(g(g(g(g(g(b)))))) 542.63/241.49 down(g(g(g(g(g(c)))))) 542.63/241.49 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.49 down(f(f(f(f(f(f(a))))))) 542.63/241.49 down(f(f(f(f(f(f(b))))))) 542.63/241.49 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.49 down(f(f(f(f(f(f(c))))))) 542.63/241.49 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.49 down(g(g(g(g(g(g(a))))))) 542.63/241.49 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.49 down(g(g(g(g(g(g(b))))))) 542.63/241.49 down(g(g(g(g(g(g(c))))))) 542.63/241.49 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.49 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.49 f_flat(up(x0)) 542.63/241.49 g_flat(up(x0)) 542.63/241.49 542.63/241.49 We have to consider all minimal (P,Q,R)-chains. 542.63/241.49 ---------------------------------------- 542.63/241.49 542.63/241.49 (295) DependencyGraphProof (EQUIVALENT) 542.63/241.49 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 542.63/241.49 ---------------------------------------- 542.63/241.49 542.63/241.49 (296) 542.63/241.49 Obligation: 542.63/241.49 Q DP problem: 542.63/241.49 The TRS P consists of the following rules: 542.63/241.49 542.63/241.49 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.49 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.49 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.49 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.49 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) 542.63/241.49 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.49 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.49 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.49 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.49 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.49 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.49 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.49 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.49 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.49 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.49 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.49 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.49 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.49 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.49 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.49 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.49 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.49 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.49 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.49 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.49 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.49 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.49 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.49 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.49 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.49 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.63/241.49 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.63/241.49 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.49 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.63/241.49 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.63/241.49 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.63/241.49 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.63/241.49 542.63/241.49 The TRS R consists of the following rules: 542.63/241.49 542.63/241.49 down(a) -> up(f(a)) 542.63/241.49 down(b) -> up(g(b)) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.63/241.49 down(f(a)) -> f_flat(down(a)) 542.63/241.49 down(f(b)) -> f_flat(down(b)) 542.63/241.49 down(f(g(y4))) -> f_flat(down(g(y4))) 542.63/241.49 down(f(c)) -> f_flat(down(c)) 542.63/241.49 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.63/241.49 down(g(a)) -> g_flat(down(a)) 542.63/241.49 down(g(f(y6))) -> g_flat(down(f(y6))) 542.63/241.49 down(g(b)) -> g_flat(down(b)) 542.63/241.49 down(g(c)) -> g_flat(down(c)) 542.63/241.49 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.63/241.49 down(f(f(a))) -> f_flat(down(f(a))) 542.63/241.49 down(f(f(b))) -> f_flat(down(f(b))) 542.63/241.49 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.63/241.49 down(f(f(c))) -> f_flat(down(f(c))) 542.63/241.49 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.63/241.49 down(g(g(a))) -> g_flat(down(g(a))) 542.63/241.49 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.63/241.49 down(g(g(b))) -> g_flat(down(g(b))) 542.63/241.49 down(g(g(c))) -> g_flat(down(g(c))) 542.63/241.49 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.63/241.49 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.63/241.49 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.63/241.49 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.63/241.49 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.63/241.49 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.63/241.49 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.63/241.49 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.63/241.49 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.63/241.49 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.63/241.49 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.63/241.49 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.63/241.49 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.63/241.49 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.63/241.49 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.63/241.49 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.63/241.49 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.63/241.49 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.63/241.49 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.63/241.49 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.63/241.49 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.63/241.49 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.63/241.49 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.63/241.49 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.63/241.49 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.63/241.49 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.63/241.49 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.63/241.49 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.63/241.49 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.63/241.49 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.63/241.49 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.63/241.49 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.63/241.49 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.63/241.49 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.63/241.49 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.63/241.49 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.63/241.49 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.63/241.49 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.63/241.49 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.63/241.49 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.63/241.49 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.63/241.49 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.49 g_flat(up(x_1)) -> up(g(x_1)) 542.63/241.49 f_flat(up(x_1)) -> up(f(x_1)) 542.63/241.49 542.63/241.49 The set Q consists of the following terms: 542.63/241.49 542.63/241.49 down(a) 542.63/241.49 down(b) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.63/241.49 down(f(a)) 542.63/241.49 down(f(b)) 542.63/241.49 down(f(g(x0))) 542.63/241.49 down(f(c)) 542.63/241.49 down(f(fresh_constant)) 542.63/241.49 down(g(a)) 542.63/241.49 down(g(f(x0))) 542.63/241.49 down(g(b)) 542.63/241.49 down(g(c)) 542.63/241.49 down(g(fresh_constant)) 542.63/241.49 down(f(f(a))) 542.63/241.49 down(f(f(b))) 542.63/241.49 down(f(f(g(x0)))) 542.63/241.49 down(f(f(c))) 542.63/241.49 down(f(f(fresh_constant))) 542.63/241.49 down(g(g(a))) 542.63/241.49 down(g(g(f(x0)))) 542.63/241.49 down(g(g(b))) 542.63/241.49 down(g(g(c))) 542.63/241.49 down(g(g(fresh_constant))) 542.63/241.49 down(f(f(f(a)))) 542.63/241.49 down(f(f(f(b)))) 542.63/241.49 down(f(f(f(g(x0))))) 542.63/241.49 down(f(f(f(c)))) 542.63/241.49 down(f(f(f(fresh_constant)))) 542.63/241.49 down(g(g(g(a)))) 542.63/241.49 down(g(g(g(f(x0))))) 542.63/241.49 down(g(g(g(b)))) 542.63/241.49 down(g(g(g(c)))) 542.63/241.49 down(g(g(g(fresh_constant)))) 542.63/241.49 down(f(f(f(f(a))))) 542.63/241.49 down(f(f(f(f(b))))) 542.63/241.49 down(f(f(f(f(g(x0)))))) 542.63/241.49 down(f(f(f(f(c))))) 542.63/241.49 down(f(f(f(f(fresh_constant))))) 542.63/241.49 down(g(g(g(g(a))))) 542.63/241.49 down(g(g(g(g(f(x0)))))) 542.63/241.49 down(g(g(g(g(b))))) 542.63/241.49 down(g(g(g(g(c))))) 542.63/241.49 down(g(g(g(g(fresh_constant))))) 542.63/241.49 down(f(f(f(f(f(a)))))) 542.63/241.49 down(f(f(f(f(f(b)))))) 542.63/241.49 down(f(f(f(f(f(g(x0))))))) 542.63/241.49 down(f(f(f(f(f(c)))))) 542.63/241.49 down(f(f(f(f(f(fresh_constant)))))) 542.63/241.49 down(g(g(g(g(g(a)))))) 542.63/241.49 down(g(g(g(g(g(f(x0))))))) 542.63/241.49 down(g(g(g(g(g(b)))))) 542.63/241.49 down(g(g(g(g(g(c)))))) 542.63/241.49 down(g(g(g(g(g(fresh_constant)))))) 542.63/241.49 down(f(f(f(f(f(f(a))))))) 542.63/241.49 down(f(f(f(f(f(f(b))))))) 542.63/241.49 down(f(f(f(f(f(f(g(x0)))))))) 542.63/241.49 down(f(f(f(f(f(f(c))))))) 542.63/241.49 down(f(f(f(f(f(f(fresh_constant))))))) 542.63/241.49 down(g(g(g(g(g(g(a))))))) 542.63/241.49 down(g(g(g(g(g(g(f(x0)))))))) 542.63/241.49 down(g(g(g(g(g(g(b))))))) 542.63/241.49 down(g(g(g(g(g(g(c))))))) 542.63/241.49 down(g(g(g(g(g(g(fresh_constant))))))) 542.63/241.49 down(f(f(f(f(f(f(f(a)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(b)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(g(x0))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(c)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(a)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(f(x0))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(b)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(c)))))))) 542.63/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(a))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(b))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(c))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(a))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(b))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(c))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.63/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.63/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.49 f_flat(up(x0)) 542.63/241.49 g_flat(up(x0)) 542.63/241.49 542.63/241.49 We have to consider all minimal (P,Q,R)-chains. 542.63/241.49 ---------------------------------------- 542.63/241.49 542.63/241.49 (297) TransformationProof (EQUIVALENT) 542.63/241.49 By rewriting [LPAR04] the rule TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(down(g(fresh_constant))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.63/241.49 542.63/241.49 (TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(g_flat(down(fresh_constant))))),TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(g_flat(down(fresh_constant)))))) 542.63/241.49 542.63/241.49 542.63/241.49 ---------------------------------------- 542.63/241.49 542.63/241.49 (298) 542.63/241.49 Obligation: 542.63/241.49 Q DP problem: 542.63/241.49 The TRS P consists of the following rules: 542.63/241.49 542.63/241.49 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.63/241.49 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.63/241.49 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.63/241.49 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.63/241.49 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.63/241.49 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.63/241.49 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.63/241.49 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.63/241.49 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.63/241.49 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.63/241.49 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.63/241.49 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.63/241.49 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.63/241.49 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.63/241.49 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.63/241.49 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.63/241.49 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.63/241.49 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.63/241.49 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.63/241.49 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.63/241.49 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.63/241.49 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.63/241.49 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.63/241.49 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.63/241.49 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.63/241.49 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.63/241.49 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.63/241.49 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.63/241.49 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.63/241.49 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.63/241.49 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.63/241.49 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.63/241.49 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.63/241.49 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.63/241.49 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.63/241.49 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.63/241.49 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.63/241.49 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.63/241.49 TOP(up(g(g(g(fresh_constant))))) -> TOP(g_flat(g_flat(g_flat(down(fresh_constant))))) 542.63/241.49 542.63/241.49 The TRS R consists of the following rules: 542.72/241.49 542.72/241.49 down(a) -> up(f(a)) 542.72/241.49 down(b) -> up(g(b)) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.49 down(f(a)) -> f_flat(down(a)) 542.72/241.49 down(f(b)) -> f_flat(down(b)) 542.72/241.49 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.49 down(f(c)) -> f_flat(down(c)) 542.72/241.49 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.49 down(g(a)) -> g_flat(down(a)) 542.72/241.49 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.49 down(g(b)) -> g_flat(down(b)) 542.72/241.49 down(g(c)) -> g_flat(down(c)) 542.72/241.49 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.49 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.49 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.49 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.49 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.49 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.49 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.49 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.49 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.49 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.49 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.49 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.49 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.49 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.49 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.49 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.49 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.49 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.49 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.49 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.49 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.49 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.49 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.49 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.49 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.49 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.49 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.49 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.49 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.49 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.49 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.49 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.49 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.49 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.49 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.49 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.49 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.49 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.49 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.49 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.49 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.49 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.49 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.49 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.49 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.49 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.49 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.49 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.49 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.49 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.49 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.49 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.49 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.49 542.72/241.49 The set Q consists of the following terms: 542.72/241.49 542.72/241.49 down(a) 542.72/241.49 down(b) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.49 down(f(a)) 542.72/241.49 down(f(b)) 542.72/241.49 down(f(g(x0))) 542.72/241.49 down(f(c)) 542.72/241.49 down(f(fresh_constant)) 542.72/241.49 down(g(a)) 542.72/241.49 down(g(f(x0))) 542.72/241.49 down(g(b)) 542.72/241.49 down(g(c)) 542.72/241.49 down(g(fresh_constant)) 542.72/241.49 down(f(f(a))) 542.72/241.49 down(f(f(b))) 542.72/241.49 down(f(f(g(x0)))) 542.72/241.49 down(f(f(c))) 542.72/241.49 down(f(f(fresh_constant))) 542.72/241.49 down(g(g(a))) 542.72/241.49 down(g(g(f(x0)))) 542.72/241.49 down(g(g(b))) 542.72/241.49 down(g(g(c))) 542.72/241.49 down(g(g(fresh_constant))) 542.72/241.49 down(f(f(f(a)))) 542.72/241.49 down(f(f(f(b)))) 542.72/241.49 down(f(f(f(g(x0))))) 542.72/241.49 down(f(f(f(c)))) 542.72/241.49 down(f(f(f(fresh_constant)))) 542.72/241.49 down(g(g(g(a)))) 542.72/241.49 down(g(g(g(f(x0))))) 542.72/241.49 down(g(g(g(b)))) 542.72/241.49 down(g(g(g(c)))) 542.72/241.49 down(g(g(g(fresh_constant)))) 542.72/241.49 down(f(f(f(f(a))))) 542.72/241.49 down(f(f(f(f(b))))) 542.72/241.49 down(f(f(f(f(g(x0)))))) 542.72/241.49 down(f(f(f(f(c))))) 542.72/241.49 down(f(f(f(f(fresh_constant))))) 542.72/241.49 down(g(g(g(g(a))))) 542.72/241.49 down(g(g(g(g(f(x0)))))) 542.72/241.49 down(g(g(g(g(b))))) 542.72/241.49 down(g(g(g(g(c))))) 542.72/241.49 down(g(g(g(g(fresh_constant))))) 542.72/241.49 down(f(f(f(f(f(a)))))) 542.72/241.49 down(f(f(f(f(f(b)))))) 542.72/241.49 down(f(f(f(f(f(g(x0))))))) 542.72/241.49 down(f(f(f(f(f(c)))))) 542.72/241.49 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.49 down(g(g(g(g(g(a)))))) 542.72/241.49 down(g(g(g(g(g(f(x0))))))) 542.72/241.49 down(g(g(g(g(g(b)))))) 542.72/241.49 down(g(g(g(g(g(c)))))) 542.72/241.49 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.49 down(f(f(f(f(f(f(a))))))) 542.72/241.49 down(f(f(f(f(f(f(b))))))) 542.72/241.49 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.49 down(f(f(f(f(f(f(c))))))) 542.72/241.49 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.49 down(g(g(g(g(g(g(a))))))) 542.72/241.49 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.49 down(g(g(g(g(g(g(b))))))) 542.72/241.49 down(g(g(g(g(g(g(c))))))) 542.72/241.49 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.49 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 f_flat(up(x0)) 542.72/241.49 g_flat(up(x0)) 542.72/241.49 542.72/241.49 We have to consider all minimal (P,Q,R)-chains. 542.72/241.49 ---------------------------------------- 542.72/241.49 542.72/241.49 (299) DependencyGraphProof (EQUIVALENT) 542.72/241.49 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 542.72/241.49 ---------------------------------------- 542.72/241.49 542.72/241.49 (300) 542.72/241.49 Obligation: 542.72/241.49 Q DP problem: 542.72/241.49 The TRS P consists of the following rules: 542.72/241.49 542.72/241.49 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.49 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.49 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.49 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.49 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) 542.72/241.49 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.72/241.49 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.72/241.49 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.72/241.49 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.72/241.49 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.72/241.49 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.72/241.49 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.72/241.49 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.72/241.49 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.49 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.49 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.49 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.49 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.49 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.49 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.49 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.49 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.49 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.49 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.49 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.49 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.49 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.49 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.49 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.49 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.49 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.49 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.49 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.49 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.49 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.49 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.49 542.72/241.49 The TRS R consists of the following rules: 542.72/241.49 542.72/241.49 down(a) -> up(f(a)) 542.72/241.49 down(b) -> up(g(b)) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.49 down(f(a)) -> f_flat(down(a)) 542.72/241.49 down(f(b)) -> f_flat(down(b)) 542.72/241.49 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.49 down(f(c)) -> f_flat(down(c)) 542.72/241.49 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.49 down(g(a)) -> g_flat(down(a)) 542.72/241.49 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.49 down(g(b)) -> g_flat(down(b)) 542.72/241.49 down(g(c)) -> g_flat(down(c)) 542.72/241.49 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.49 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.49 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.49 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.49 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.49 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.49 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.49 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.49 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.49 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.49 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.49 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.49 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.49 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.49 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.49 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.49 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.49 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.49 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.49 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.49 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.49 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.49 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.49 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.49 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.49 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.49 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.49 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.49 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.49 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.49 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.49 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.49 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.49 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.49 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.49 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.49 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.49 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.49 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.49 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.49 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.49 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.49 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.49 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.49 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.49 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.49 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.49 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.49 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.49 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.49 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.49 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.49 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.49 542.72/241.49 The set Q consists of the following terms: 542.72/241.49 542.72/241.49 down(a) 542.72/241.49 down(b) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.49 down(f(a)) 542.72/241.49 down(f(b)) 542.72/241.49 down(f(g(x0))) 542.72/241.49 down(f(c)) 542.72/241.49 down(f(fresh_constant)) 542.72/241.49 down(g(a)) 542.72/241.49 down(g(f(x0))) 542.72/241.49 down(g(b)) 542.72/241.49 down(g(c)) 542.72/241.49 down(g(fresh_constant)) 542.72/241.49 down(f(f(a))) 542.72/241.49 down(f(f(b))) 542.72/241.49 down(f(f(g(x0)))) 542.72/241.49 down(f(f(c))) 542.72/241.49 down(f(f(fresh_constant))) 542.72/241.49 down(g(g(a))) 542.72/241.49 down(g(g(f(x0)))) 542.72/241.49 down(g(g(b))) 542.72/241.49 down(g(g(c))) 542.72/241.49 down(g(g(fresh_constant))) 542.72/241.49 down(f(f(f(a)))) 542.72/241.49 down(f(f(f(b)))) 542.72/241.49 down(f(f(f(g(x0))))) 542.72/241.49 down(f(f(f(c)))) 542.72/241.49 down(f(f(f(fresh_constant)))) 542.72/241.49 down(g(g(g(a)))) 542.72/241.49 down(g(g(g(f(x0))))) 542.72/241.49 down(g(g(g(b)))) 542.72/241.49 down(g(g(g(c)))) 542.72/241.49 down(g(g(g(fresh_constant)))) 542.72/241.49 down(f(f(f(f(a))))) 542.72/241.49 down(f(f(f(f(b))))) 542.72/241.49 down(f(f(f(f(g(x0)))))) 542.72/241.49 down(f(f(f(f(c))))) 542.72/241.49 down(f(f(f(f(fresh_constant))))) 542.72/241.49 down(g(g(g(g(a))))) 542.72/241.49 down(g(g(g(g(f(x0)))))) 542.72/241.49 down(g(g(g(g(b))))) 542.72/241.49 down(g(g(g(g(c))))) 542.72/241.49 down(g(g(g(g(fresh_constant))))) 542.72/241.49 down(f(f(f(f(f(a)))))) 542.72/241.49 down(f(f(f(f(f(b)))))) 542.72/241.49 down(f(f(f(f(f(g(x0))))))) 542.72/241.49 down(f(f(f(f(f(c)))))) 542.72/241.49 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.49 down(g(g(g(g(g(a)))))) 542.72/241.49 down(g(g(g(g(g(f(x0))))))) 542.72/241.49 down(g(g(g(g(g(b)))))) 542.72/241.49 down(g(g(g(g(g(c)))))) 542.72/241.49 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.49 down(f(f(f(f(f(f(a))))))) 542.72/241.49 down(f(f(f(f(f(f(b))))))) 542.72/241.49 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.49 down(f(f(f(f(f(f(c))))))) 542.72/241.49 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.49 down(g(g(g(g(g(g(a))))))) 542.72/241.49 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.49 down(g(g(g(g(g(g(b))))))) 542.72/241.49 down(g(g(g(g(g(g(c))))))) 542.72/241.49 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.49 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 f_flat(up(x0)) 542.72/241.49 g_flat(up(x0)) 542.72/241.49 542.72/241.49 We have to consider all minimal (P,Q,R)-chains. 542.72/241.49 ---------------------------------------- 542.72/241.49 542.72/241.49 (301) TransformationProof (EQUIVALENT) 542.72/241.49 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(down(g(g(a)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.49 542.72/241.49 (TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))),TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a))))))) 542.72/241.49 542.72/241.49 542.72/241.49 ---------------------------------------- 542.72/241.49 542.72/241.49 (302) 542.72/241.49 Obligation: 542.72/241.49 Q DP problem: 542.72/241.49 The TRS P consists of the following rules: 542.72/241.49 542.72/241.49 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.49 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.49 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.49 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.49 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) 542.72/241.49 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.72/241.49 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.72/241.49 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.72/241.49 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.72/241.49 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.72/241.49 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.72/241.49 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.72/241.49 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.49 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.49 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.49 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.49 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.49 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.49 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.49 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.49 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.49 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.49 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.49 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.49 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.49 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.49 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.49 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.49 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.49 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.49 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.49 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.49 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.49 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.49 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.49 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.49 542.72/241.49 The TRS R consists of the following rules: 542.72/241.49 542.72/241.49 down(a) -> up(f(a)) 542.72/241.49 down(b) -> up(g(b)) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.49 down(f(a)) -> f_flat(down(a)) 542.72/241.49 down(f(b)) -> f_flat(down(b)) 542.72/241.49 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.49 down(f(c)) -> f_flat(down(c)) 542.72/241.49 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.49 down(g(a)) -> g_flat(down(a)) 542.72/241.49 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.49 down(g(b)) -> g_flat(down(b)) 542.72/241.49 down(g(c)) -> g_flat(down(c)) 542.72/241.49 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.49 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.49 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.49 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.49 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.49 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.49 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.49 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.49 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.49 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.49 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.49 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.49 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.49 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.49 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.49 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.49 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.49 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.49 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.49 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.49 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.49 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.49 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.49 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.49 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.49 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.49 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.49 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.49 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.49 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.49 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.49 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.49 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.49 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.49 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.49 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.49 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.49 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.49 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.49 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.49 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.49 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.49 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.49 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.49 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.49 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.49 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.49 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.49 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.49 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.49 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.49 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.49 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.49 542.72/241.49 The set Q consists of the following terms: 542.72/241.49 542.72/241.49 down(a) 542.72/241.49 down(b) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.49 down(f(a)) 542.72/241.49 down(f(b)) 542.72/241.49 down(f(g(x0))) 542.72/241.49 down(f(c)) 542.72/241.49 down(f(fresh_constant)) 542.72/241.49 down(g(a)) 542.72/241.49 down(g(f(x0))) 542.72/241.49 down(g(b)) 542.72/241.49 down(g(c)) 542.72/241.49 down(g(fresh_constant)) 542.72/241.49 down(f(f(a))) 542.72/241.49 down(f(f(b))) 542.72/241.49 down(f(f(g(x0)))) 542.72/241.49 down(f(f(c))) 542.72/241.49 down(f(f(fresh_constant))) 542.72/241.49 down(g(g(a))) 542.72/241.49 down(g(g(f(x0)))) 542.72/241.49 down(g(g(b))) 542.72/241.49 down(g(g(c))) 542.72/241.49 down(g(g(fresh_constant))) 542.72/241.49 down(f(f(f(a)))) 542.72/241.49 down(f(f(f(b)))) 542.72/241.49 down(f(f(f(g(x0))))) 542.72/241.49 down(f(f(f(c)))) 542.72/241.49 down(f(f(f(fresh_constant)))) 542.72/241.49 down(g(g(g(a)))) 542.72/241.49 down(g(g(g(f(x0))))) 542.72/241.49 down(g(g(g(b)))) 542.72/241.49 down(g(g(g(c)))) 542.72/241.49 down(g(g(g(fresh_constant)))) 542.72/241.49 down(f(f(f(f(a))))) 542.72/241.49 down(f(f(f(f(b))))) 542.72/241.49 down(f(f(f(f(g(x0)))))) 542.72/241.49 down(f(f(f(f(c))))) 542.72/241.49 down(f(f(f(f(fresh_constant))))) 542.72/241.49 down(g(g(g(g(a))))) 542.72/241.49 down(g(g(g(g(f(x0)))))) 542.72/241.49 down(g(g(g(g(b))))) 542.72/241.49 down(g(g(g(g(c))))) 542.72/241.49 down(g(g(g(g(fresh_constant))))) 542.72/241.49 down(f(f(f(f(f(a)))))) 542.72/241.49 down(f(f(f(f(f(b)))))) 542.72/241.49 down(f(f(f(f(f(g(x0))))))) 542.72/241.49 down(f(f(f(f(f(c)))))) 542.72/241.49 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.49 down(g(g(g(g(g(a)))))) 542.72/241.49 down(g(g(g(g(g(f(x0))))))) 542.72/241.49 down(g(g(g(g(g(b)))))) 542.72/241.49 down(g(g(g(g(g(c)))))) 542.72/241.49 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.49 down(f(f(f(f(f(f(a))))))) 542.72/241.49 down(f(f(f(f(f(f(b))))))) 542.72/241.49 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.49 down(f(f(f(f(f(f(c))))))) 542.72/241.49 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.49 down(g(g(g(g(g(g(a))))))) 542.72/241.49 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.49 down(g(g(g(g(g(g(b))))))) 542.72/241.49 down(g(g(g(g(g(g(c))))))) 542.72/241.49 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.49 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 f_flat(up(x0)) 542.72/241.49 g_flat(up(x0)) 542.72/241.49 542.72/241.49 We have to consider all minimal (P,Q,R)-chains. 542.72/241.49 ---------------------------------------- 542.72/241.49 542.72/241.49 (303) TransformationProof (EQUIVALENT) 542.72/241.49 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(down(g(g(f(x0))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.49 542.72/241.49 (TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))),TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 542.72/241.49 542.72/241.49 542.72/241.49 ---------------------------------------- 542.72/241.49 542.72/241.49 (304) 542.72/241.49 Obligation: 542.72/241.49 Q DP problem: 542.72/241.49 The TRS P consists of the following rules: 542.72/241.49 542.72/241.49 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.49 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.49 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.49 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.49 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) 542.72/241.49 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.72/241.49 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.72/241.49 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.72/241.49 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.72/241.49 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.72/241.49 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.72/241.49 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.49 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.49 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.49 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.49 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.49 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.49 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.49 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.49 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.49 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.49 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.49 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.49 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.49 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.49 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.49 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.49 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.49 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.49 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.49 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.49 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.49 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.49 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.49 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.49 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.49 542.72/241.49 The TRS R consists of the following rules: 542.72/241.49 542.72/241.49 down(a) -> up(f(a)) 542.72/241.49 down(b) -> up(g(b)) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.49 down(f(a)) -> f_flat(down(a)) 542.72/241.49 down(f(b)) -> f_flat(down(b)) 542.72/241.49 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.49 down(f(c)) -> f_flat(down(c)) 542.72/241.49 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.49 down(g(a)) -> g_flat(down(a)) 542.72/241.49 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.49 down(g(b)) -> g_flat(down(b)) 542.72/241.49 down(g(c)) -> g_flat(down(c)) 542.72/241.49 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.49 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.49 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.49 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.49 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.49 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.49 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.49 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.49 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.49 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.49 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.49 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.49 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.49 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.49 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.49 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.49 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.49 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.49 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.49 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.49 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.49 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.49 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.49 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.49 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.49 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.49 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.49 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.49 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.49 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.49 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.49 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.49 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.49 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.49 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.49 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.49 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.49 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.49 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.49 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.49 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.49 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.49 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.49 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.49 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.49 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.49 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.49 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.49 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.49 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.49 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.49 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.49 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.49 542.72/241.49 The set Q consists of the following terms: 542.72/241.49 542.72/241.49 down(a) 542.72/241.49 down(b) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.49 down(f(a)) 542.72/241.49 down(f(b)) 542.72/241.49 down(f(g(x0))) 542.72/241.49 down(f(c)) 542.72/241.49 down(f(fresh_constant)) 542.72/241.49 down(g(a)) 542.72/241.49 down(g(f(x0))) 542.72/241.49 down(g(b)) 542.72/241.49 down(g(c)) 542.72/241.49 down(g(fresh_constant)) 542.72/241.49 down(f(f(a))) 542.72/241.49 down(f(f(b))) 542.72/241.49 down(f(f(g(x0)))) 542.72/241.49 down(f(f(c))) 542.72/241.49 down(f(f(fresh_constant))) 542.72/241.49 down(g(g(a))) 542.72/241.49 down(g(g(f(x0)))) 542.72/241.49 down(g(g(b))) 542.72/241.49 down(g(g(c))) 542.72/241.49 down(g(g(fresh_constant))) 542.72/241.49 down(f(f(f(a)))) 542.72/241.49 down(f(f(f(b)))) 542.72/241.49 down(f(f(f(g(x0))))) 542.72/241.49 down(f(f(f(c)))) 542.72/241.49 down(f(f(f(fresh_constant)))) 542.72/241.49 down(g(g(g(a)))) 542.72/241.49 down(g(g(g(f(x0))))) 542.72/241.49 down(g(g(g(b)))) 542.72/241.49 down(g(g(g(c)))) 542.72/241.49 down(g(g(g(fresh_constant)))) 542.72/241.49 down(f(f(f(f(a))))) 542.72/241.49 down(f(f(f(f(b))))) 542.72/241.49 down(f(f(f(f(g(x0)))))) 542.72/241.49 down(f(f(f(f(c))))) 542.72/241.49 down(f(f(f(f(fresh_constant))))) 542.72/241.49 down(g(g(g(g(a))))) 542.72/241.49 down(g(g(g(g(f(x0)))))) 542.72/241.49 down(g(g(g(g(b))))) 542.72/241.49 down(g(g(g(g(c))))) 542.72/241.49 down(g(g(g(g(fresh_constant))))) 542.72/241.49 down(f(f(f(f(f(a)))))) 542.72/241.49 down(f(f(f(f(f(b)))))) 542.72/241.49 down(f(f(f(f(f(g(x0))))))) 542.72/241.49 down(f(f(f(f(f(c)))))) 542.72/241.49 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.49 down(g(g(g(g(g(a)))))) 542.72/241.49 down(g(g(g(g(g(f(x0))))))) 542.72/241.49 down(g(g(g(g(g(b)))))) 542.72/241.49 down(g(g(g(g(g(c)))))) 542.72/241.49 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.49 down(f(f(f(f(f(f(a))))))) 542.72/241.49 down(f(f(f(f(f(f(b))))))) 542.72/241.49 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.49 down(f(f(f(f(f(f(c))))))) 542.72/241.49 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.49 down(g(g(g(g(g(g(a))))))) 542.72/241.49 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.49 down(g(g(g(g(g(g(b))))))) 542.72/241.49 down(g(g(g(g(g(g(c))))))) 542.72/241.49 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.49 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.49 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 f_flat(up(x0)) 542.72/241.49 g_flat(up(x0)) 542.72/241.49 542.72/241.49 We have to consider all minimal (P,Q,R)-chains. 542.72/241.49 ---------------------------------------- 542.72/241.49 542.72/241.49 (305) TransformationProof (EQUIVALENT) 542.72/241.49 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(down(f(f(c)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.49 542.72/241.49 (TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))),TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c))))))) 542.72/241.49 542.72/241.49 542.72/241.49 ---------------------------------------- 542.72/241.49 542.72/241.49 (306) 542.72/241.49 Obligation: 542.72/241.49 Q DP problem: 542.72/241.49 The TRS P consists of the following rules: 542.72/241.49 542.72/241.49 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.49 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.49 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.49 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.49 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) 542.72/241.49 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.72/241.49 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.72/241.49 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.72/241.49 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.72/241.49 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.72/241.49 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.49 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.49 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.49 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.49 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.49 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.49 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.49 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.49 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.49 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.49 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.49 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.49 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.49 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.49 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.49 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.49 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.49 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.49 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.49 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.49 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.49 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.49 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.49 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.49 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.49 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.49 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.49 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.49 542.72/241.49 The TRS R consists of the following rules: 542.72/241.49 542.72/241.49 down(a) -> up(f(a)) 542.72/241.49 down(b) -> up(g(b)) 542.72/241.49 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.49 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.49 down(f(a)) -> f_flat(down(a)) 542.72/241.49 down(f(b)) -> f_flat(down(b)) 542.72/241.49 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.49 down(f(c)) -> f_flat(down(c)) 542.72/241.49 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.49 down(g(a)) -> g_flat(down(a)) 542.72/241.49 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.49 down(g(b)) -> g_flat(down(b)) 542.72/241.49 down(g(c)) -> g_flat(down(c)) 542.72/241.49 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.49 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.49 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.49 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.49 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.49 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.49 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.49 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.49 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.49 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.49 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.49 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.49 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.49 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.49 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.49 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.49 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.49 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.49 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.49 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.50 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.50 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.50 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.50 542.72/241.50 The set Q consists of the following terms: 542.72/241.50 542.72/241.50 down(a) 542.72/241.50 down(b) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.50 down(f(a)) 542.72/241.50 down(f(b)) 542.72/241.50 down(f(g(x0))) 542.72/241.50 down(f(c)) 542.72/241.50 down(f(fresh_constant)) 542.72/241.50 down(g(a)) 542.72/241.50 down(g(f(x0))) 542.72/241.50 down(g(b)) 542.72/241.50 down(g(c)) 542.72/241.50 down(g(fresh_constant)) 542.72/241.50 down(f(f(a))) 542.72/241.50 down(f(f(b))) 542.72/241.50 down(f(f(g(x0)))) 542.72/241.50 down(f(f(c))) 542.72/241.50 down(f(f(fresh_constant))) 542.72/241.50 down(g(g(a))) 542.72/241.50 down(g(g(f(x0)))) 542.72/241.50 down(g(g(b))) 542.72/241.50 down(g(g(c))) 542.72/241.50 down(g(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) 542.72/241.50 down(f(f(f(g(x0))))) 542.72/241.50 down(f(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) 542.72/241.50 down(g(g(g(f(x0))))) 542.72/241.50 down(g(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(x0)))))) 542.72/241.50 down(f(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(x0)))))) 542.72/241.50 down(g(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(x0))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(x0))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 f_flat(up(x0)) 542.72/241.50 g_flat(up(x0)) 542.72/241.50 542.72/241.50 We have to consider all minimal (P,Q,R)-chains. 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (307) TransformationProof (EQUIVALENT) 542.72/241.50 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(down(f(f(fresh_constant)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.50 542.72/241.50 (TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))),TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 542.72/241.50 542.72/241.50 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (308) 542.72/241.50 Obligation: 542.72/241.50 Q DP problem: 542.72/241.50 The TRS P consists of the following rules: 542.72/241.50 542.72/241.50 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.50 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.50 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.50 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.50 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) 542.72/241.50 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.72/241.50 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.72/241.50 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.72/241.50 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.72/241.50 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.50 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.50 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.50 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.50 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.50 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.50 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.50 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.50 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.50 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.50 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.50 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.50 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.50 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.50 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.50 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.50 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.50 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.50 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.50 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.50 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.50 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.50 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.50 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.50 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.50 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.50 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.50 542.72/241.50 The TRS R consists of the following rules: 542.72/241.50 542.72/241.50 down(a) -> up(f(a)) 542.72/241.50 down(b) -> up(g(b)) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.50 down(f(a)) -> f_flat(down(a)) 542.72/241.50 down(f(b)) -> f_flat(down(b)) 542.72/241.50 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.50 down(f(c)) -> f_flat(down(c)) 542.72/241.50 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.50 down(g(a)) -> g_flat(down(a)) 542.72/241.50 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.50 down(g(b)) -> g_flat(down(b)) 542.72/241.50 down(g(c)) -> g_flat(down(c)) 542.72/241.50 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.50 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.50 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.50 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.50 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.50 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.50 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.50 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.50 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.50 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.50 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.50 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.50 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.50 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.50 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.50 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.50 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.50 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.50 542.72/241.50 The set Q consists of the following terms: 542.72/241.50 542.72/241.50 down(a) 542.72/241.50 down(b) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.50 down(f(a)) 542.72/241.50 down(f(b)) 542.72/241.50 down(f(g(x0))) 542.72/241.50 down(f(c)) 542.72/241.50 down(f(fresh_constant)) 542.72/241.50 down(g(a)) 542.72/241.50 down(g(f(x0))) 542.72/241.50 down(g(b)) 542.72/241.50 down(g(c)) 542.72/241.50 down(g(fresh_constant)) 542.72/241.50 down(f(f(a))) 542.72/241.50 down(f(f(b))) 542.72/241.50 down(f(f(g(x0)))) 542.72/241.50 down(f(f(c))) 542.72/241.50 down(f(f(fresh_constant))) 542.72/241.50 down(g(g(a))) 542.72/241.50 down(g(g(f(x0)))) 542.72/241.50 down(g(g(b))) 542.72/241.50 down(g(g(c))) 542.72/241.50 down(g(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) 542.72/241.50 down(f(f(f(g(x0))))) 542.72/241.50 down(f(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) 542.72/241.50 down(g(g(g(f(x0))))) 542.72/241.50 down(g(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(x0)))))) 542.72/241.50 down(f(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(x0)))))) 542.72/241.50 down(g(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(x0))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(x0))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 f_flat(up(x0)) 542.72/241.50 g_flat(up(x0)) 542.72/241.50 542.72/241.50 We have to consider all minimal (P,Q,R)-chains. 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (309) TransformationProof (EQUIVALENT) 542.72/241.50 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(down(f(f(f(a))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.50 542.72/241.50 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a)))))))) 542.72/241.50 542.72/241.50 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (310) 542.72/241.50 Obligation: 542.72/241.50 Q DP problem: 542.72/241.50 The TRS P consists of the following rules: 542.72/241.50 542.72/241.50 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.50 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.50 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.50 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.50 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) 542.72/241.50 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.72/241.50 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.72/241.50 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.72/241.50 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.50 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.50 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.50 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.50 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.50 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.50 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.50 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.50 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.50 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.50 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.50 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.50 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.50 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.50 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.50 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.50 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.50 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.50 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.50 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.50 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.50 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.50 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.50 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.50 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.50 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.50 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.50 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.50 542.72/241.50 The TRS R consists of the following rules: 542.72/241.50 542.72/241.50 down(a) -> up(f(a)) 542.72/241.50 down(b) -> up(g(b)) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.50 down(f(a)) -> f_flat(down(a)) 542.72/241.50 down(f(b)) -> f_flat(down(b)) 542.72/241.50 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.50 down(f(c)) -> f_flat(down(c)) 542.72/241.50 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.50 down(g(a)) -> g_flat(down(a)) 542.72/241.50 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.50 down(g(b)) -> g_flat(down(b)) 542.72/241.50 down(g(c)) -> g_flat(down(c)) 542.72/241.50 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.50 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.50 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.50 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.50 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.50 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.50 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.50 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.50 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.50 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.50 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.50 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.50 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.50 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.50 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.50 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.50 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.50 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.50 542.72/241.50 The set Q consists of the following terms: 542.72/241.50 542.72/241.50 down(a) 542.72/241.50 down(b) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.50 down(f(a)) 542.72/241.50 down(f(b)) 542.72/241.50 down(f(g(x0))) 542.72/241.50 down(f(c)) 542.72/241.50 down(f(fresh_constant)) 542.72/241.50 down(g(a)) 542.72/241.50 down(g(f(x0))) 542.72/241.50 down(g(b)) 542.72/241.50 down(g(c)) 542.72/241.50 down(g(fresh_constant)) 542.72/241.50 down(f(f(a))) 542.72/241.50 down(f(f(b))) 542.72/241.50 down(f(f(g(x0)))) 542.72/241.50 down(f(f(c))) 542.72/241.50 down(f(f(fresh_constant))) 542.72/241.50 down(g(g(a))) 542.72/241.50 down(g(g(f(x0)))) 542.72/241.50 down(g(g(b))) 542.72/241.50 down(g(g(c))) 542.72/241.50 down(g(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) 542.72/241.50 down(f(f(f(g(x0))))) 542.72/241.50 down(f(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) 542.72/241.50 down(g(g(g(f(x0))))) 542.72/241.50 down(g(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(x0)))))) 542.72/241.50 down(f(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(x0)))))) 542.72/241.50 down(g(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(x0))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(x0))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 f_flat(up(x0)) 542.72/241.50 g_flat(up(x0)) 542.72/241.50 542.72/241.50 We have to consider all minimal (P,Q,R)-chains. 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (311) TransformationProof (EQUIVALENT) 542.72/241.50 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(down(f(f(f(b))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.50 542.72/241.50 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b)))))))) 542.72/241.50 542.72/241.50 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (312) 542.72/241.50 Obligation: 542.72/241.50 Q DP problem: 542.72/241.50 The TRS P consists of the following rules: 542.72/241.50 542.72/241.50 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.50 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.50 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.50 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.50 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) 542.72/241.50 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.72/241.50 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.72/241.50 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.50 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.50 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.50 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.50 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.50 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.50 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.50 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.50 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.50 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.50 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.50 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.50 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.50 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.50 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.50 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.50 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.50 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.50 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.50 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.50 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.50 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.50 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.50 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.50 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.50 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.50 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.50 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.50 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.50 542.72/241.50 The TRS R consists of the following rules: 542.72/241.50 542.72/241.50 down(a) -> up(f(a)) 542.72/241.50 down(b) -> up(g(b)) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.50 down(f(a)) -> f_flat(down(a)) 542.72/241.50 down(f(b)) -> f_flat(down(b)) 542.72/241.50 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.50 down(f(c)) -> f_flat(down(c)) 542.72/241.50 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.50 down(g(a)) -> g_flat(down(a)) 542.72/241.50 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.50 down(g(b)) -> g_flat(down(b)) 542.72/241.50 down(g(c)) -> g_flat(down(c)) 542.72/241.50 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.50 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.50 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.50 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.50 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.50 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.50 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.50 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.50 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.50 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.50 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.50 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.50 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.50 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.50 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.50 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.50 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.50 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.50 542.72/241.50 The set Q consists of the following terms: 542.72/241.50 542.72/241.50 down(a) 542.72/241.50 down(b) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.50 down(f(a)) 542.72/241.50 down(f(b)) 542.72/241.50 down(f(g(x0))) 542.72/241.50 down(f(c)) 542.72/241.50 down(f(fresh_constant)) 542.72/241.50 down(g(a)) 542.72/241.50 down(g(f(x0))) 542.72/241.50 down(g(b)) 542.72/241.50 down(g(c)) 542.72/241.50 down(g(fresh_constant)) 542.72/241.50 down(f(f(a))) 542.72/241.50 down(f(f(b))) 542.72/241.50 down(f(f(g(x0)))) 542.72/241.50 down(f(f(c))) 542.72/241.50 down(f(f(fresh_constant))) 542.72/241.50 down(g(g(a))) 542.72/241.50 down(g(g(f(x0)))) 542.72/241.50 down(g(g(b))) 542.72/241.50 down(g(g(c))) 542.72/241.50 down(g(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) 542.72/241.50 down(f(f(f(g(x0))))) 542.72/241.50 down(f(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) 542.72/241.50 down(g(g(g(f(x0))))) 542.72/241.50 down(g(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(x0)))))) 542.72/241.50 down(f(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(x0)))))) 542.72/241.50 down(g(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(x0))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(x0))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 f_flat(up(x0)) 542.72/241.50 g_flat(up(x0)) 542.72/241.50 542.72/241.50 We have to consider all minimal (P,Q,R)-chains. 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (313) TransformationProof (EQUIVALENT) 542.72/241.50 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(down(f(f(f(g(x0)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.50 542.72/241.50 (TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))),TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 542.72/241.50 542.72/241.50 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (314) 542.72/241.50 Obligation: 542.72/241.50 Q DP problem: 542.72/241.50 The TRS P consists of the following rules: 542.72/241.50 542.72/241.50 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.50 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.50 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.50 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.50 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) 542.72/241.50 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.72/241.50 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.50 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.50 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.50 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.50 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.50 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.50 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.50 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.50 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.50 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.50 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.50 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.50 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.50 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.50 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.50 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.50 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.50 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.50 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.50 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.50 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.50 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.50 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.50 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.50 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.50 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.50 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.50 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.50 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.50 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.50 542.72/241.50 The TRS R consists of the following rules: 542.72/241.50 542.72/241.50 down(a) -> up(f(a)) 542.72/241.50 down(b) -> up(g(b)) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.50 down(f(a)) -> f_flat(down(a)) 542.72/241.50 down(f(b)) -> f_flat(down(b)) 542.72/241.50 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.50 down(f(c)) -> f_flat(down(c)) 542.72/241.50 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.50 down(g(a)) -> g_flat(down(a)) 542.72/241.50 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.50 down(g(b)) -> g_flat(down(b)) 542.72/241.50 down(g(c)) -> g_flat(down(c)) 542.72/241.50 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.50 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.50 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.50 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.50 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.50 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.50 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.50 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.50 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.50 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.50 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.50 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.50 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.50 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.50 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.50 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.50 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.50 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.50 542.72/241.50 The set Q consists of the following terms: 542.72/241.50 542.72/241.50 down(a) 542.72/241.50 down(b) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.50 down(f(a)) 542.72/241.50 down(f(b)) 542.72/241.50 down(f(g(x0))) 542.72/241.50 down(f(c)) 542.72/241.50 down(f(fresh_constant)) 542.72/241.50 down(g(a)) 542.72/241.50 down(g(f(x0))) 542.72/241.50 down(g(b)) 542.72/241.50 down(g(c)) 542.72/241.50 down(g(fresh_constant)) 542.72/241.50 down(f(f(a))) 542.72/241.50 down(f(f(b))) 542.72/241.50 down(f(f(g(x0)))) 542.72/241.50 down(f(f(c))) 542.72/241.50 down(f(f(fresh_constant))) 542.72/241.50 down(g(g(a))) 542.72/241.50 down(g(g(f(x0)))) 542.72/241.50 down(g(g(b))) 542.72/241.50 down(g(g(c))) 542.72/241.50 down(g(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) 542.72/241.50 down(f(f(f(g(x0))))) 542.72/241.50 down(f(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) 542.72/241.50 down(g(g(g(f(x0))))) 542.72/241.50 down(g(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(x0)))))) 542.72/241.50 down(f(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(x0)))))) 542.72/241.50 down(g(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(x0))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(x0))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 f_flat(up(x0)) 542.72/241.50 g_flat(up(x0)) 542.72/241.50 542.72/241.50 We have to consider all minimal (P,Q,R)-chains. 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (315) TransformationProof (EQUIVALENT) 542.72/241.50 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(down(g(g(b)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.50 542.72/241.50 (TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))),TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b))))))) 542.72/241.50 542.72/241.50 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (316) 542.72/241.50 Obligation: 542.72/241.50 Q DP problem: 542.72/241.50 The TRS P consists of the following rules: 542.72/241.50 542.72/241.50 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.50 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.50 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.50 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.50 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) 542.72/241.50 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.50 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.50 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.50 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.50 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.50 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.50 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.50 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.50 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.50 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.50 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.50 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.50 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.50 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.50 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.50 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.50 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.50 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.50 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.50 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.50 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.50 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.50 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.50 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.50 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.50 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.50 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.50 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.50 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.50 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.50 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.50 542.72/241.50 The TRS R consists of the following rules: 542.72/241.50 542.72/241.50 down(a) -> up(f(a)) 542.72/241.50 down(b) -> up(g(b)) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.50 down(f(a)) -> f_flat(down(a)) 542.72/241.50 down(f(b)) -> f_flat(down(b)) 542.72/241.50 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.50 down(f(c)) -> f_flat(down(c)) 542.72/241.50 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.50 down(g(a)) -> g_flat(down(a)) 542.72/241.50 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.50 down(g(b)) -> g_flat(down(b)) 542.72/241.50 down(g(c)) -> g_flat(down(c)) 542.72/241.50 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.50 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.50 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.50 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.50 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.50 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.50 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.50 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.50 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.50 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.50 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.50 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.50 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.50 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.50 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.50 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.50 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.50 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.50 542.72/241.50 The set Q consists of the following terms: 542.72/241.50 542.72/241.50 down(a) 542.72/241.50 down(b) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.50 down(f(a)) 542.72/241.50 down(f(b)) 542.72/241.50 down(f(g(x0))) 542.72/241.50 down(f(c)) 542.72/241.50 down(f(fresh_constant)) 542.72/241.50 down(g(a)) 542.72/241.50 down(g(f(x0))) 542.72/241.50 down(g(b)) 542.72/241.50 down(g(c)) 542.72/241.50 down(g(fresh_constant)) 542.72/241.50 down(f(f(a))) 542.72/241.50 down(f(f(b))) 542.72/241.50 down(f(f(g(x0)))) 542.72/241.50 down(f(f(c))) 542.72/241.50 down(f(f(fresh_constant))) 542.72/241.50 down(g(g(a))) 542.72/241.50 down(g(g(f(x0)))) 542.72/241.50 down(g(g(b))) 542.72/241.50 down(g(g(c))) 542.72/241.50 down(g(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) 542.72/241.50 down(f(f(f(g(x0))))) 542.72/241.50 down(f(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) 542.72/241.50 down(g(g(g(f(x0))))) 542.72/241.50 down(g(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(x0)))))) 542.72/241.50 down(f(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(x0)))))) 542.72/241.50 down(g(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(x0))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(x0))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 f_flat(up(x0)) 542.72/241.50 g_flat(up(x0)) 542.72/241.50 542.72/241.50 We have to consider all minimal (P,Q,R)-chains. 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (317) TransformationProof (EQUIVALENT) 542.72/241.50 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(down(g(g(c)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.50 542.72/241.50 (TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))),TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c))))))) 542.72/241.50 542.72/241.50 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (318) 542.72/241.50 Obligation: 542.72/241.50 Q DP problem: 542.72/241.50 The TRS P consists of the following rules: 542.72/241.50 542.72/241.50 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.50 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.50 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.50 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.50 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) 542.72/241.50 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.50 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.50 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.50 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.50 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.50 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.50 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.50 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.50 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.50 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.50 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.50 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.50 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.50 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.50 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.50 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.50 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.50 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.50 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.50 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.50 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.50 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.50 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.50 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.50 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.50 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.50 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.50 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.50 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.50 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.50 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.50 542.72/241.50 The TRS R consists of the following rules: 542.72/241.50 542.72/241.50 down(a) -> up(f(a)) 542.72/241.50 down(b) -> up(g(b)) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.50 down(f(a)) -> f_flat(down(a)) 542.72/241.50 down(f(b)) -> f_flat(down(b)) 542.72/241.50 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.50 down(f(c)) -> f_flat(down(c)) 542.72/241.50 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.50 down(g(a)) -> g_flat(down(a)) 542.72/241.50 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.50 down(g(b)) -> g_flat(down(b)) 542.72/241.50 down(g(c)) -> g_flat(down(c)) 542.72/241.50 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.50 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.50 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.50 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.50 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.50 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.50 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.50 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.50 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.50 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.50 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.50 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.50 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.50 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.50 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.50 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.50 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.50 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.50 542.72/241.50 The set Q consists of the following terms: 542.72/241.50 542.72/241.50 down(a) 542.72/241.50 down(b) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.50 down(f(a)) 542.72/241.50 down(f(b)) 542.72/241.50 down(f(g(x0))) 542.72/241.50 down(f(c)) 542.72/241.50 down(f(fresh_constant)) 542.72/241.50 down(g(a)) 542.72/241.50 down(g(f(x0))) 542.72/241.50 down(g(b)) 542.72/241.50 down(g(c)) 542.72/241.50 down(g(fresh_constant)) 542.72/241.50 down(f(f(a))) 542.72/241.50 down(f(f(b))) 542.72/241.50 down(f(f(g(x0)))) 542.72/241.50 down(f(f(c))) 542.72/241.50 down(f(f(fresh_constant))) 542.72/241.50 down(g(g(a))) 542.72/241.50 down(g(g(f(x0)))) 542.72/241.50 down(g(g(b))) 542.72/241.50 down(g(g(c))) 542.72/241.50 down(g(g(fresh_constant))) 542.72/241.50 down(f(f(f(a)))) 542.72/241.50 down(f(f(f(b)))) 542.72/241.50 down(f(f(f(g(x0))))) 542.72/241.50 down(f(f(f(c)))) 542.72/241.50 down(f(f(f(fresh_constant)))) 542.72/241.50 down(g(g(g(a)))) 542.72/241.50 down(g(g(g(f(x0))))) 542.72/241.50 down(g(g(g(b)))) 542.72/241.50 down(g(g(g(c)))) 542.72/241.50 down(g(g(g(fresh_constant)))) 542.72/241.50 down(f(f(f(f(a))))) 542.72/241.50 down(f(f(f(f(b))))) 542.72/241.50 down(f(f(f(f(g(x0)))))) 542.72/241.50 down(f(f(f(f(c))))) 542.72/241.50 down(f(f(f(f(fresh_constant))))) 542.72/241.50 down(g(g(g(g(a))))) 542.72/241.50 down(g(g(g(g(f(x0)))))) 542.72/241.50 down(g(g(g(g(b))))) 542.72/241.50 down(g(g(g(g(c))))) 542.72/241.50 down(g(g(g(g(fresh_constant))))) 542.72/241.50 down(f(f(f(f(f(a)))))) 542.72/241.50 down(f(f(f(f(f(b)))))) 542.72/241.50 down(f(f(f(f(f(g(x0))))))) 542.72/241.50 down(f(f(f(f(f(c)))))) 542.72/241.50 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.50 down(g(g(g(g(g(a)))))) 542.72/241.50 down(g(g(g(g(g(f(x0))))))) 542.72/241.50 down(g(g(g(g(g(b)))))) 542.72/241.50 down(g(g(g(g(g(c)))))) 542.72/241.50 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.50 down(f(f(f(f(f(f(a))))))) 542.72/241.50 down(f(f(f(f(f(f(b))))))) 542.72/241.50 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.50 down(f(f(f(f(f(f(c))))))) 542.72/241.50 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.50 down(g(g(g(g(g(g(a))))))) 542.72/241.50 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.50 down(g(g(g(g(g(g(b))))))) 542.72/241.50 down(g(g(g(g(g(g(c))))))) 542.72/241.50 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.50 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.50 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.50 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.50 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.50 f_flat(up(x0)) 542.72/241.50 g_flat(up(x0)) 542.72/241.50 542.72/241.50 We have to consider all minimal (P,Q,R)-chains. 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (319) TransformationProof (EQUIVALENT) 542.72/241.50 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(down(g(g(fresh_constant)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.50 542.72/241.50 (TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))),TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 542.72/241.50 542.72/241.50 542.72/241.50 ---------------------------------------- 542.72/241.50 542.72/241.50 (320) 542.72/241.50 Obligation: 542.72/241.50 Q DP problem: 542.72/241.50 The TRS P consists of the following rules: 542.72/241.50 542.72/241.50 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.50 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.50 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.50 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.50 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) 542.72/241.50 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.50 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.50 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.50 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.50 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.50 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.51 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.51 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.51 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.51 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.51 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.51 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.51 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.51 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.51 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.51 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.51 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.51 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.51 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.51 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.51 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.51 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.51 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.51 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.51 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.51 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.51 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.51 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.51 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.51 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.51 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.51 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.51 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.51 542.72/241.51 The TRS R consists of the following rules: 542.72/241.51 542.72/241.51 down(a) -> up(f(a)) 542.72/241.51 down(b) -> up(g(b)) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.51 down(f(a)) -> f_flat(down(a)) 542.72/241.51 down(f(b)) -> f_flat(down(b)) 542.72/241.51 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.51 down(f(c)) -> f_flat(down(c)) 542.72/241.51 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.51 down(g(a)) -> g_flat(down(a)) 542.72/241.51 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.51 down(g(b)) -> g_flat(down(b)) 542.72/241.51 down(g(c)) -> g_flat(down(c)) 542.72/241.51 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.51 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.51 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.51 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.51 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.51 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.51 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.51 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.51 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.51 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.51 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.51 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.51 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.51 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.51 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.51 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.51 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.51 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.51 542.72/241.51 The set Q consists of the following terms: 542.72/241.51 542.72/241.51 down(a) 542.72/241.51 down(b) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.51 down(f(a)) 542.72/241.51 down(f(b)) 542.72/241.51 down(f(g(x0))) 542.72/241.51 down(f(c)) 542.72/241.51 down(f(fresh_constant)) 542.72/241.51 down(g(a)) 542.72/241.51 down(g(f(x0))) 542.72/241.51 down(g(b)) 542.72/241.51 down(g(c)) 542.72/241.51 down(g(fresh_constant)) 542.72/241.51 down(f(f(a))) 542.72/241.51 down(f(f(b))) 542.72/241.51 down(f(f(g(x0)))) 542.72/241.51 down(f(f(c))) 542.72/241.51 down(f(f(fresh_constant))) 542.72/241.51 down(g(g(a))) 542.72/241.51 down(g(g(f(x0)))) 542.72/241.51 down(g(g(b))) 542.72/241.51 down(g(g(c))) 542.72/241.51 down(g(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) 542.72/241.51 down(f(f(f(g(x0))))) 542.72/241.51 down(f(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) 542.72/241.51 down(g(g(g(f(x0))))) 542.72/241.51 down(g(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(x0)))))) 542.72/241.51 down(f(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(x0)))))) 542.72/241.51 down(g(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(x0))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(x0))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 f_flat(up(x0)) 542.72/241.51 g_flat(up(x0)) 542.72/241.51 542.72/241.51 We have to consider all minimal (P,Q,R)-chains. 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (321) TransformationProof (EQUIVALENT) 542.72/241.51 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(down(g(g(g(a))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.51 542.72/241.51 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a)))))))) 542.72/241.51 542.72/241.51 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (322) 542.72/241.51 Obligation: 542.72/241.51 Q DP problem: 542.72/241.51 The TRS P consists of the following rules: 542.72/241.51 542.72/241.51 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.51 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.51 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.51 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.51 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.51 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.51 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.51 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.51 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.51 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.51 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.51 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.51 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.51 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.51 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.51 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.51 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.51 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.51 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.51 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.51 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.51 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.51 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.51 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.51 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.51 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.51 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.51 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.51 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.51 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.51 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.51 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.51 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.51 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.51 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.51 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.51 542.72/241.51 The TRS R consists of the following rules: 542.72/241.51 542.72/241.51 down(a) -> up(f(a)) 542.72/241.51 down(b) -> up(g(b)) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.51 down(f(a)) -> f_flat(down(a)) 542.72/241.51 down(f(b)) -> f_flat(down(b)) 542.72/241.51 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.51 down(f(c)) -> f_flat(down(c)) 542.72/241.51 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.51 down(g(a)) -> g_flat(down(a)) 542.72/241.51 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.51 down(g(b)) -> g_flat(down(b)) 542.72/241.51 down(g(c)) -> g_flat(down(c)) 542.72/241.51 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.51 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.51 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.51 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.51 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.51 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.51 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.51 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.51 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.51 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.51 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.51 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.51 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.51 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.51 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.51 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.51 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.51 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.51 542.72/241.51 The set Q consists of the following terms: 542.72/241.51 542.72/241.51 down(a) 542.72/241.51 down(b) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.51 down(f(a)) 542.72/241.51 down(f(b)) 542.72/241.51 down(f(g(x0))) 542.72/241.51 down(f(c)) 542.72/241.51 down(f(fresh_constant)) 542.72/241.51 down(g(a)) 542.72/241.51 down(g(f(x0))) 542.72/241.51 down(g(b)) 542.72/241.51 down(g(c)) 542.72/241.51 down(g(fresh_constant)) 542.72/241.51 down(f(f(a))) 542.72/241.51 down(f(f(b))) 542.72/241.51 down(f(f(g(x0)))) 542.72/241.51 down(f(f(c))) 542.72/241.51 down(f(f(fresh_constant))) 542.72/241.51 down(g(g(a))) 542.72/241.51 down(g(g(f(x0)))) 542.72/241.51 down(g(g(b))) 542.72/241.51 down(g(g(c))) 542.72/241.51 down(g(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) 542.72/241.51 down(f(f(f(g(x0))))) 542.72/241.51 down(f(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) 542.72/241.51 down(g(g(g(f(x0))))) 542.72/241.51 down(g(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(x0)))))) 542.72/241.51 down(f(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(x0)))))) 542.72/241.51 down(g(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(x0))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(x0))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 f_flat(up(x0)) 542.72/241.51 g_flat(up(x0)) 542.72/241.51 542.72/241.51 We have to consider all minimal (P,Q,R)-chains. 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (323) TransformationProof (EQUIVALENT) 542.72/241.51 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(down(g(g(g(f(x0)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.51 542.72/241.51 (TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))),TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 542.72/241.51 542.72/241.51 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (324) 542.72/241.51 Obligation: 542.72/241.51 Q DP problem: 542.72/241.51 The TRS P consists of the following rules: 542.72/241.51 542.72/241.51 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.51 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.51 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.51 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.51 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) 542.72/241.51 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.51 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.51 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.51 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.51 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.51 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.51 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.51 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.51 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.51 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.51 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.51 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.51 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.51 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.51 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.51 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.51 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.51 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.51 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.51 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.51 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.51 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.51 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.51 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.51 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.51 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.51 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.51 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.51 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.51 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.51 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.51 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.51 542.72/241.51 The TRS R consists of the following rules: 542.72/241.51 542.72/241.51 down(a) -> up(f(a)) 542.72/241.51 down(b) -> up(g(b)) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.51 down(f(a)) -> f_flat(down(a)) 542.72/241.51 down(f(b)) -> f_flat(down(b)) 542.72/241.51 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.51 down(f(c)) -> f_flat(down(c)) 542.72/241.51 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.51 down(g(a)) -> g_flat(down(a)) 542.72/241.51 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.51 down(g(b)) -> g_flat(down(b)) 542.72/241.51 down(g(c)) -> g_flat(down(c)) 542.72/241.51 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.51 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.51 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.51 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.51 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.51 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.51 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.51 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.51 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.51 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.51 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.51 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.51 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.51 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.51 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.51 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.51 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.51 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.51 542.72/241.51 The set Q consists of the following terms: 542.72/241.51 542.72/241.51 down(a) 542.72/241.51 down(b) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.51 down(f(a)) 542.72/241.51 down(f(b)) 542.72/241.51 down(f(g(x0))) 542.72/241.51 down(f(c)) 542.72/241.51 down(f(fresh_constant)) 542.72/241.51 down(g(a)) 542.72/241.51 down(g(f(x0))) 542.72/241.51 down(g(b)) 542.72/241.51 down(g(c)) 542.72/241.51 down(g(fresh_constant)) 542.72/241.51 down(f(f(a))) 542.72/241.51 down(f(f(b))) 542.72/241.51 down(f(f(g(x0)))) 542.72/241.51 down(f(f(c))) 542.72/241.51 down(f(f(fresh_constant))) 542.72/241.51 down(g(g(a))) 542.72/241.51 down(g(g(f(x0)))) 542.72/241.51 down(g(g(b))) 542.72/241.51 down(g(g(c))) 542.72/241.51 down(g(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) 542.72/241.51 down(f(f(f(g(x0))))) 542.72/241.51 down(f(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) 542.72/241.51 down(g(g(g(f(x0))))) 542.72/241.51 down(g(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(x0)))))) 542.72/241.51 down(f(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(x0)))))) 542.72/241.51 down(g(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(x0))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(x0))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 f_flat(up(x0)) 542.72/241.51 g_flat(up(x0)) 542.72/241.51 542.72/241.51 We have to consider all minimal (P,Q,R)-chains. 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (325) TransformationProof (EQUIVALENT) 542.72/241.51 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(down(f(f(f(c))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.51 542.72/241.51 (TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))),TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c)))))))) 542.72/241.51 542.72/241.51 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (326) 542.72/241.51 Obligation: 542.72/241.51 Q DP problem: 542.72/241.51 The TRS P consists of the following rules: 542.72/241.51 542.72/241.51 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.51 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.51 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.51 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.51 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.51 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.51 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.51 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.51 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.51 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.51 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.51 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.51 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.51 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.51 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.51 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.51 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.51 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.51 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.51 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.51 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.51 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.51 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.51 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.51 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.51 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.51 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.51 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.51 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.51 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.51 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.51 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.51 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.51 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.51 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.51 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.51 542.72/241.51 The TRS R consists of the following rules: 542.72/241.51 542.72/241.51 down(a) -> up(f(a)) 542.72/241.51 down(b) -> up(g(b)) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.51 down(f(a)) -> f_flat(down(a)) 542.72/241.51 down(f(b)) -> f_flat(down(b)) 542.72/241.51 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.51 down(f(c)) -> f_flat(down(c)) 542.72/241.51 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.51 down(g(a)) -> g_flat(down(a)) 542.72/241.51 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.51 down(g(b)) -> g_flat(down(b)) 542.72/241.51 down(g(c)) -> g_flat(down(c)) 542.72/241.51 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.51 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.51 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.51 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.51 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.51 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.51 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.51 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.51 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.51 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.51 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.51 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.51 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.51 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.51 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.51 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.51 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.51 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.51 542.72/241.51 The set Q consists of the following terms: 542.72/241.51 542.72/241.51 down(a) 542.72/241.51 down(b) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.51 down(f(a)) 542.72/241.51 down(f(b)) 542.72/241.51 down(f(g(x0))) 542.72/241.51 down(f(c)) 542.72/241.51 down(f(fresh_constant)) 542.72/241.51 down(g(a)) 542.72/241.51 down(g(f(x0))) 542.72/241.51 down(g(b)) 542.72/241.51 down(g(c)) 542.72/241.51 down(g(fresh_constant)) 542.72/241.51 down(f(f(a))) 542.72/241.51 down(f(f(b))) 542.72/241.51 down(f(f(g(x0)))) 542.72/241.51 down(f(f(c))) 542.72/241.51 down(f(f(fresh_constant))) 542.72/241.51 down(g(g(a))) 542.72/241.51 down(g(g(f(x0)))) 542.72/241.51 down(g(g(b))) 542.72/241.51 down(g(g(c))) 542.72/241.51 down(g(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) 542.72/241.51 down(f(f(f(g(x0))))) 542.72/241.51 down(f(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) 542.72/241.51 down(g(g(g(f(x0))))) 542.72/241.51 down(g(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(x0)))))) 542.72/241.51 down(f(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(x0)))))) 542.72/241.51 down(g(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(x0))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(x0))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 f_flat(up(x0)) 542.72/241.51 g_flat(up(x0)) 542.72/241.51 542.72/241.51 We have to consider all minimal (P,Q,R)-chains. 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (327) TransformationProof (EQUIVALENT) 542.72/241.51 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(down(f(f(f(fresh_constant))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.51 542.72/241.51 (TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))),TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 542.72/241.51 542.72/241.51 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (328) 542.72/241.51 Obligation: 542.72/241.51 Q DP problem: 542.72/241.51 The TRS P consists of the following rules: 542.72/241.51 542.72/241.51 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.51 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.51 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.51 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.51 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.51 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.51 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.51 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.51 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.51 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.51 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.51 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.51 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.51 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.51 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.51 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.51 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.51 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.51 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.51 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.51 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.51 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.51 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.51 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.51 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.51 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.51 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.51 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.51 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.51 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.51 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.51 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.51 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.51 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.51 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.51 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.51 542.72/241.51 The TRS R consists of the following rules: 542.72/241.51 542.72/241.51 down(a) -> up(f(a)) 542.72/241.51 down(b) -> up(g(b)) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.51 down(f(a)) -> f_flat(down(a)) 542.72/241.51 down(f(b)) -> f_flat(down(b)) 542.72/241.51 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.51 down(f(c)) -> f_flat(down(c)) 542.72/241.51 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.51 down(g(a)) -> g_flat(down(a)) 542.72/241.51 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.51 down(g(b)) -> g_flat(down(b)) 542.72/241.51 down(g(c)) -> g_flat(down(c)) 542.72/241.51 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.51 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.51 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.51 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.51 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.51 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.51 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.51 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.51 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.51 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.51 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.51 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.51 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.51 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.51 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.51 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.51 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.51 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.51 542.72/241.51 The set Q consists of the following terms: 542.72/241.51 542.72/241.51 down(a) 542.72/241.51 down(b) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.51 down(f(a)) 542.72/241.51 down(f(b)) 542.72/241.51 down(f(g(x0))) 542.72/241.51 down(f(c)) 542.72/241.51 down(f(fresh_constant)) 542.72/241.51 down(g(a)) 542.72/241.51 down(g(f(x0))) 542.72/241.51 down(g(b)) 542.72/241.51 down(g(c)) 542.72/241.51 down(g(fresh_constant)) 542.72/241.51 down(f(f(a))) 542.72/241.51 down(f(f(b))) 542.72/241.51 down(f(f(g(x0)))) 542.72/241.51 down(f(f(c))) 542.72/241.51 down(f(f(fresh_constant))) 542.72/241.51 down(g(g(a))) 542.72/241.51 down(g(g(f(x0)))) 542.72/241.51 down(g(g(b))) 542.72/241.51 down(g(g(c))) 542.72/241.51 down(g(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) 542.72/241.51 down(f(f(f(g(x0))))) 542.72/241.51 down(f(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) 542.72/241.51 down(g(g(g(f(x0))))) 542.72/241.51 down(g(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(x0)))))) 542.72/241.51 down(f(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(x0)))))) 542.72/241.51 down(g(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(x0))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(x0))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 f_flat(up(x0)) 542.72/241.51 g_flat(up(x0)) 542.72/241.51 542.72/241.51 We have to consider all minimal (P,Q,R)-chains. 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (329) TransformationProof (EQUIVALENT) 542.72/241.51 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(a)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.51 542.72/241.51 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 542.72/241.51 542.72/241.51 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (330) 542.72/241.51 Obligation: 542.72/241.51 Q DP problem: 542.72/241.51 The TRS P consists of the following rules: 542.72/241.51 542.72/241.51 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.51 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.51 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.51 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.51 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.51 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.51 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.51 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.51 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.51 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.51 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.51 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.51 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.51 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.51 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.51 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.51 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.51 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.51 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.51 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.51 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.51 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.51 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.51 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.51 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.51 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.51 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.51 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.51 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.51 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.51 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.51 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.51 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.51 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.51 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.51 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.51 542.72/241.51 The TRS R consists of the following rules: 542.72/241.51 542.72/241.51 down(a) -> up(f(a)) 542.72/241.51 down(b) -> up(g(b)) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.51 down(f(a)) -> f_flat(down(a)) 542.72/241.51 down(f(b)) -> f_flat(down(b)) 542.72/241.51 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.51 down(f(c)) -> f_flat(down(c)) 542.72/241.51 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.51 down(g(a)) -> g_flat(down(a)) 542.72/241.51 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.51 down(g(b)) -> g_flat(down(b)) 542.72/241.51 down(g(c)) -> g_flat(down(c)) 542.72/241.51 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.51 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.51 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.51 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.51 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.51 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.51 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.51 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.51 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.51 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.51 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.51 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.51 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.51 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.51 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.51 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.51 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.51 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.51 542.72/241.51 The set Q consists of the following terms: 542.72/241.51 542.72/241.51 down(a) 542.72/241.51 down(b) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.51 down(f(a)) 542.72/241.51 down(f(b)) 542.72/241.51 down(f(g(x0))) 542.72/241.51 down(f(c)) 542.72/241.51 down(f(fresh_constant)) 542.72/241.51 down(g(a)) 542.72/241.51 down(g(f(x0))) 542.72/241.51 down(g(b)) 542.72/241.51 down(g(c)) 542.72/241.51 down(g(fresh_constant)) 542.72/241.51 down(f(f(a))) 542.72/241.51 down(f(f(b))) 542.72/241.51 down(f(f(g(x0)))) 542.72/241.51 down(f(f(c))) 542.72/241.51 down(f(f(fresh_constant))) 542.72/241.51 down(g(g(a))) 542.72/241.51 down(g(g(f(x0)))) 542.72/241.51 down(g(g(b))) 542.72/241.51 down(g(g(c))) 542.72/241.51 down(g(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) 542.72/241.51 down(f(f(f(g(x0))))) 542.72/241.51 down(f(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) 542.72/241.51 down(g(g(g(f(x0))))) 542.72/241.51 down(g(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(x0)))))) 542.72/241.51 down(f(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(x0)))))) 542.72/241.51 down(g(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(x0))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(x0))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 f_flat(up(x0)) 542.72/241.51 g_flat(up(x0)) 542.72/241.51 542.72/241.51 We have to consider all minimal (P,Q,R)-chains. 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (331) TransformationProof (EQUIVALENT) 542.72/241.51 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(b)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.51 542.72/241.51 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 542.72/241.51 542.72/241.51 542.72/241.51 ---------------------------------------- 542.72/241.51 542.72/241.51 (332) 542.72/241.51 Obligation: 542.72/241.51 Q DP problem: 542.72/241.51 The TRS P consists of the following rules: 542.72/241.51 542.72/241.51 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.51 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.51 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.51 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.51 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.51 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.51 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.51 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.51 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.51 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.51 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.51 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.51 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.51 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.51 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.51 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.51 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.51 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.51 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.51 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.51 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.51 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.51 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.51 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.51 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.51 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.51 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.51 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.51 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.51 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.51 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.51 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.51 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.51 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.51 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.51 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.51 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.51 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.51 542.72/241.51 The TRS R consists of the following rules: 542.72/241.51 542.72/241.51 down(a) -> up(f(a)) 542.72/241.51 down(b) -> up(g(b)) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.51 down(f(a)) -> f_flat(down(a)) 542.72/241.51 down(f(b)) -> f_flat(down(b)) 542.72/241.51 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.51 down(f(c)) -> f_flat(down(c)) 542.72/241.51 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.51 down(g(a)) -> g_flat(down(a)) 542.72/241.51 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.51 down(g(b)) -> g_flat(down(b)) 542.72/241.51 down(g(c)) -> g_flat(down(c)) 542.72/241.51 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.51 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.51 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.51 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.51 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.51 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.51 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.51 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.51 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.51 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.51 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.51 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.51 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.51 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.51 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.51 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.51 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.51 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.51 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.51 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.51 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.51 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.51 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.51 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.51 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.51 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.51 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.51 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.51 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.51 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.51 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.51 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.51 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.51 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.51 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.51 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.51 542.72/241.51 The set Q consists of the following terms: 542.72/241.51 542.72/241.51 down(a) 542.72/241.51 down(b) 542.72/241.51 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.51 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.51 down(f(a)) 542.72/241.51 down(f(b)) 542.72/241.51 down(f(g(x0))) 542.72/241.51 down(f(c)) 542.72/241.51 down(f(fresh_constant)) 542.72/241.51 down(g(a)) 542.72/241.51 down(g(f(x0))) 542.72/241.51 down(g(b)) 542.72/241.51 down(g(c)) 542.72/241.51 down(g(fresh_constant)) 542.72/241.51 down(f(f(a))) 542.72/241.51 down(f(f(b))) 542.72/241.51 down(f(f(g(x0)))) 542.72/241.51 down(f(f(c))) 542.72/241.51 down(f(f(fresh_constant))) 542.72/241.51 down(g(g(a))) 542.72/241.51 down(g(g(f(x0)))) 542.72/241.51 down(g(g(b))) 542.72/241.51 down(g(g(c))) 542.72/241.51 down(g(g(fresh_constant))) 542.72/241.51 down(f(f(f(a)))) 542.72/241.51 down(f(f(f(b)))) 542.72/241.51 down(f(f(f(g(x0))))) 542.72/241.51 down(f(f(f(c)))) 542.72/241.51 down(f(f(f(fresh_constant)))) 542.72/241.51 down(g(g(g(a)))) 542.72/241.51 down(g(g(g(f(x0))))) 542.72/241.51 down(g(g(g(b)))) 542.72/241.51 down(g(g(g(c)))) 542.72/241.51 down(g(g(g(fresh_constant)))) 542.72/241.51 down(f(f(f(f(a))))) 542.72/241.51 down(f(f(f(f(b))))) 542.72/241.51 down(f(f(f(f(g(x0)))))) 542.72/241.51 down(f(f(f(f(c))))) 542.72/241.51 down(f(f(f(f(fresh_constant))))) 542.72/241.51 down(g(g(g(g(a))))) 542.72/241.51 down(g(g(g(g(f(x0)))))) 542.72/241.51 down(g(g(g(g(b))))) 542.72/241.51 down(g(g(g(g(c))))) 542.72/241.51 down(g(g(g(g(fresh_constant))))) 542.72/241.51 down(f(f(f(f(f(a)))))) 542.72/241.51 down(f(f(f(f(f(b)))))) 542.72/241.51 down(f(f(f(f(f(g(x0))))))) 542.72/241.51 down(f(f(f(f(f(c)))))) 542.72/241.51 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(x0))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 f_flat(up(x0)) 542.72/241.52 g_flat(up(x0)) 542.72/241.52 542.72/241.52 We have to consider all minimal (P,Q,R)-chains. 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (333) TransformationProof (EQUIVALENT) 542.72/241.52 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(g(x0))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.52 542.72/241.52 (TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))),TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 542.72/241.52 542.72/241.52 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (334) 542.72/241.52 Obligation: 542.72/241.52 Q DP problem: 542.72/241.52 The TRS P consists of the following rules: 542.72/241.52 542.72/241.52 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.52 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.52 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.52 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.52 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) 542.72/241.52 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.52 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.52 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.52 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.52 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.52 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.52 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.52 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.52 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.52 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.52 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.52 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.52 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.52 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.52 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.52 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.52 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.52 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.52 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.52 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.52 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.52 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.52 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.52 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.52 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.52 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.52 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.52 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.52 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.52 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.52 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.52 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.52 542.72/241.52 The TRS R consists of the following rules: 542.72/241.52 542.72/241.52 down(a) -> up(f(a)) 542.72/241.52 down(b) -> up(g(b)) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.52 down(f(a)) -> f_flat(down(a)) 542.72/241.52 down(f(b)) -> f_flat(down(b)) 542.72/241.52 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.52 down(f(c)) -> f_flat(down(c)) 542.72/241.52 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.52 down(g(a)) -> g_flat(down(a)) 542.72/241.52 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.52 down(g(b)) -> g_flat(down(b)) 542.72/241.52 down(g(c)) -> g_flat(down(c)) 542.72/241.52 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.52 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.52 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.52 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.52 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.52 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.52 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.52 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.52 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.52 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.52 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.52 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.52 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.52 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.52 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.52 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.52 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.52 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.52 542.72/241.52 The set Q consists of the following terms: 542.72/241.52 542.72/241.52 down(a) 542.72/241.52 down(b) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.52 down(f(a)) 542.72/241.52 down(f(b)) 542.72/241.52 down(f(g(x0))) 542.72/241.52 down(f(c)) 542.72/241.52 down(f(fresh_constant)) 542.72/241.52 down(g(a)) 542.72/241.52 down(g(f(x0))) 542.72/241.52 down(g(b)) 542.72/241.52 down(g(c)) 542.72/241.52 down(g(fresh_constant)) 542.72/241.52 down(f(f(a))) 542.72/241.52 down(f(f(b))) 542.72/241.52 down(f(f(g(x0)))) 542.72/241.52 down(f(f(c))) 542.72/241.52 down(f(f(fresh_constant))) 542.72/241.52 down(g(g(a))) 542.72/241.52 down(g(g(f(x0)))) 542.72/241.52 down(g(g(b))) 542.72/241.52 down(g(g(c))) 542.72/241.52 down(g(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) 542.72/241.52 down(f(f(f(g(x0))))) 542.72/241.52 down(f(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) 542.72/241.52 down(g(g(g(f(x0))))) 542.72/241.52 down(g(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(x0)))))) 542.72/241.52 down(f(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(x0)))))) 542.72/241.52 down(g(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(x0))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(x0))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 f_flat(up(x0)) 542.72/241.52 g_flat(up(x0)) 542.72/241.52 542.72/241.52 We have to consider all minimal (P,Q,R)-chains. 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (335) TransformationProof (EQUIVALENT) 542.72/241.52 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(down(g(g(g(b))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.52 542.72/241.52 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b)))))))) 542.72/241.52 542.72/241.52 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (336) 542.72/241.52 Obligation: 542.72/241.52 Q DP problem: 542.72/241.52 The TRS P consists of the following rules: 542.72/241.52 542.72/241.52 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.52 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.52 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.52 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.52 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) 542.72/241.52 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.52 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.52 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.52 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.52 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.52 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.52 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.52 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.52 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.52 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.52 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.52 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.52 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.52 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.52 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.52 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.52 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.52 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.52 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.52 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.52 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.52 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.52 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.52 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.52 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.52 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.52 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.52 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.52 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.52 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.52 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.52 542.72/241.52 The TRS R consists of the following rules: 542.72/241.52 542.72/241.52 down(a) -> up(f(a)) 542.72/241.52 down(b) -> up(g(b)) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.52 down(f(a)) -> f_flat(down(a)) 542.72/241.52 down(f(b)) -> f_flat(down(b)) 542.72/241.52 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.52 down(f(c)) -> f_flat(down(c)) 542.72/241.52 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.52 down(g(a)) -> g_flat(down(a)) 542.72/241.52 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.52 down(g(b)) -> g_flat(down(b)) 542.72/241.52 down(g(c)) -> g_flat(down(c)) 542.72/241.52 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.52 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.52 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.52 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.52 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.52 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.52 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.52 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.52 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.52 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.52 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.52 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.52 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.52 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.52 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.52 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.52 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.52 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.52 542.72/241.52 The set Q consists of the following terms: 542.72/241.52 542.72/241.52 down(a) 542.72/241.52 down(b) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.52 down(f(a)) 542.72/241.52 down(f(b)) 542.72/241.52 down(f(g(x0))) 542.72/241.52 down(f(c)) 542.72/241.52 down(f(fresh_constant)) 542.72/241.52 down(g(a)) 542.72/241.52 down(g(f(x0))) 542.72/241.52 down(g(b)) 542.72/241.52 down(g(c)) 542.72/241.52 down(g(fresh_constant)) 542.72/241.52 down(f(f(a))) 542.72/241.52 down(f(f(b))) 542.72/241.52 down(f(f(g(x0)))) 542.72/241.52 down(f(f(c))) 542.72/241.52 down(f(f(fresh_constant))) 542.72/241.52 down(g(g(a))) 542.72/241.52 down(g(g(f(x0)))) 542.72/241.52 down(g(g(b))) 542.72/241.52 down(g(g(c))) 542.72/241.52 down(g(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) 542.72/241.52 down(f(f(f(g(x0))))) 542.72/241.52 down(f(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) 542.72/241.52 down(g(g(g(f(x0))))) 542.72/241.52 down(g(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(x0)))))) 542.72/241.52 down(f(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(x0)))))) 542.72/241.52 down(g(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(x0))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(x0))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 f_flat(up(x0)) 542.72/241.52 g_flat(up(x0)) 542.72/241.52 542.72/241.52 We have to consider all minimal (P,Q,R)-chains. 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (337) TransformationProof (EQUIVALENT) 542.72/241.52 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(down(g(g(g(c))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.52 542.72/241.52 (TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))),TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c)))))))) 542.72/241.52 542.72/241.52 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (338) 542.72/241.52 Obligation: 542.72/241.52 Q DP problem: 542.72/241.52 The TRS P consists of the following rules: 542.72/241.52 542.72/241.52 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.52 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.52 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.52 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.52 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.52 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.52 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.52 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.52 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.52 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.52 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.52 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.52 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.52 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.52 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.52 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.52 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.52 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.52 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.52 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.52 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.52 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.52 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.52 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.52 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.52 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.52 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.52 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.52 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.52 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.52 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.52 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.52 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.52 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.52 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.52 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.52 542.72/241.52 The TRS R consists of the following rules: 542.72/241.52 542.72/241.52 down(a) -> up(f(a)) 542.72/241.52 down(b) -> up(g(b)) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.52 down(f(a)) -> f_flat(down(a)) 542.72/241.52 down(f(b)) -> f_flat(down(b)) 542.72/241.52 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.52 down(f(c)) -> f_flat(down(c)) 542.72/241.52 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.52 down(g(a)) -> g_flat(down(a)) 542.72/241.52 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.52 down(g(b)) -> g_flat(down(b)) 542.72/241.52 down(g(c)) -> g_flat(down(c)) 542.72/241.52 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.52 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.52 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.52 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.52 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.52 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.52 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.52 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.52 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.52 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.52 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.52 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.52 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.52 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.52 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.52 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.52 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.52 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.52 542.72/241.52 The set Q consists of the following terms: 542.72/241.52 542.72/241.52 down(a) 542.72/241.52 down(b) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.52 down(f(a)) 542.72/241.52 down(f(b)) 542.72/241.52 down(f(g(x0))) 542.72/241.52 down(f(c)) 542.72/241.52 down(f(fresh_constant)) 542.72/241.52 down(g(a)) 542.72/241.52 down(g(f(x0))) 542.72/241.52 down(g(b)) 542.72/241.52 down(g(c)) 542.72/241.52 down(g(fresh_constant)) 542.72/241.52 down(f(f(a))) 542.72/241.52 down(f(f(b))) 542.72/241.52 down(f(f(g(x0)))) 542.72/241.52 down(f(f(c))) 542.72/241.52 down(f(f(fresh_constant))) 542.72/241.52 down(g(g(a))) 542.72/241.52 down(g(g(f(x0)))) 542.72/241.52 down(g(g(b))) 542.72/241.52 down(g(g(c))) 542.72/241.52 down(g(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) 542.72/241.52 down(f(f(f(g(x0))))) 542.72/241.52 down(f(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) 542.72/241.52 down(g(g(g(f(x0))))) 542.72/241.52 down(g(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(x0)))))) 542.72/241.52 down(f(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(x0)))))) 542.72/241.52 down(g(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(x0))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(x0))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 f_flat(up(x0)) 542.72/241.52 g_flat(up(x0)) 542.72/241.52 542.72/241.52 We have to consider all minimal (P,Q,R)-chains. 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (339) TransformationProof (EQUIVALENT) 542.72/241.52 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(down(g(g(g(fresh_constant))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.52 542.72/241.52 (TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))),TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 542.72/241.52 542.72/241.52 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (340) 542.72/241.52 Obligation: 542.72/241.52 Q DP problem: 542.72/241.52 The TRS P consists of the following rules: 542.72/241.52 542.72/241.52 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.52 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.52 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.52 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.52 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.52 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.52 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.52 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.52 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.52 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.52 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.52 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.52 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.52 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.52 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.52 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.52 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.52 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.52 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.52 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.52 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.52 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.52 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.52 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.52 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.52 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.52 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.52 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.52 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.52 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.52 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.52 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.52 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.52 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.52 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.52 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.72/241.52 542.72/241.52 The TRS R consists of the following rules: 542.72/241.52 542.72/241.52 down(a) -> up(f(a)) 542.72/241.52 down(b) -> up(g(b)) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.52 down(f(a)) -> f_flat(down(a)) 542.72/241.52 down(f(b)) -> f_flat(down(b)) 542.72/241.52 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.52 down(f(c)) -> f_flat(down(c)) 542.72/241.52 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.52 down(g(a)) -> g_flat(down(a)) 542.72/241.52 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.52 down(g(b)) -> g_flat(down(b)) 542.72/241.52 down(g(c)) -> g_flat(down(c)) 542.72/241.52 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.52 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.52 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.52 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.52 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.52 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.52 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.52 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.52 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.52 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.52 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.52 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.52 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.52 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.52 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.52 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.52 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.52 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.52 542.72/241.52 The set Q consists of the following terms: 542.72/241.52 542.72/241.52 down(a) 542.72/241.52 down(b) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.52 down(f(a)) 542.72/241.52 down(f(b)) 542.72/241.52 down(f(g(x0))) 542.72/241.52 down(f(c)) 542.72/241.52 down(f(fresh_constant)) 542.72/241.52 down(g(a)) 542.72/241.52 down(g(f(x0))) 542.72/241.52 down(g(b)) 542.72/241.52 down(g(c)) 542.72/241.52 down(g(fresh_constant)) 542.72/241.52 down(f(f(a))) 542.72/241.52 down(f(f(b))) 542.72/241.52 down(f(f(g(x0)))) 542.72/241.52 down(f(f(c))) 542.72/241.52 down(f(f(fresh_constant))) 542.72/241.52 down(g(g(a))) 542.72/241.52 down(g(g(f(x0)))) 542.72/241.52 down(g(g(b))) 542.72/241.52 down(g(g(c))) 542.72/241.52 down(g(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) 542.72/241.52 down(f(f(f(g(x0))))) 542.72/241.52 down(f(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) 542.72/241.52 down(g(g(g(f(x0))))) 542.72/241.52 down(g(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(x0)))))) 542.72/241.52 down(f(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(x0)))))) 542.72/241.52 down(g(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(x0))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(x0))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 f_flat(up(x0)) 542.72/241.52 g_flat(up(x0)) 542.72/241.52 542.72/241.52 We have to consider all minimal (P,Q,R)-chains. 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (341) TransformationProof (EQUIVALENT) 542.72/241.52 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(a)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.52 542.72/241.52 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 542.72/241.52 542.72/241.52 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (342) 542.72/241.52 Obligation: 542.72/241.52 Q DP problem: 542.72/241.52 The TRS P consists of the following rules: 542.72/241.52 542.72/241.52 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.52 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.52 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.52 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.52 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.52 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.52 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.52 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.52 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.52 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.52 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.52 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.52 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.52 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.52 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.52 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.52 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.52 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.52 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.52 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.52 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.52 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.52 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.52 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.52 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.52 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.52 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.52 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.52 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.52 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.52 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.52 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.52 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.52 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.52 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.52 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.72/241.52 542.72/241.52 The TRS R consists of the following rules: 542.72/241.52 542.72/241.52 down(a) -> up(f(a)) 542.72/241.52 down(b) -> up(g(b)) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.52 down(f(a)) -> f_flat(down(a)) 542.72/241.52 down(f(b)) -> f_flat(down(b)) 542.72/241.52 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.52 down(f(c)) -> f_flat(down(c)) 542.72/241.52 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.52 down(g(a)) -> g_flat(down(a)) 542.72/241.52 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.52 down(g(b)) -> g_flat(down(b)) 542.72/241.52 down(g(c)) -> g_flat(down(c)) 542.72/241.52 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.52 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.52 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.52 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.52 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.52 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.52 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.52 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.52 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.52 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.52 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.52 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.52 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.52 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.52 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.52 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.52 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.52 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.52 542.72/241.52 The set Q consists of the following terms: 542.72/241.52 542.72/241.52 down(a) 542.72/241.52 down(b) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.52 down(f(a)) 542.72/241.52 down(f(b)) 542.72/241.52 down(f(g(x0))) 542.72/241.52 down(f(c)) 542.72/241.52 down(f(fresh_constant)) 542.72/241.52 down(g(a)) 542.72/241.52 down(g(f(x0))) 542.72/241.52 down(g(b)) 542.72/241.52 down(g(c)) 542.72/241.52 down(g(fresh_constant)) 542.72/241.52 down(f(f(a))) 542.72/241.52 down(f(f(b))) 542.72/241.52 down(f(f(g(x0)))) 542.72/241.52 down(f(f(c))) 542.72/241.52 down(f(f(fresh_constant))) 542.72/241.52 down(g(g(a))) 542.72/241.52 down(g(g(f(x0)))) 542.72/241.52 down(g(g(b))) 542.72/241.52 down(g(g(c))) 542.72/241.52 down(g(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) 542.72/241.52 down(f(f(f(g(x0))))) 542.72/241.52 down(f(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) 542.72/241.52 down(g(g(g(f(x0))))) 542.72/241.52 down(g(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(x0)))))) 542.72/241.52 down(f(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(x0)))))) 542.72/241.52 down(g(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(x0))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(x0))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 f_flat(up(x0)) 542.72/241.52 g_flat(up(x0)) 542.72/241.52 542.72/241.52 We have to consider all minimal (P,Q,R)-chains. 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (343) TransformationProof (EQUIVALENT) 542.72/241.52 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(f(x0))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.52 542.72/241.52 (TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))),TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 542.72/241.52 542.72/241.52 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (344) 542.72/241.52 Obligation: 542.72/241.52 Q DP problem: 542.72/241.52 The TRS P consists of the following rules: 542.72/241.52 542.72/241.52 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.52 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.52 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.52 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.52 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.52 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.52 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.52 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.52 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.52 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.52 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.52 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.52 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.52 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.52 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.52 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.52 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.52 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.52 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.52 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.52 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.52 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.52 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.52 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.52 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.52 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.52 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.52 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.52 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.52 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.52 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.52 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.52 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.52 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.52 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.52 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.72/241.52 542.72/241.52 The TRS R consists of the following rules: 542.72/241.52 542.72/241.52 down(a) -> up(f(a)) 542.72/241.52 down(b) -> up(g(b)) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.52 down(f(a)) -> f_flat(down(a)) 542.72/241.52 down(f(b)) -> f_flat(down(b)) 542.72/241.52 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.52 down(f(c)) -> f_flat(down(c)) 542.72/241.52 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.52 down(g(a)) -> g_flat(down(a)) 542.72/241.52 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.52 down(g(b)) -> g_flat(down(b)) 542.72/241.52 down(g(c)) -> g_flat(down(c)) 542.72/241.52 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.52 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.52 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.52 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.52 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.52 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.52 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.52 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.52 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.52 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.52 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.52 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.52 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.52 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.52 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.52 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.52 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.52 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.52 542.72/241.52 The set Q consists of the following terms: 542.72/241.52 542.72/241.52 down(a) 542.72/241.52 down(b) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.52 down(f(a)) 542.72/241.52 down(f(b)) 542.72/241.52 down(f(g(x0))) 542.72/241.52 down(f(c)) 542.72/241.52 down(f(fresh_constant)) 542.72/241.52 down(g(a)) 542.72/241.52 down(g(f(x0))) 542.72/241.52 down(g(b)) 542.72/241.52 down(g(c)) 542.72/241.52 down(g(fresh_constant)) 542.72/241.52 down(f(f(a))) 542.72/241.52 down(f(f(b))) 542.72/241.52 down(f(f(g(x0)))) 542.72/241.52 down(f(f(c))) 542.72/241.52 down(f(f(fresh_constant))) 542.72/241.52 down(g(g(a))) 542.72/241.52 down(g(g(f(x0)))) 542.72/241.52 down(g(g(b))) 542.72/241.52 down(g(g(c))) 542.72/241.52 down(g(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) 542.72/241.52 down(f(f(f(g(x0))))) 542.72/241.52 down(f(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) 542.72/241.52 down(g(g(g(f(x0))))) 542.72/241.52 down(g(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(x0)))))) 542.72/241.52 down(f(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(x0)))))) 542.72/241.52 down(g(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(x0))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(x0))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) 542.72/241.52 down(f(f(f(f(f(f(b))))))) 542.72/241.52 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.52 down(f(f(f(f(f(f(c))))))) 542.72/241.52 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.52 down(g(g(g(g(g(g(a))))))) 542.72/241.52 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.52 down(g(g(g(g(g(g(b))))))) 542.72/241.52 down(g(g(g(g(g(g(c))))))) 542.72/241.52 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.52 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.52 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 f_flat(up(x0)) 542.72/241.52 g_flat(up(x0)) 542.72/241.52 542.72/241.52 We have to consider all minimal (P,Q,R)-chains. 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (345) TransformationProof (EQUIVALENT) 542.72/241.52 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(c)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.52 542.72/241.52 (TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))),TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 542.72/241.52 542.72/241.52 542.72/241.52 ---------------------------------------- 542.72/241.52 542.72/241.52 (346) 542.72/241.52 Obligation: 542.72/241.52 Q DP problem: 542.72/241.52 The TRS P consists of the following rules: 542.72/241.52 542.72/241.52 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.52 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.52 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.52 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.52 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.52 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.52 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.52 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.52 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.52 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.52 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.52 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.52 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.52 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.52 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.52 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.52 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.52 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.52 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.52 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.52 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.52 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.52 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.52 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.52 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.52 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.52 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.52 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.52 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.52 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.52 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.52 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.52 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.52 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.52 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.52 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.52 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.72/241.52 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.72/241.52 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.72/241.52 542.72/241.52 The TRS R consists of the following rules: 542.72/241.52 542.72/241.52 down(a) -> up(f(a)) 542.72/241.52 down(b) -> up(g(b)) 542.72/241.52 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.52 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.52 down(f(a)) -> f_flat(down(a)) 542.72/241.52 down(f(b)) -> f_flat(down(b)) 542.72/241.52 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.52 down(f(c)) -> f_flat(down(c)) 542.72/241.52 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.52 down(g(a)) -> g_flat(down(a)) 542.72/241.52 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.52 down(g(b)) -> g_flat(down(b)) 542.72/241.52 down(g(c)) -> g_flat(down(c)) 542.72/241.52 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.52 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.52 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.52 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.52 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.52 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.52 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.52 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.52 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.52 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.52 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.52 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.52 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.52 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.52 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.52 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.52 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.52 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.52 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.52 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.52 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.52 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.52 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.52 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.52 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.52 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.52 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.52 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.52 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.52 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.52 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.52 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.52 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.52 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.52 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.52 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.52 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.52 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.52 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.52 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.52 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.52 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.53 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.53 542.72/241.53 The set Q consists of the following terms: 542.72/241.53 542.72/241.53 down(a) 542.72/241.53 down(b) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.53 down(f(a)) 542.72/241.53 down(f(b)) 542.72/241.53 down(f(g(x0))) 542.72/241.53 down(f(c)) 542.72/241.53 down(f(fresh_constant)) 542.72/241.53 down(g(a)) 542.72/241.53 down(g(f(x0))) 542.72/241.53 down(g(b)) 542.72/241.53 down(g(c)) 542.72/241.53 down(g(fresh_constant)) 542.72/241.53 down(f(f(a))) 542.72/241.53 down(f(f(b))) 542.72/241.53 down(f(f(g(x0)))) 542.72/241.53 down(f(f(c))) 542.72/241.53 down(f(f(fresh_constant))) 542.72/241.53 down(g(g(a))) 542.72/241.53 down(g(g(f(x0)))) 542.72/241.53 down(g(g(b))) 542.72/241.53 down(g(g(c))) 542.72/241.53 down(g(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) 542.72/241.53 down(f(f(f(g(x0))))) 542.72/241.53 down(f(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) 542.72/241.53 down(g(g(g(f(x0))))) 542.72/241.53 down(g(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(x0)))))) 542.72/241.53 down(f(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(x0)))))) 542.72/241.53 down(g(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(x0))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(x0))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 f_flat(up(x0)) 542.72/241.53 g_flat(up(x0)) 542.72/241.53 542.72/241.53 We have to consider all minimal (P,Q,R)-chains. 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (347) TransformationProof (EQUIVALENT) 542.72/241.53 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.53 542.72/241.53 (TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))),TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 542.72/241.53 542.72/241.53 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (348) 542.72/241.53 Obligation: 542.72/241.53 Q DP problem: 542.72/241.53 The TRS P consists of the following rules: 542.72/241.53 542.72/241.53 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.53 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.53 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.53 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.53 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.53 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.53 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.53 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.53 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.53 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.53 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.53 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.53 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.53 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.53 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.53 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.53 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.53 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.53 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.53 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.53 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.53 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.53 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.53 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.53 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.53 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.53 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.53 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.53 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.53 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.53 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.53 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.53 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.53 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.53 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.53 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.72/241.53 542.72/241.53 The TRS R consists of the following rules: 542.72/241.53 542.72/241.53 down(a) -> up(f(a)) 542.72/241.53 down(b) -> up(g(b)) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.53 down(f(a)) -> f_flat(down(a)) 542.72/241.53 down(f(b)) -> f_flat(down(b)) 542.72/241.53 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.53 down(f(c)) -> f_flat(down(c)) 542.72/241.53 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.53 down(g(a)) -> g_flat(down(a)) 542.72/241.53 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.53 down(g(b)) -> g_flat(down(b)) 542.72/241.53 down(g(c)) -> g_flat(down(c)) 542.72/241.53 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.53 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.53 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.53 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.53 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.53 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.53 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.53 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.53 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.53 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.53 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.53 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.53 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.53 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.53 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.53 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.53 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.53 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.53 542.72/241.53 The set Q consists of the following terms: 542.72/241.53 542.72/241.53 down(a) 542.72/241.53 down(b) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.53 down(f(a)) 542.72/241.53 down(f(b)) 542.72/241.53 down(f(g(x0))) 542.72/241.53 down(f(c)) 542.72/241.53 down(f(fresh_constant)) 542.72/241.53 down(g(a)) 542.72/241.53 down(g(f(x0))) 542.72/241.53 down(g(b)) 542.72/241.53 down(g(c)) 542.72/241.53 down(g(fresh_constant)) 542.72/241.53 down(f(f(a))) 542.72/241.53 down(f(f(b))) 542.72/241.53 down(f(f(g(x0)))) 542.72/241.53 down(f(f(c))) 542.72/241.53 down(f(f(fresh_constant))) 542.72/241.53 down(g(g(a))) 542.72/241.53 down(g(g(f(x0)))) 542.72/241.53 down(g(g(b))) 542.72/241.53 down(g(g(c))) 542.72/241.53 down(g(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) 542.72/241.53 down(f(f(f(g(x0))))) 542.72/241.53 down(f(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) 542.72/241.53 down(g(g(g(f(x0))))) 542.72/241.53 down(g(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(x0)))))) 542.72/241.53 down(f(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(x0)))))) 542.72/241.53 down(g(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(x0))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(x0))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 f_flat(up(x0)) 542.72/241.53 g_flat(up(x0)) 542.72/241.53 542.72/241.53 We have to consider all minimal (P,Q,R)-chains. 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (349) TransformationProof (EQUIVALENT) 542.72/241.53 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(a))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.53 542.72/241.53 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 542.72/241.53 542.72/241.53 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (350) 542.72/241.53 Obligation: 542.72/241.53 Q DP problem: 542.72/241.53 The TRS P consists of the following rules: 542.72/241.53 542.72/241.53 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.53 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.53 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.53 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.53 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.53 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.53 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.53 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.53 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.53 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.53 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.53 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.53 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.53 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.53 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.53 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.53 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.53 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.53 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.53 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.53 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.53 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.53 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.53 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.53 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.53 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.53 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.53 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.53 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.53 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.53 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.53 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.53 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.53 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.53 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.53 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.72/241.53 542.72/241.53 The TRS R consists of the following rules: 542.72/241.53 542.72/241.53 down(a) -> up(f(a)) 542.72/241.53 down(b) -> up(g(b)) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.53 down(f(a)) -> f_flat(down(a)) 542.72/241.53 down(f(b)) -> f_flat(down(b)) 542.72/241.53 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.53 down(f(c)) -> f_flat(down(c)) 542.72/241.53 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.53 down(g(a)) -> g_flat(down(a)) 542.72/241.53 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.53 down(g(b)) -> g_flat(down(b)) 542.72/241.53 down(g(c)) -> g_flat(down(c)) 542.72/241.53 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.53 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.53 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.53 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.53 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.53 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.53 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.53 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.53 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.53 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.53 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.53 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.53 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.53 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.53 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.53 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.53 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.53 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.53 542.72/241.53 The set Q consists of the following terms: 542.72/241.53 542.72/241.53 down(a) 542.72/241.53 down(b) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.53 down(f(a)) 542.72/241.53 down(f(b)) 542.72/241.53 down(f(g(x0))) 542.72/241.53 down(f(c)) 542.72/241.53 down(f(fresh_constant)) 542.72/241.53 down(g(a)) 542.72/241.53 down(g(f(x0))) 542.72/241.53 down(g(b)) 542.72/241.53 down(g(c)) 542.72/241.53 down(g(fresh_constant)) 542.72/241.53 down(f(f(a))) 542.72/241.53 down(f(f(b))) 542.72/241.53 down(f(f(g(x0)))) 542.72/241.53 down(f(f(c))) 542.72/241.53 down(f(f(fresh_constant))) 542.72/241.53 down(g(g(a))) 542.72/241.53 down(g(g(f(x0)))) 542.72/241.53 down(g(g(b))) 542.72/241.53 down(g(g(c))) 542.72/241.53 down(g(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) 542.72/241.53 down(f(f(f(g(x0))))) 542.72/241.53 down(f(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) 542.72/241.53 down(g(g(g(f(x0))))) 542.72/241.53 down(g(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(x0)))))) 542.72/241.53 down(f(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(x0)))))) 542.72/241.53 down(g(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(x0))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(x0))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 f_flat(up(x0)) 542.72/241.53 g_flat(up(x0)) 542.72/241.53 542.72/241.53 We have to consider all minimal (P,Q,R)-chains. 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (351) TransformationProof (EQUIVALENT) 542.72/241.53 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(b))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.53 542.72/241.53 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 542.72/241.53 542.72/241.53 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (352) 542.72/241.53 Obligation: 542.72/241.53 Q DP problem: 542.72/241.53 The TRS P consists of the following rules: 542.72/241.53 542.72/241.53 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.53 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.53 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.53 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.53 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.53 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.53 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.53 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.53 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.53 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.53 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.53 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.53 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.53 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.53 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.53 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.53 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.53 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.53 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.53 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.53 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.53 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.53 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.53 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.53 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.53 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.53 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.53 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.53 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.53 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.53 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.53 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.53 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.53 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.53 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.53 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.72/241.53 542.72/241.53 The TRS R consists of the following rules: 542.72/241.53 542.72/241.53 down(a) -> up(f(a)) 542.72/241.53 down(b) -> up(g(b)) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.53 down(f(a)) -> f_flat(down(a)) 542.72/241.53 down(f(b)) -> f_flat(down(b)) 542.72/241.53 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.53 down(f(c)) -> f_flat(down(c)) 542.72/241.53 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.53 down(g(a)) -> g_flat(down(a)) 542.72/241.53 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.53 down(g(b)) -> g_flat(down(b)) 542.72/241.53 down(g(c)) -> g_flat(down(c)) 542.72/241.53 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.53 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.53 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.53 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.53 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.53 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.53 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.53 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.53 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.53 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.53 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.53 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.53 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.53 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.53 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.53 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.53 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.53 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.53 542.72/241.53 The set Q consists of the following terms: 542.72/241.53 542.72/241.53 down(a) 542.72/241.53 down(b) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.53 down(f(a)) 542.72/241.53 down(f(b)) 542.72/241.53 down(f(g(x0))) 542.72/241.53 down(f(c)) 542.72/241.53 down(f(fresh_constant)) 542.72/241.53 down(g(a)) 542.72/241.53 down(g(f(x0))) 542.72/241.53 down(g(b)) 542.72/241.53 down(g(c)) 542.72/241.53 down(g(fresh_constant)) 542.72/241.53 down(f(f(a))) 542.72/241.53 down(f(f(b))) 542.72/241.53 down(f(f(g(x0)))) 542.72/241.53 down(f(f(c))) 542.72/241.53 down(f(f(fresh_constant))) 542.72/241.53 down(g(g(a))) 542.72/241.53 down(g(g(f(x0)))) 542.72/241.53 down(g(g(b))) 542.72/241.53 down(g(g(c))) 542.72/241.53 down(g(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) 542.72/241.53 down(f(f(f(g(x0))))) 542.72/241.53 down(f(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) 542.72/241.53 down(g(g(g(f(x0))))) 542.72/241.53 down(g(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(x0)))))) 542.72/241.53 down(f(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(x0)))))) 542.72/241.53 down(g(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(x0))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(x0))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 f_flat(up(x0)) 542.72/241.53 g_flat(up(x0)) 542.72/241.53 542.72/241.53 We have to consider all minimal (P,Q,R)-chains. 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (353) TransformationProof (EQUIVALENT) 542.72/241.53 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.53 542.72/241.53 (TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))),TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 542.72/241.53 542.72/241.53 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (354) 542.72/241.53 Obligation: 542.72/241.53 Q DP problem: 542.72/241.53 The TRS P consists of the following rules: 542.72/241.53 542.72/241.53 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.53 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.53 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.53 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.53 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.53 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.53 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.53 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.53 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.53 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.53 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.53 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.53 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.53 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.53 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.53 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.53 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.53 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.53 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.53 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.53 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.53 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.53 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.53 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.53 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.53 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.53 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.53 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.53 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.53 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.53 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.53 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.53 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.53 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.53 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.53 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.72/241.53 542.72/241.53 The TRS R consists of the following rules: 542.72/241.53 542.72/241.53 down(a) -> up(f(a)) 542.72/241.53 down(b) -> up(g(b)) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.53 down(f(a)) -> f_flat(down(a)) 542.72/241.53 down(f(b)) -> f_flat(down(b)) 542.72/241.53 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.53 down(f(c)) -> f_flat(down(c)) 542.72/241.53 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.53 down(g(a)) -> g_flat(down(a)) 542.72/241.53 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.53 down(g(b)) -> g_flat(down(b)) 542.72/241.53 down(g(c)) -> g_flat(down(c)) 542.72/241.53 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.53 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.53 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.53 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.53 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.53 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.53 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.53 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.53 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.53 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.53 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.53 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.53 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.53 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.53 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.53 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.53 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.53 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.53 542.72/241.53 The set Q consists of the following terms: 542.72/241.53 542.72/241.53 down(a) 542.72/241.53 down(b) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.53 down(f(a)) 542.72/241.53 down(f(b)) 542.72/241.53 down(f(g(x0))) 542.72/241.53 down(f(c)) 542.72/241.53 down(f(fresh_constant)) 542.72/241.53 down(g(a)) 542.72/241.53 down(g(f(x0))) 542.72/241.53 down(g(b)) 542.72/241.53 down(g(c)) 542.72/241.53 down(g(fresh_constant)) 542.72/241.53 down(f(f(a))) 542.72/241.53 down(f(f(b))) 542.72/241.53 down(f(f(g(x0)))) 542.72/241.53 down(f(f(c))) 542.72/241.53 down(f(f(fresh_constant))) 542.72/241.53 down(g(g(a))) 542.72/241.53 down(g(g(f(x0)))) 542.72/241.53 down(g(g(b))) 542.72/241.53 down(g(g(c))) 542.72/241.53 down(g(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) 542.72/241.53 down(f(f(f(g(x0))))) 542.72/241.53 down(f(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) 542.72/241.53 down(g(g(g(f(x0))))) 542.72/241.53 down(g(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(x0)))))) 542.72/241.53 down(f(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(x0)))))) 542.72/241.53 down(g(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(x0))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(x0))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 f_flat(up(x0)) 542.72/241.53 g_flat(up(x0)) 542.72/241.53 542.72/241.53 We have to consider all minimal (P,Q,R)-chains. 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (355) TransformationProof (EQUIVALENT) 542.72/241.53 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(b)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.72/241.53 542.72/241.53 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 542.72/241.53 542.72/241.53 542.72/241.53 ---------------------------------------- 542.72/241.53 542.72/241.53 (356) 542.72/241.53 Obligation: 542.72/241.53 Q DP problem: 542.72/241.53 The TRS P consists of the following rules: 542.72/241.53 542.72/241.53 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.72/241.53 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.72/241.53 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.72/241.53 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.72/241.53 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.72/241.53 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.72/241.53 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.72/241.53 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.72/241.53 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.72/241.53 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.72/241.53 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.72/241.53 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.72/241.53 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.72/241.53 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.72/241.53 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.72/241.53 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.72/241.53 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.72/241.53 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.72/241.53 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.72/241.53 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.72/241.53 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.72/241.53 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.72/241.53 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.72/241.53 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.72/241.53 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.72/241.53 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.72/241.53 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.72/241.53 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.72/241.53 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.72/241.53 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.72/241.53 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.72/241.53 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.72/241.53 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.72/241.53 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.72/241.53 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.72/241.53 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.72/241.53 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.72/241.53 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.72/241.53 542.72/241.53 The TRS R consists of the following rules: 542.72/241.53 542.72/241.53 down(a) -> up(f(a)) 542.72/241.53 down(b) -> up(g(b)) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.72/241.53 down(f(a)) -> f_flat(down(a)) 542.72/241.53 down(f(b)) -> f_flat(down(b)) 542.72/241.53 down(f(g(y4))) -> f_flat(down(g(y4))) 542.72/241.53 down(f(c)) -> f_flat(down(c)) 542.72/241.53 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.72/241.53 down(g(a)) -> g_flat(down(a)) 542.72/241.53 down(g(f(y6))) -> g_flat(down(f(y6))) 542.72/241.53 down(g(b)) -> g_flat(down(b)) 542.72/241.53 down(g(c)) -> g_flat(down(c)) 542.72/241.53 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.72/241.53 down(f(f(a))) -> f_flat(down(f(a))) 542.72/241.53 down(f(f(b))) -> f_flat(down(f(b))) 542.72/241.53 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.72/241.53 down(f(f(c))) -> f_flat(down(f(c))) 542.72/241.53 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.72/241.53 down(g(g(a))) -> g_flat(down(g(a))) 542.72/241.53 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.72/241.53 down(g(g(b))) -> g_flat(down(g(b))) 542.72/241.53 down(g(g(c))) -> g_flat(down(g(c))) 542.72/241.53 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.72/241.53 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.72/241.53 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.72/241.53 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.72/241.53 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.72/241.53 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.72/241.53 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.72/241.53 g_flat(up(x_1)) -> up(g(x_1)) 542.72/241.53 f_flat(up(x_1)) -> up(f(x_1)) 542.72/241.53 542.72/241.53 The set Q consists of the following terms: 542.72/241.53 542.72/241.53 down(a) 542.72/241.53 down(b) 542.72/241.53 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.72/241.53 down(f(a)) 542.72/241.53 down(f(b)) 542.72/241.53 down(f(g(x0))) 542.72/241.53 down(f(c)) 542.72/241.53 down(f(fresh_constant)) 542.72/241.53 down(g(a)) 542.72/241.53 down(g(f(x0))) 542.72/241.53 down(g(b)) 542.72/241.53 down(g(c)) 542.72/241.53 down(g(fresh_constant)) 542.72/241.53 down(f(f(a))) 542.72/241.53 down(f(f(b))) 542.72/241.53 down(f(f(g(x0)))) 542.72/241.53 down(f(f(c))) 542.72/241.53 down(f(f(fresh_constant))) 542.72/241.53 down(g(g(a))) 542.72/241.53 down(g(g(f(x0)))) 542.72/241.53 down(g(g(b))) 542.72/241.53 down(g(g(c))) 542.72/241.53 down(g(g(fresh_constant))) 542.72/241.53 down(f(f(f(a)))) 542.72/241.53 down(f(f(f(b)))) 542.72/241.53 down(f(f(f(g(x0))))) 542.72/241.53 down(f(f(f(c)))) 542.72/241.53 down(f(f(f(fresh_constant)))) 542.72/241.53 down(g(g(g(a)))) 542.72/241.53 down(g(g(g(f(x0))))) 542.72/241.53 down(g(g(g(b)))) 542.72/241.53 down(g(g(g(c)))) 542.72/241.53 down(g(g(g(fresh_constant)))) 542.72/241.53 down(f(f(f(f(a))))) 542.72/241.53 down(f(f(f(f(b))))) 542.72/241.53 down(f(f(f(f(g(x0)))))) 542.72/241.53 down(f(f(f(f(c))))) 542.72/241.53 down(f(f(f(f(fresh_constant))))) 542.72/241.53 down(g(g(g(g(a))))) 542.72/241.53 down(g(g(g(g(f(x0)))))) 542.72/241.53 down(g(g(g(g(b))))) 542.72/241.53 down(g(g(g(g(c))))) 542.72/241.53 down(g(g(g(g(fresh_constant))))) 542.72/241.53 down(f(f(f(f(f(a)))))) 542.72/241.53 down(f(f(f(f(f(b)))))) 542.72/241.53 down(f(f(f(f(f(g(x0))))))) 542.72/241.53 down(f(f(f(f(f(c)))))) 542.72/241.53 down(f(f(f(f(f(fresh_constant)))))) 542.72/241.53 down(g(g(g(g(g(a)))))) 542.72/241.53 down(g(g(g(g(g(f(x0))))))) 542.72/241.53 down(g(g(g(g(g(b)))))) 542.72/241.53 down(g(g(g(g(g(c)))))) 542.72/241.53 down(g(g(g(g(g(fresh_constant)))))) 542.72/241.53 down(f(f(f(f(f(f(a))))))) 542.72/241.53 down(f(f(f(f(f(f(b))))))) 542.72/241.53 down(f(f(f(f(f(f(g(x0)))))))) 542.72/241.53 down(f(f(f(f(f(f(c))))))) 542.72/241.53 down(f(f(f(f(f(f(fresh_constant))))))) 542.72/241.53 down(g(g(g(g(g(g(a))))))) 542.72/241.53 down(g(g(g(g(g(g(f(x0)))))))) 542.72/241.53 down(g(g(g(g(g(g(b))))))) 542.72/241.53 down(g(g(g(g(g(g(c))))))) 542.72/241.53 down(g(g(g(g(g(g(fresh_constant))))))) 542.72/241.53 down(f(f(f(f(f(f(f(a)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(b)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(g(x0))))))))) 542.72/241.53 down(f(f(f(f(f(f(f(c)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(a)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(f(x0))))))))) 542.72/241.53 down(g(g(g(g(g(g(g(b)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(c)))))))) 542.72/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.72/241.53 down(f(f(f(f(f(f(f(f(a))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(b))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(c))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(a))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(b))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(c))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.53 f_flat(up(x0)) 542.85/241.53 g_flat(up(x0)) 542.85/241.53 542.85/241.53 We have to consider all minimal (P,Q,R)-chains. 542.85/241.53 ---------------------------------------- 542.85/241.53 542.85/241.53 (357) TransformationProof (EQUIVALENT) 542.85/241.53 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(c)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.85/241.53 542.85/241.53 (TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))),TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 542.85/241.53 542.85/241.53 542.85/241.53 ---------------------------------------- 542.85/241.53 542.85/241.53 (358) 542.85/241.53 Obligation: 542.85/241.53 Q DP problem: 542.85/241.53 The TRS P consists of the following rules: 542.85/241.53 542.85/241.53 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.85/241.53 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.85/241.53 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.85/241.53 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.85/241.53 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.85/241.53 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.85/241.53 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.85/241.53 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.85/241.53 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.85/241.53 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.85/241.53 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.85/241.53 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.85/241.53 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.85/241.53 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.85/241.53 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.85/241.53 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.85/241.53 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.85/241.53 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.85/241.53 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.85/241.53 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.85/241.53 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.85/241.53 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.85/241.53 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.85/241.53 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.85/241.53 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.85/241.53 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.85/241.53 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.85/241.53 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.85/241.53 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.85/241.53 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.85/241.53 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.85/241.53 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.85/241.53 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.85/241.53 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.85/241.53 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.85/241.53 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.85/241.53 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.85/241.53 542.85/241.53 The TRS R consists of the following rules: 542.85/241.53 542.85/241.53 down(a) -> up(f(a)) 542.85/241.53 down(b) -> up(g(b)) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.85/241.53 down(f(a)) -> f_flat(down(a)) 542.85/241.53 down(f(b)) -> f_flat(down(b)) 542.85/241.53 down(f(g(y4))) -> f_flat(down(g(y4))) 542.85/241.53 down(f(c)) -> f_flat(down(c)) 542.85/241.53 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.85/241.53 down(g(a)) -> g_flat(down(a)) 542.85/241.53 down(g(f(y6))) -> g_flat(down(f(y6))) 542.85/241.53 down(g(b)) -> g_flat(down(b)) 542.85/241.53 down(g(c)) -> g_flat(down(c)) 542.85/241.53 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.85/241.53 down(f(f(a))) -> f_flat(down(f(a))) 542.85/241.53 down(f(f(b))) -> f_flat(down(f(b))) 542.85/241.53 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.85/241.53 down(f(f(c))) -> f_flat(down(f(c))) 542.85/241.53 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.85/241.53 down(g(g(a))) -> g_flat(down(g(a))) 542.85/241.53 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.85/241.53 down(g(g(b))) -> g_flat(down(g(b))) 542.85/241.53 down(g(g(c))) -> g_flat(down(g(c))) 542.85/241.53 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.85/241.53 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.85/241.53 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.85/241.53 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.85/241.53 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.85/241.53 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.85/241.53 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.85/241.53 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.85/241.53 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.85/241.53 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.85/241.53 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.85/241.53 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.85/241.53 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.85/241.53 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.85/241.53 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.85/241.53 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.85/241.53 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.85/241.53 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.85/241.53 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.85/241.53 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.85/241.53 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.85/241.53 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.85/241.53 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.85/241.53 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.85/241.53 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.85/241.53 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.85/241.53 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.85/241.53 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.85/241.53 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.85/241.53 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.85/241.53 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.85/241.53 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.85/241.53 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.85/241.53 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.85/241.53 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.85/241.53 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.85/241.53 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.85/241.53 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.85/241.53 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.85/241.53 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.85/241.53 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.85/241.53 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.85/241.53 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.85/241.53 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.85/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.53 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.85/241.53 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.85/241.53 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.85/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.53 g_flat(up(x_1)) -> up(g(x_1)) 542.85/241.53 f_flat(up(x_1)) -> up(f(x_1)) 542.85/241.53 542.85/241.53 The set Q consists of the following terms: 542.85/241.53 542.85/241.53 down(a) 542.85/241.53 down(b) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.85/241.53 down(f(a)) 542.85/241.53 down(f(b)) 542.85/241.53 down(f(g(x0))) 542.85/241.53 down(f(c)) 542.85/241.53 down(f(fresh_constant)) 542.85/241.53 down(g(a)) 542.85/241.53 down(g(f(x0))) 542.85/241.53 down(g(b)) 542.85/241.53 down(g(c)) 542.85/241.53 down(g(fresh_constant)) 542.85/241.53 down(f(f(a))) 542.85/241.53 down(f(f(b))) 542.85/241.53 down(f(f(g(x0)))) 542.85/241.53 down(f(f(c))) 542.85/241.53 down(f(f(fresh_constant))) 542.85/241.53 down(g(g(a))) 542.85/241.53 down(g(g(f(x0)))) 542.85/241.53 down(g(g(b))) 542.85/241.53 down(g(g(c))) 542.85/241.53 down(g(g(fresh_constant))) 542.85/241.53 down(f(f(f(a)))) 542.85/241.53 down(f(f(f(b)))) 542.85/241.53 down(f(f(f(g(x0))))) 542.85/241.53 down(f(f(f(c)))) 542.85/241.53 down(f(f(f(fresh_constant)))) 542.85/241.53 down(g(g(g(a)))) 542.85/241.53 down(g(g(g(f(x0))))) 542.85/241.53 down(g(g(g(b)))) 542.85/241.53 down(g(g(g(c)))) 542.85/241.53 down(g(g(g(fresh_constant)))) 542.85/241.53 down(f(f(f(f(a))))) 542.85/241.53 down(f(f(f(f(b))))) 542.85/241.53 down(f(f(f(f(g(x0)))))) 542.85/241.53 down(f(f(f(f(c))))) 542.85/241.53 down(f(f(f(f(fresh_constant))))) 542.85/241.53 down(g(g(g(g(a))))) 542.85/241.53 down(g(g(g(g(f(x0)))))) 542.85/241.53 down(g(g(g(g(b))))) 542.85/241.53 down(g(g(g(g(c))))) 542.85/241.53 down(g(g(g(g(fresh_constant))))) 542.85/241.53 down(f(f(f(f(f(a)))))) 542.85/241.53 down(f(f(f(f(f(b)))))) 542.85/241.53 down(f(f(f(f(f(g(x0))))))) 542.85/241.53 down(f(f(f(f(f(c)))))) 542.85/241.53 down(f(f(f(f(f(fresh_constant)))))) 542.85/241.53 down(g(g(g(g(g(a)))))) 542.85/241.53 down(g(g(g(g(g(f(x0))))))) 542.85/241.53 down(g(g(g(g(g(b)))))) 542.85/241.53 down(g(g(g(g(g(c)))))) 542.85/241.53 down(g(g(g(g(g(fresh_constant)))))) 542.85/241.53 down(f(f(f(f(f(f(a))))))) 542.85/241.53 down(f(f(f(f(f(f(b))))))) 542.85/241.53 down(f(f(f(f(f(f(g(x0)))))))) 542.85/241.53 down(f(f(f(f(f(f(c))))))) 542.85/241.53 down(f(f(f(f(f(f(fresh_constant))))))) 542.85/241.53 down(g(g(g(g(g(g(a))))))) 542.85/241.53 down(g(g(g(g(g(g(f(x0)))))))) 542.85/241.53 down(g(g(g(g(g(g(b))))))) 542.85/241.53 down(g(g(g(g(g(g(c))))))) 542.85/241.53 down(g(g(g(g(g(g(fresh_constant))))))) 542.85/241.53 down(f(f(f(f(f(f(f(a)))))))) 542.85/241.53 down(f(f(f(f(f(f(f(b)))))))) 542.85/241.53 down(f(f(f(f(f(f(f(g(x0))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(c)))))))) 542.85/241.53 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.53 down(g(g(g(g(g(g(g(a)))))))) 542.85/241.53 down(g(g(g(g(g(g(g(f(x0))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(b)))))))) 542.85/241.53 down(g(g(g(g(g(g(g(c)))))))) 542.85/241.53 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(a))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(b))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(c))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(a))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(b))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(c))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.53 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.53 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.53 f_flat(up(x0)) 542.85/241.53 g_flat(up(x0)) 542.85/241.53 542.85/241.53 We have to consider all minimal (P,Q,R)-chains. 542.85/241.53 ---------------------------------------- 542.85/241.53 542.85/241.53 (359) TransformationProof (EQUIVALENT) 542.85/241.53 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.85/241.53 542.85/241.53 (TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))),TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 542.85/241.53 542.85/241.53 542.85/241.53 ---------------------------------------- 542.85/241.53 542.85/241.53 (360) 542.85/241.53 Obligation: 542.85/241.53 Q DP problem: 542.85/241.53 The TRS P consists of the following rules: 542.85/241.53 542.85/241.53 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.85/241.53 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.85/241.53 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.85/241.53 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.85/241.53 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.85/241.53 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.85/241.53 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.85/241.53 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.85/241.53 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.85/241.53 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.85/241.53 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.85/241.53 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.85/241.53 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.85/241.53 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.85/241.53 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.85/241.53 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.85/241.53 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.85/241.53 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.85/241.53 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.85/241.53 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.85/241.53 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.85/241.53 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.85/241.53 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.85/241.53 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.85/241.53 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.85/241.53 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.85/241.53 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.85/241.53 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.85/241.53 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.85/241.53 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.85/241.54 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.85/241.54 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.85/241.54 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.85/241.54 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.85/241.54 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.85/241.54 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.85/241.54 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.85/241.54 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.85/241.54 542.85/241.54 The TRS R consists of the following rules: 542.85/241.54 542.85/241.54 down(a) -> up(f(a)) 542.85/241.54 down(b) -> up(g(b)) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.85/241.54 down(f(a)) -> f_flat(down(a)) 542.85/241.54 down(f(b)) -> f_flat(down(b)) 542.85/241.54 down(f(g(y4))) -> f_flat(down(g(y4))) 542.85/241.54 down(f(c)) -> f_flat(down(c)) 542.85/241.54 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.85/241.54 down(g(a)) -> g_flat(down(a)) 542.85/241.54 down(g(f(y6))) -> g_flat(down(f(y6))) 542.85/241.54 down(g(b)) -> g_flat(down(b)) 542.85/241.54 down(g(c)) -> g_flat(down(c)) 542.85/241.54 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.85/241.54 down(f(f(a))) -> f_flat(down(f(a))) 542.85/241.54 down(f(f(b))) -> f_flat(down(f(b))) 542.85/241.54 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.85/241.54 down(f(f(c))) -> f_flat(down(f(c))) 542.85/241.54 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.85/241.54 down(g(g(a))) -> g_flat(down(g(a))) 542.85/241.54 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.85/241.54 down(g(g(b))) -> g_flat(down(g(b))) 542.85/241.54 down(g(g(c))) -> g_flat(down(g(c))) 542.85/241.54 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.85/241.54 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.85/241.54 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.85/241.54 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.85/241.54 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.85/241.54 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.85/241.54 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.85/241.54 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.85/241.54 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.85/241.54 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.85/241.54 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.85/241.54 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.85/241.54 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.85/241.54 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.85/241.54 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.85/241.54 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.85/241.54 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.85/241.54 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.85/241.54 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.85/241.54 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.85/241.54 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.85/241.54 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.85/241.54 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.85/241.54 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.85/241.54 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.85/241.54 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.85/241.54 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.85/241.54 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.85/241.54 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.85/241.54 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.85/241.54 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.85/241.54 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.85/241.54 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.85/241.54 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.85/241.54 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.85/241.54 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.85/241.54 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.85/241.54 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.85/241.54 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.85/241.54 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.85/241.54 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.85/241.54 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 g_flat(up(x_1)) -> up(g(x_1)) 542.85/241.54 f_flat(up(x_1)) -> up(f(x_1)) 542.85/241.54 542.85/241.54 The set Q consists of the following terms: 542.85/241.54 542.85/241.54 down(a) 542.85/241.54 down(b) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.85/241.54 down(f(a)) 542.85/241.54 down(f(b)) 542.85/241.54 down(f(g(x0))) 542.85/241.54 down(f(c)) 542.85/241.54 down(f(fresh_constant)) 542.85/241.54 down(g(a)) 542.85/241.54 down(g(f(x0))) 542.85/241.54 down(g(b)) 542.85/241.54 down(g(c)) 542.85/241.54 down(g(fresh_constant)) 542.85/241.54 down(f(f(a))) 542.85/241.54 down(f(f(b))) 542.85/241.54 down(f(f(g(x0)))) 542.85/241.54 down(f(f(c))) 542.85/241.54 down(f(f(fresh_constant))) 542.85/241.54 down(g(g(a))) 542.85/241.54 down(g(g(f(x0)))) 542.85/241.54 down(g(g(b))) 542.85/241.54 down(g(g(c))) 542.85/241.54 down(g(g(fresh_constant))) 542.85/241.54 down(f(f(f(a)))) 542.85/241.54 down(f(f(f(b)))) 542.85/241.54 down(f(f(f(g(x0))))) 542.85/241.54 down(f(f(f(c)))) 542.85/241.54 down(f(f(f(fresh_constant)))) 542.85/241.54 down(g(g(g(a)))) 542.85/241.54 down(g(g(g(f(x0))))) 542.85/241.54 down(g(g(g(b)))) 542.85/241.54 down(g(g(g(c)))) 542.85/241.54 down(g(g(g(fresh_constant)))) 542.85/241.54 down(f(f(f(f(a))))) 542.85/241.54 down(f(f(f(f(b))))) 542.85/241.54 down(f(f(f(f(g(x0)))))) 542.85/241.54 down(f(f(f(f(c))))) 542.85/241.54 down(f(f(f(f(fresh_constant))))) 542.85/241.54 down(g(g(g(g(a))))) 542.85/241.54 down(g(g(g(g(f(x0)))))) 542.85/241.54 down(g(g(g(g(b))))) 542.85/241.54 down(g(g(g(g(c))))) 542.85/241.54 down(g(g(g(g(fresh_constant))))) 542.85/241.54 down(f(f(f(f(f(a)))))) 542.85/241.54 down(f(f(f(f(f(b)))))) 542.85/241.54 down(f(f(f(f(f(g(x0))))))) 542.85/241.54 down(f(f(f(f(f(c)))))) 542.85/241.54 down(f(f(f(f(f(fresh_constant)))))) 542.85/241.54 down(g(g(g(g(g(a)))))) 542.85/241.54 down(g(g(g(g(g(f(x0))))))) 542.85/241.54 down(g(g(g(g(g(b)))))) 542.85/241.54 down(g(g(g(g(g(c)))))) 542.85/241.54 down(g(g(g(g(g(fresh_constant)))))) 542.85/241.54 down(f(f(f(f(f(f(a))))))) 542.85/241.54 down(f(f(f(f(f(f(b))))))) 542.85/241.54 down(f(f(f(f(f(f(g(x0)))))))) 542.85/241.54 down(f(f(f(f(f(f(c))))))) 542.85/241.54 down(f(f(f(f(f(f(fresh_constant))))))) 542.85/241.54 down(g(g(g(g(g(g(a))))))) 542.85/241.54 down(g(g(g(g(g(g(f(x0)))))))) 542.85/241.54 down(g(g(g(g(g(g(b))))))) 542.85/241.54 down(g(g(g(g(g(g(c))))))) 542.85/241.54 down(g(g(g(g(g(g(fresh_constant))))))) 542.85/241.54 down(f(f(f(f(f(f(f(a)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(b)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(g(x0))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(c)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(a)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(f(x0))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(b)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(c)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(a))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(b))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(c))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(a))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(b))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(c))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 f_flat(up(x0)) 542.85/241.54 g_flat(up(x0)) 542.85/241.54 542.85/241.54 We have to consider all minimal (P,Q,R)-chains. 542.85/241.54 ---------------------------------------- 542.85/241.54 542.85/241.54 (361) TransformationProof (EQUIVALENT) 542.85/241.54 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(a))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.85/241.54 542.85/241.54 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 542.85/241.54 542.85/241.54 542.85/241.54 ---------------------------------------- 542.85/241.54 542.85/241.54 (362) 542.85/241.54 Obligation: 542.85/241.54 Q DP problem: 542.85/241.54 The TRS P consists of the following rules: 542.85/241.54 542.85/241.54 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.85/241.54 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.85/241.54 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.85/241.54 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.85/241.54 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.85/241.54 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.85/241.54 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.85/241.54 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.85/241.54 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.85/241.54 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.85/241.54 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.85/241.54 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.85/241.54 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.85/241.54 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.85/241.54 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.85/241.54 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.85/241.54 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.85/241.54 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.85/241.54 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.85/241.54 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.85/241.54 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.85/241.54 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.85/241.54 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.85/241.54 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.85/241.54 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.85/241.54 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.85/241.54 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.85/241.54 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.85/241.54 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.85/241.54 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.85/241.54 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.85/241.54 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.85/241.54 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.85/241.54 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.85/241.54 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.85/241.54 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.85/241.54 542.85/241.54 The TRS R consists of the following rules: 542.85/241.54 542.85/241.54 down(a) -> up(f(a)) 542.85/241.54 down(b) -> up(g(b)) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.85/241.54 down(f(a)) -> f_flat(down(a)) 542.85/241.54 down(f(b)) -> f_flat(down(b)) 542.85/241.54 down(f(g(y4))) -> f_flat(down(g(y4))) 542.85/241.54 down(f(c)) -> f_flat(down(c)) 542.85/241.54 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.85/241.54 down(g(a)) -> g_flat(down(a)) 542.85/241.54 down(g(f(y6))) -> g_flat(down(f(y6))) 542.85/241.54 down(g(b)) -> g_flat(down(b)) 542.85/241.54 down(g(c)) -> g_flat(down(c)) 542.85/241.54 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.85/241.54 down(f(f(a))) -> f_flat(down(f(a))) 542.85/241.54 down(f(f(b))) -> f_flat(down(f(b))) 542.85/241.54 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.85/241.54 down(f(f(c))) -> f_flat(down(f(c))) 542.85/241.54 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.85/241.54 down(g(g(a))) -> g_flat(down(g(a))) 542.85/241.54 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.85/241.54 down(g(g(b))) -> g_flat(down(g(b))) 542.85/241.54 down(g(g(c))) -> g_flat(down(g(c))) 542.85/241.54 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.85/241.54 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.85/241.54 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.85/241.54 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.85/241.54 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.85/241.54 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.85/241.54 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.85/241.54 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.85/241.54 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.85/241.54 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.85/241.54 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.85/241.54 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.85/241.54 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.85/241.54 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.85/241.54 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.85/241.54 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.85/241.54 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.85/241.54 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.85/241.54 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.85/241.54 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.85/241.54 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.85/241.54 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.85/241.54 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.85/241.54 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.85/241.54 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.85/241.54 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.85/241.54 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.85/241.54 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.85/241.54 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.85/241.54 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.85/241.54 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.85/241.54 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.85/241.54 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.85/241.54 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.85/241.54 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.85/241.54 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.85/241.54 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.85/241.54 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.85/241.54 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.85/241.54 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.85/241.54 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.85/241.54 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 g_flat(up(x_1)) -> up(g(x_1)) 542.85/241.54 f_flat(up(x_1)) -> up(f(x_1)) 542.85/241.54 542.85/241.54 The set Q consists of the following terms: 542.85/241.54 542.85/241.54 down(a) 542.85/241.54 down(b) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.85/241.54 down(f(a)) 542.85/241.54 down(f(b)) 542.85/241.54 down(f(g(x0))) 542.85/241.54 down(f(c)) 542.85/241.54 down(f(fresh_constant)) 542.85/241.54 down(g(a)) 542.85/241.54 down(g(f(x0))) 542.85/241.54 down(g(b)) 542.85/241.54 down(g(c)) 542.85/241.54 down(g(fresh_constant)) 542.85/241.54 down(f(f(a))) 542.85/241.54 down(f(f(b))) 542.85/241.54 down(f(f(g(x0)))) 542.85/241.54 down(f(f(c))) 542.85/241.54 down(f(f(fresh_constant))) 542.85/241.54 down(g(g(a))) 542.85/241.54 down(g(g(f(x0)))) 542.85/241.54 down(g(g(b))) 542.85/241.54 down(g(g(c))) 542.85/241.54 down(g(g(fresh_constant))) 542.85/241.54 down(f(f(f(a)))) 542.85/241.54 down(f(f(f(b)))) 542.85/241.54 down(f(f(f(g(x0))))) 542.85/241.54 down(f(f(f(c)))) 542.85/241.54 down(f(f(f(fresh_constant)))) 542.85/241.54 down(g(g(g(a)))) 542.85/241.54 down(g(g(g(f(x0))))) 542.85/241.54 down(g(g(g(b)))) 542.85/241.54 down(g(g(g(c)))) 542.85/241.54 down(g(g(g(fresh_constant)))) 542.85/241.54 down(f(f(f(f(a))))) 542.85/241.54 down(f(f(f(f(b))))) 542.85/241.54 down(f(f(f(f(g(x0)))))) 542.85/241.54 down(f(f(f(f(c))))) 542.85/241.54 down(f(f(f(f(fresh_constant))))) 542.85/241.54 down(g(g(g(g(a))))) 542.85/241.54 down(g(g(g(g(f(x0)))))) 542.85/241.54 down(g(g(g(g(b))))) 542.85/241.54 down(g(g(g(g(c))))) 542.85/241.54 down(g(g(g(g(fresh_constant))))) 542.85/241.54 down(f(f(f(f(f(a)))))) 542.85/241.54 down(f(f(f(f(f(b)))))) 542.85/241.54 down(f(f(f(f(f(g(x0))))))) 542.85/241.54 down(f(f(f(f(f(c)))))) 542.85/241.54 down(f(f(f(f(f(fresh_constant)))))) 542.85/241.54 down(g(g(g(g(g(a)))))) 542.85/241.54 down(g(g(g(g(g(f(x0))))))) 542.85/241.54 down(g(g(g(g(g(b)))))) 542.85/241.54 down(g(g(g(g(g(c)))))) 542.85/241.54 down(g(g(g(g(g(fresh_constant)))))) 542.85/241.54 down(f(f(f(f(f(f(a))))))) 542.85/241.54 down(f(f(f(f(f(f(b))))))) 542.85/241.54 down(f(f(f(f(f(f(g(x0)))))))) 542.85/241.54 down(f(f(f(f(f(f(c))))))) 542.85/241.54 down(f(f(f(f(f(f(fresh_constant))))))) 542.85/241.54 down(g(g(g(g(g(g(a))))))) 542.85/241.54 down(g(g(g(g(g(g(f(x0)))))))) 542.85/241.54 down(g(g(g(g(g(g(b))))))) 542.85/241.54 down(g(g(g(g(g(g(c))))))) 542.85/241.54 down(g(g(g(g(g(g(fresh_constant))))))) 542.85/241.54 down(f(f(f(f(f(f(f(a)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(b)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(g(x0))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(c)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(a)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(f(x0))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(b)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(c)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(a))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(b))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(c))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(a))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(b))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(c))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 f_flat(up(x0)) 542.85/241.54 g_flat(up(x0)) 542.85/241.54 542.85/241.54 We have to consider all minimal (P,Q,R)-chains. 542.85/241.54 ---------------------------------------- 542.85/241.54 542.85/241.54 (363) TransformationProof (EQUIVALENT) 542.85/241.54 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.85/241.54 542.85/241.54 (TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))),TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 542.85/241.54 542.85/241.54 542.85/241.54 ---------------------------------------- 542.85/241.54 542.85/241.54 (364) 542.85/241.54 Obligation: 542.85/241.54 Q DP problem: 542.85/241.54 The TRS P consists of the following rules: 542.85/241.54 542.85/241.54 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.85/241.54 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.85/241.54 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.85/241.54 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.85/241.54 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.85/241.54 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.85/241.54 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.85/241.54 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.85/241.54 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.85/241.54 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.85/241.54 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.85/241.54 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.85/241.54 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.85/241.54 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.85/241.54 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.85/241.54 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.85/241.54 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.85/241.54 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.85/241.54 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.85/241.54 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.85/241.54 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.85/241.54 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.85/241.54 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.85/241.54 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.85/241.54 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.85/241.54 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.85/241.54 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.85/241.54 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.85/241.54 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.85/241.54 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.85/241.54 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.85/241.54 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.85/241.54 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.85/241.54 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.85/241.54 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.85/241.54 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.85/241.54 542.85/241.54 The TRS R consists of the following rules: 542.85/241.54 542.85/241.54 down(a) -> up(f(a)) 542.85/241.54 down(b) -> up(g(b)) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.85/241.54 down(f(a)) -> f_flat(down(a)) 542.85/241.54 down(f(b)) -> f_flat(down(b)) 542.85/241.54 down(f(g(y4))) -> f_flat(down(g(y4))) 542.85/241.54 down(f(c)) -> f_flat(down(c)) 542.85/241.54 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.85/241.54 down(g(a)) -> g_flat(down(a)) 542.85/241.54 down(g(f(y6))) -> g_flat(down(f(y6))) 542.85/241.54 down(g(b)) -> g_flat(down(b)) 542.85/241.54 down(g(c)) -> g_flat(down(c)) 542.85/241.54 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.85/241.54 down(f(f(a))) -> f_flat(down(f(a))) 542.85/241.54 down(f(f(b))) -> f_flat(down(f(b))) 542.85/241.54 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.85/241.54 down(f(f(c))) -> f_flat(down(f(c))) 542.85/241.54 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.85/241.54 down(g(g(a))) -> g_flat(down(g(a))) 542.85/241.54 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.85/241.54 down(g(g(b))) -> g_flat(down(g(b))) 542.85/241.54 down(g(g(c))) -> g_flat(down(g(c))) 542.85/241.54 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.85/241.54 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.85/241.54 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.85/241.54 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.85/241.54 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.85/241.54 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.85/241.54 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.85/241.54 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.85/241.54 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.85/241.54 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.85/241.54 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.85/241.54 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.85/241.54 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.85/241.54 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.85/241.54 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.85/241.54 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.85/241.54 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.85/241.54 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.85/241.54 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.85/241.54 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.85/241.54 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.85/241.54 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.85/241.54 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.85/241.54 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.85/241.54 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.85/241.54 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.85/241.54 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.85/241.54 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.85/241.54 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.85/241.54 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.85/241.54 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.85/241.54 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.85/241.54 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.85/241.54 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.85/241.54 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.85/241.54 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.85/241.54 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.85/241.54 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.85/241.54 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.85/241.54 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.85/241.54 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.85/241.54 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 g_flat(up(x_1)) -> up(g(x_1)) 542.85/241.54 f_flat(up(x_1)) -> up(f(x_1)) 542.85/241.54 542.85/241.54 The set Q consists of the following terms: 542.85/241.54 542.85/241.54 down(a) 542.85/241.54 down(b) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.85/241.54 down(f(a)) 542.85/241.54 down(f(b)) 542.85/241.54 down(f(g(x0))) 542.85/241.54 down(f(c)) 542.85/241.54 down(f(fresh_constant)) 542.85/241.54 down(g(a)) 542.85/241.54 down(g(f(x0))) 542.85/241.54 down(g(b)) 542.85/241.54 down(g(c)) 542.85/241.54 down(g(fresh_constant)) 542.85/241.54 down(f(f(a))) 542.85/241.54 down(f(f(b))) 542.85/241.54 down(f(f(g(x0)))) 542.85/241.54 down(f(f(c))) 542.85/241.54 down(f(f(fresh_constant))) 542.85/241.54 down(g(g(a))) 542.85/241.54 down(g(g(f(x0)))) 542.85/241.54 down(g(g(b))) 542.85/241.54 down(g(g(c))) 542.85/241.54 down(g(g(fresh_constant))) 542.85/241.54 down(f(f(f(a)))) 542.85/241.54 down(f(f(f(b)))) 542.85/241.54 down(f(f(f(g(x0))))) 542.85/241.54 down(f(f(f(c)))) 542.85/241.54 down(f(f(f(fresh_constant)))) 542.85/241.54 down(g(g(g(a)))) 542.85/241.54 down(g(g(g(f(x0))))) 542.85/241.54 down(g(g(g(b)))) 542.85/241.54 down(g(g(g(c)))) 542.85/241.54 down(g(g(g(fresh_constant)))) 542.85/241.54 down(f(f(f(f(a))))) 542.85/241.54 down(f(f(f(f(b))))) 542.85/241.54 down(f(f(f(f(g(x0)))))) 542.85/241.54 down(f(f(f(f(c))))) 542.85/241.54 down(f(f(f(f(fresh_constant))))) 542.85/241.54 down(g(g(g(g(a))))) 542.85/241.54 down(g(g(g(g(f(x0)))))) 542.85/241.54 down(g(g(g(g(b))))) 542.85/241.54 down(g(g(g(g(c))))) 542.85/241.54 down(g(g(g(g(fresh_constant))))) 542.85/241.54 down(f(f(f(f(f(a)))))) 542.85/241.54 down(f(f(f(f(f(b)))))) 542.85/241.54 down(f(f(f(f(f(g(x0))))))) 542.85/241.54 down(f(f(f(f(f(c)))))) 542.85/241.54 down(f(f(f(f(f(fresh_constant)))))) 542.85/241.54 down(g(g(g(g(g(a)))))) 542.85/241.54 down(g(g(g(g(g(f(x0))))))) 542.85/241.54 down(g(g(g(g(g(b)))))) 542.85/241.54 down(g(g(g(g(g(c)))))) 542.85/241.54 down(g(g(g(g(g(fresh_constant)))))) 542.85/241.54 down(f(f(f(f(f(f(a))))))) 542.85/241.54 down(f(f(f(f(f(f(b))))))) 542.85/241.54 down(f(f(f(f(f(f(g(x0)))))))) 542.85/241.54 down(f(f(f(f(f(f(c))))))) 542.85/241.54 down(f(f(f(f(f(f(fresh_constant))))))) 542.85/241.54 down(g(g(g(g(g(g(a))))))) 542.85/241.54 down(g(g(g(g(g(g(f(x0)))))))) 542.85/241.54 down(g(g(g(g(g(g(b))))))) 542.85/241.54 down(g(g(g(g(g(g(c))))))) 542.85/241.54 down(g(g(g(g(g(g(fresh_constant))))))) 542.85/241.54 down(f(f(f(f(f(f(f(a)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(b)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(g(x0))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(c)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(a)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(f(x0))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(b)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(c)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(a))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(b))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(c))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(a))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(b))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(c))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 f_flat(up(x0)) 542.85/241.54 g_flat(up(x0)) 542.85/241.54 542.85/241.54 We have to consider all minimal (P,Q,R)-chains. 542.85/241.54 ---------------------------------------- 542.85/241.54 542.85/241.54 (365) TransformationProof (EQUIVALENT) 542.85/241.54 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(c))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.85/241.54 542.85/241.54 (TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))),TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 542.85/241.54 542.85/241.54 542.85/241.54 ---------------------------------------- 542.85/241.54 542.85/241.54 (366) 542.85/241.54 Obligation: 542.85/241.54 Q DP problem: 542.85/241.54 The TRS P consists of the following rules: 542.85/241.54 542.85/241.54 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.85/241.54 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.85/241.54 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.85/241.54 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.85/241.54 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.85/241.54 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.85/241.54 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.85/241.54 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.85/241.54 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.85/241.54 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.85/241.54 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.85/241.54 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.85/241.54 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.85/241.54 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.85/241.54 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.85/241.54 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.85/241.54 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.85/241.54 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.85/241.54 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.85/241.54 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.85/241.54 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.85/241.54 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.85/241.54 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.85/241.54 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.85/241.54 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.85/241.54 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.85/241.54 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.85/241.54 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.85/241.54 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.85/241.54 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.85/241.54 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.85/241.54 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.85/241.54 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.85/241.54 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.85/241.54 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.85/241.54 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.85/241.54 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.85/241.54 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.85/241.54 542.85/241.54 The TRS R consists of the following rules: 542.85/241.54 542.85/241.54 down(a) -> up(f(a)) 542.85/241.54 down(b) -> up(g(b)) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.85/241.54 down(f(a)) -> f_flat(down(a)) 542.85/241.54 down(f(b)) -> f_flat(down(b)) 542.85/241.54 down(f(g(y4))) -> f_flat(down(g(y4))) 542.85/241.54 down(f(c)) -> f_flat(down(c)) 542.85/241.54 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.85/241.54 down(g(a)) -> g_flat(down(a)) 542.85/241.54 down(g(f(y6))) -> g_flat(down(f(y6))) 542.85/241.54 down(g(b)) -> g_flat(down(b)) 542.85/241.54 down(g(c)) -> g_flat(down(c)) 542.85/241.54 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.85/241.54 down(f(f(a))) -> f_flat(down(f(a))) 542.85/241.54 down(f(f(b))) -> f_flat(down(f(b))) 542.85/241.54 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.85/241.54 down(f(f(c))) -> f_flat(down(f(c))) 542.85/241.54 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.85/241.54 down(g(g(a))) -> g_flat(down(g(a))) 542.85/241.54 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.85/241.54 down(g(g(b))) -> g_flat(down(g(b))) 542.85/241.54 down(g(g(c))) -> g_flat(down(g(c))) 542.85/241.54 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.85/241.54 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.85/241.54 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.85/241.54 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.85/241.54 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.85/241.54 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.85/241.54 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.85/241.54 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.85/241.54 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.85/241.54 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.85/241.54 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.85/241.54 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.85/241.54 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.85/241.54 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.85/241.54 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.85/241.54 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.85/241.54 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.85/241.54 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.85/241.54 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.85/241.54 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.85/241.54 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.85/241.54 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.85/241.54 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.85/241.54 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.85/241.54 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.85/241.54 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.85/241.54 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.85/241.54 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.85/241.54 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.85/241.54 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.85/241.54 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.85/241.54 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.85/241.54 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.85/241.54 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.85/241.54 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.85/241.54 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.85/241.54 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.85/241.54 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.85/241.54 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.85/241.54 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.85/241.54 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.85/241.54 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.85/241.54 g_flat(up(x_1)) -> up(g(x_1)) 542.85/241.54 f_flat(up(x_1)) -> up(f(x_1)) 542.85/241.54 542.85/241.54 The set Q consists of the following terms: 542.85/241.54 542.85/241.54 down(a) 542.85/241.54 down(b) 542.85/241.54 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.85/241.54 down(f(a)) 542.85/241.54 down(f(b)) 542.85/241.54 down(f(g(x0))) 542.85/241.54 down(f(c)) 542.85/241.54 down(f(fresh_constant)) 542.85/241.54 down(g(a)) 542.85/241.54 down(g(f(x0))) 542.85/241.54 down(g(b)) 542.85/241.54 down(g(c)) 542.85/241.54 down(g(fresh_constant)) 542.85/241.54 down(f(f(a))) 542.85/241.54 down(f(f(b))) 542.85/241.54 down(f(f(g(x0)))) 542.85/241.54 down(f(f(c))) 542.85/241.54 down(f(f(fresh_constant))) 542.85/241.54 down(g(g(a))) 542.85/241.54 down(g(g(f(x0)))) 542.85/241.54 down(g(g(b))) 542.85/241.54 down(g(g(c))) 542.85/241.54 down(g(g(fresh_constant))) 542.85/241.54 down(f(f(f(a)))) 542.85/241.54 down(f(f(f(b)))) 542.85/241.54 down(f(f(f(g(x0))))) 542.85/241.54 down(f(f(f(c)))) 542.85/241.54 down(f(f(f(fresh_constant)))) 542.85/241.54 down(g(g(g(a)))) 542.85/241.54 down(g(g(g(f(x0))))) 542.85/241.54 down(g(g(g(b)))) 542.85/241.54 down(g(g(g(c)))) 542.85/241.54 down(g(g(g(fresh_constant)))) 542.85/241.54 down(f(f(f(f(a))))) 542.85/241.54 down(f(f(f(f(b))))) 542.85/241.54 down(f(f(f(f(g(x0)))))) 542.85/241.54 down(f(f(f(f(c))))) 542.85/241.54 down(f(f(f(f(fresh_constant))))) 542.85/241.54 down(g(g(g(g(a))))) 542.85/241.54 down(g(g(g(g(f(x0)))))) 542.85/241.54 down(g(g(g(g(b))))) 542.85/241.54 down(g(g(g(g(c))))) 542.85/241.54 down(g(g(g(g(fresh_constant))))) 542.85/241.54 down(f(f(f(f(f(a)))))) 542.85/241.54 down(f(f(f(f(f(b)))))) 542.85/241.54 down(f(f(f(f(f(g(x0))))))) 542.85/241.54 down(f(f(f(f(f(c)))))) 542.85/241.54 down(f(f(f(f(f(fresh_constant)))))) 542.85/241.54 down(g(g(g(g(g(a)))))) 542.85/241.54 down(g(g(g(g(g(f(x0))))))) 542.85/241.54 down(g(g(g(g(g(b)))))) 542.85/241.54 down(g(g(g(g(g(c)))))) 542.85/241.54 down(g(g(g(g(g(fresh_constant)))))) 542.85/241.54 down(f(f(f(f(f(f(a))))))) 542.85/241.54 down(f(f(f(f(f(f(b))))))) 542.85/241.54 down(f(f(f(f(f(f(g(x0)))))))) 542.85/241.54 down(f(f(f(f(f(f(c))))))) 542.85/241.54 down(f(f(f(f(f(f(fresh_constant))))))) 542.85/241.54 down(g(g(g(g(g(g(a))))))) 542.85/241.54 down(g(g(g(g(g(g(f(x0)))))))) 542.85/241.54 down(g(g(g(g(g(g(b))))))) 542.85/241.54 down(g(g(g(g(g(g(c))))))) 542.85/241.54 down(g(g(g(g(g(g(fresh_constant))))))) 542.85/241.54 down(f(f(f(f(f(f(f(a)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(b)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(g(x0))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(c)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(a)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(f(x0))))))))) 542.85/241.54 down(g(g(g(g(g(g(g(b)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(c)))))))) 542.85/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(a))))))))) 542.85/241.54 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.54 f_flat(up(x0)) 542.88/241.54 g_flat(up(x0)) 542.88/241.54 542.88/241.54 We have to consider all minimal (P,Q,R)-chains. 542.88/241.54 ---------------------------------------- 542.88/241.54 542.88/241.54 (367) TransformationProof (EQUIVALENT) 542.88/241.54 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.54 542.88/241.54 (TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))),TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 542.88/241.54 542.88/241.54 542.88/241.54 ---------------------------------------- 542.88/241.54 542.88/241.54 (368) 542.88/241.54 Obligation: 542.88/241.54 Q DP problem: 542.88/241.54 The TRS P consists of the following rules: 542.88/241.54 542.88/241.54 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.54 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.54 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.54 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.54 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.54 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.54 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.54 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.54 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.54 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.54 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.54 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.54 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.54 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.54 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.54 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.54 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.54 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.54 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.54 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.54 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.54 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.54 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.54 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.54 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.54 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.54 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.54 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.54 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.54 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.54 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.54 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.54 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.54 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.54 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.54 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.54 542.88/241.54 The TRS R consists of the following rules: 542.88/241.54 542.88/241.54 down(a) -> up(f(a)) 542.88/241.54 down(b) -> up(g(b)) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.54 down(f(a)) -> f_flat(down(a)) 542.88/241.54 down(f(b)) -> f_flat(down(b)) 542.88/241.54 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.54 down(f(c)) -> f_flat(down(c)) 542.88/241.54 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.54 down(g(a)) -> g_flat(down(a)) 542.88/241.54 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.54 down(g(b)) -> g_flat(down(b)) 542.88/241.54 down(g(c)) -> g_flat(down(c)) 542.88/241.54 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.54 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.54 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.54 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.54 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.54 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.54 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.54 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.54 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.54 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.54 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.54 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.54 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.54 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.54 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.54 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.54 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.54 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.54 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.54 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.54 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.54 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.54 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.54 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.54 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.54 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.54 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.54 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.54 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.54 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.54 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.54 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.54 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.54 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.54 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.54 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.54 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.54 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.54 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.54 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.54 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.54 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.54 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.54 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.54 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.54 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.54 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.54 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.54 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.54 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.54 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.54 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.54 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.54 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.54 542.88/241.54 The set Q consists of the following terms: 542.88/241.54 542.88/241.54 down(a) 542.88/241.54 down(b) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.54 down(f(a)) 542.88/241.54 down(f(b)) 542.88/241.54 down(f(g(x0))) 542.88/241.54 down(f(c)) 542.88/241.54 down(f(fresh_constant)) 542.88/241.54 down(g(a)) 542.88/241.54 down(g(f(x0))) 542.88/241.54 down(g(b)) 542.88/241.54 down(g(c)) 542.88/241.54 down(g(fresh_constant)) 542.88/241.54 down(f(f(a))) 542.88/241.54 down(f(f(b))) 542.88/241.54 down(f(f(g(x0)))) 542.88/241.54 down(f(f(c))) 542.88/241.54 down(f(f(fresh_constant))) 542.88/241.54 down(g(g(a))) 542.88/241.54 down(g(g(f(x0)))) 542.88/241.54 down(g(g(b))) 542.88/241.54 down(g(g(c))) 542.88/241.54 down(g(g(fresh_constant))) 542.88/241.54 down(f(f(f(a)))) 542.88/241.54 down(f(f(f(b)))) 542.88/241.54 down(f(f(f(g(x0))))) 542.88/241.54 down(f(f(f(c)))) 542.88/241.54 down(f(f(f(fresh_constant)))) 542.88/241.54 down(g(g(g(a)))) 542.88/241.54 down(g(g(g(f(x0))))) 542.88/241.54 down(g(g(g(b)))) 542.88/241.54 down(g(g(g(c)))) 542.88/241.54 down(g(g(g(fresh_constant)))) 542.88/241.54 down(f(f(f(f(a))))) 542.88/241.54 down(f(f(f(f(b))))) 542.88/241.54 down(f(f(f(f(g(x0)))))) 542.88/241.54 down(f(f(f(f(c))))) 542.88/241.54 down(f(f(f(f(fresh_constant))))) 542.88/241.54 down(g(g(g(g(a))))) 542.88/241.54 down(g(g(g(g(f(x0)))))) 542.88/241.54 down(g(g(g(g(b))))) 542.88/241.54 down(g(g(g(g(c))))) 542.88/241.54 down(g(g(g(g(fresh_constant))))) 542.88/241.54 down(f(f(f(f(f(a)))))) 542.88/241.54 down(f(f(f(f(f(b)))))) 542.88/241.54 down(f(f(f(f(f(g(x0))))))) 542.88/241.54 down(f(f(f(f(f(c)))))) 542.88/241.54 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.54 down(g(g(g(g(g(a)))))) 542.88/241.54 down(g(g(g(g(g(f(x0))))))) 542.88/241.54 down(g(g(g(g(g(b)))))) 542.88/241.54 down(g(g(g(g(g(c)))))) 542.88/241.54 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.54 down(f(f(f(f(f(f(a))))))) 542.88/241.54 down(f(f(f(f(f(f(b))))))) 542.88/241.54 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.54 down(f(f(f(f(f(f(c))))))) 542.88/241.54 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.54 down(g(g(g(g(g(g(a))))))) 542.88/241.54 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.54 down(g(g(g(g(g(g(b))))))) 542.88/241.54 down(g(g(g(g(g(g(c))))))) 542.88/241.54 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.54 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.54 f_flat(up(x0)) 542.88/241.54 g_flat(up(x0)) 542.88/241.54 542.88/241.54 We have to consider all minimal (P,Q,R)-chains. 542.88/241.54 ---------------------------------------- 542.88/241.54 542.88/241.54 (369) TransformationProof (EQUIVALENT) 542.88/241.54 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.54 542.88/241.54 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 542.88/241.54 542.88/241.54 542.88/241.54 ---------------------------------------- 542.88/241.54 542.88/241.54 (370) 542.88/241.54 Obligation: 542.88/241.54 Q DP problem: 542.88/241.54 The TRS P consists of the following rules: 542.88/241.54 542.88/241.54 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.54 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.54 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.54 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.54 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.54 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.54 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.54 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.54 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.54 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.54 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.54 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.54 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.54 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.54 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.54 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.54 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.54 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.54 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.54 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.54 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.54 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.54 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.54 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.54 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.54 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.54 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.54 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.54 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.54 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.54 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.54 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.54 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.54 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.54 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.54 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.54 542.88/241.54 The TRS R consists of the following rules: 542.88/241.54 542.88/241.54 down(a) -> up(f(a)) 542.88/241.54 down(b) -> up(g(b)) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.54 down(f(a)) -> f_flat(down(a)) 542.88/241.54 down(f(b)) -> f_flat(down(b)) 542.88/241.54 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.54 down(f(c)) -> f_flat(down(c)) 542.88/241.54 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.54 down(g(a)) -> g_flat(down(a)) 542.88/241.54 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.54 down(g(b)) -> g_flat(down(b)) 542.88/241.54 down(g(c)) -> g_flat(down(c)) 542.88/241.54 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.54 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.54 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.54 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.54 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.54 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.54 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.54 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.54 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.54 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.54 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.54 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.54 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.54 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.54 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.54 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.54 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.54 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.54 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.54 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.54 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.54 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.54 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.54 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.54 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.54 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.54 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.54 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.54 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.54 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.54 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.54 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.54 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.54 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.54 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.54 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.54 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.54 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.54 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.54 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.54 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.54 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.54 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.54 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.54 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.54 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.54 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.54 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.54 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.54 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.54 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.54 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.54 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.54 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.54 542.88/241.54 The set Q consists of the following terms: 542.88/241.54 542.88/241.54 down(a) 542.88/241.54 down(b) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.54 down(f(a)) 542.88/241.54 down(f(b)) 542.88/241.54 down(f(g(x0))) 542.88/241.54 down(f(c)) 542.88/241.54 down(f(fresh_constant)) 542.88/241.54 down(g(a)) 542.88/241.54 down(g(f(x0))) 542.88/241.54 down(g(b)) 542.88/241.54 down(g(c)) 542.88/241.54 down(g(fresh_constant)) 542.88/241.54 down(f(f(a))) 542.88/241.54 down(f(f(b))) 542.88/241.54 down(f(f(g(x0)))) 542.88/241.54 down(f(f(c))) 542.88/241.54 down(f(f(fresh_constant))) 542.88/241.54 down(g(g(a))) 542.88/241.54 down(g(g(f(x0)))) 542.88/241.54 down(g(g(b))) 542.88/241.54 down(g(g(c))) 542.88/241.54 down(g(g(fresh_constant))) 542.88/241.54 down(f(f(f(a)))) 542.88/241.54 down(f(f(f(b)))) 542.88/241.54 down(f(f(f(g(x0))))) 542.88/241.54 down(f(f(f(c)))) 542.88/241.54 down(f(f(f(fresh_constant)))) 542.88/241.54 down(g(g(g(a)))) 542.88/241.54 down(g(g(g(f(x0))))) 542.88/241.54 down(g(g(g(b)))) 542.88/241.54 down(g(g(g(c)))) 542.88/241.54 down(g(g(g(fresh_constant)))) 542.88/241.54 down(f(f(f(f(a))))) 542.88/241.54 down(f(f(f(f(b))))) 542.88/241.54 down(f(f(f(f(g(x0)))))) 542.88/241.54 down(f(f(f(f(c))))) 542.88/241.54 down(f(f(f(f(fresh_constant))))) 542.88/241.54 down(g(g(g(g(a))))) 542.88/241.54 down(g(g(g(g(f(x0)))))) 542.88/241.54 down(g(g(g(g(b))))) 542.88/241.54 down(g(g(g(g(c))))) 542.88/241.54 down(g(g(g(g(fresh_constant))))) 542.88/241.54 down(f(f(f(f(f(a)))))) 542.88/241.54 down(f(f(f(f(f(b)))))) 542.88/241.54 down(f(f(f(f(f(g(x0))))))) 542.88/241.54 down(f(f(f(f(f(c)))))) 542.88/241.54 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.54 down(g(g(g(g(g(a)))))) 542.88/241.54 down(g(g(g(g(g(f(x0))))))) 542.88/241.54 down(g(g(g(g(g(b)))))) 542.88/241.54 down(g(g(g(g(g(c)))))) 542.88/241.54 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.54 down(f(f(f(f(f(f(a))))))) 542.88/241.54 down(f(f(f(f(f(f(b))))))) 542.88/241.54 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.54 down(f(f(f(f(f(f(c))))))) 542.88/241.54 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.54 down(g(g(g(g(g(g(a))))))) 542.88/241.54 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.54 down(g(g(g(g(g(g(b))))))) 542.88/241.54 down(g(g(g(g(g(g(c))))))) 542.88/241.54 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.54 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.54 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.54 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.54 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.54 f_flat(up(x0)) 542.88/241.54 g_flat(up(x0)) 542.88/241.54 542.88/241.54 We have to consider all minimal (P,Q,R)-chains. 542.88/241.54 ---------------------------------------- 542.88/241.54 542.88/241.54 (371) TransformationProof (EQUIVALENT) 542.88/241.54 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.54 542.88/241.54 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 542.88/241.54 542.88/241.54 542.88/241.54 ---------------------------------------- 542.88/241.54 542.88/241.54 (372) 542.88/241.54 Obligation: 542.88/241.54 Q DP problem: 542.88/241.54 The TRS P consists of the following rules: 542.88/241.54 542.88/241.54 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.54 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.54 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.54 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.54 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.88/241.54 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.55 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.55 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.55 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.55 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.55 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.55 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.55 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.55 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.55 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.55 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.55 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.55 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.55 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.55 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.55 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.55 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.55 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.55 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.55 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.55 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.55 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.55 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.55 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.55 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.55 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.55 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.55 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.55 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.55 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.55 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.55 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.55 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.55 542.88/241.55 The TRS R consists of the following rules: 542.88/241.55 542.88/241.55 down(a) -> up(f(a)) 542.88/241.55 down(b) -> up(g(b)) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.55 down(f(a)) -> f_flat(down(a)) 542.88/241.55 down(f(b)) -> f_flat(down(b)) 542.88/241.55 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.55 down(f(c)) -> f_flat(down(c)) 542.88/241.55 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.55 down(g(a)) -> g_flat(down(a)) 542.88/241.55 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.55 down(g(b)) -> g_flat(down(b)) 542.88/241.55 down(g(c)) -> g_flat(down(c)) 542.88/241.55 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.55 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.55 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.55 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.55 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.55 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.55 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.55 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.55 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.55 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.55 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.55 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.55 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.55 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.55 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.55 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.55 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.55 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.55 542.88/241.55 The set Q consists of the following terms: 542.88/241.55 542.88/241.55 down(a) 542.88/241.55 down(b) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.55 down(f(a)) 542.88/241.55 down(f(b)) 542.88/241.55 down(f(g(x0))) 542.88/241.55 down(f(c)) 542.88/241.55 down(f(fresh_constant)) 542.88/241.55 down(g(a)) 542.88/241.55 down(g(f(x0))) 542.88/241.55 down(g(b)) 542.88/241.55 down(g(c)) 542.88/241.55 down(g(fresh_constant)) 542.88/241.55 down(f(f(a))) 542.88/241.55 down(f(f(b))) 542.88/241.55 down(f(f(g(x0)))) 542.88/241.55 down(f(f(c))) 542.88/241.55 down(f(f(fresh_constant))) 542.88/241.55 down(g(g(a))) 542.88/241.55 down(g(g(f(x0)))) 542.88/241.55 down(g(g(b))) 542.88/241.55 down(g(g(c))) 542.88/241.55 down(g(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) 542.88/241.55 down(f(f(f(g(x0))))) 542.88/241.55 down(f(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) 542.88/241.55 down(g(g(g(f(x0))))) 542.88/241.55 down(g(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(x0)))))) 542.88/241.55 down(f(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(x0)))))) 542.88/241.55 down(g(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(x0))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(x0))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 f_flat(up(x0)) 542.88/241.55 g_flat(up(x0)) 542.88/241.55 542.88/241.55 We have to consider all minimal (P,Q,R)-chains. 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (373) TransformationProof (EQUIVALENT) 542.88/241.55 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.55 542.88/241.55 (TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))),TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 542.88/241.55 542.88/241.55 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (374) 542.88/241.55 Obligation: 542.88/241.55 Q DP problem: 542.88/241.55 The TRS P consists of the following rules: 542.88/241.55 542.88/241.55 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.55 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.55 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.55 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.55 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.55 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.55 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.55 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.55 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.55 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.55 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.55 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.55 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.55 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.55 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.55 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.55 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.55 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.55 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.55 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.55 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.55 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.55 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.55 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.55 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.55 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.55 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.55 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.55 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.55 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.55 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.55 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.55 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.55 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.55 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.55 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 542.88/241.55 The TRS R consists of the following rules: 542.88/241.55 542.88/241.55 down(a) -> up(f(a)) 542.88/241.55 down(b) -> up(g(b)) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.55 down(f(a)) -> f_flat(down(a)) 542.88/241.55 down(f(b)) -> f_flat(down(b)) 542.88/241.55 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.55 down(f(c)) -> f_flat(down(c)) 542.88/241.55 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.55 down(g(a)) -> g_flat(down(a)) 542.88/241.55 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.55 down(g(b)) -> g_flat(down(b)) 542.88/241.55 down(g(c)) -> g_flat(down(c)) 542.88/241.55 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.55 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.55 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.55 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.55 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.55 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.55 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.55 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.55 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.55 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.55 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.55 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.55 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.55 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.55 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.55 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.55 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.55 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.55 542.88/241.55 The set Q consists of the following terms: 542.88/241.55 542.88/241.55 down(a) 542.88/241.55 down(b) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.55 down(f(a)) 542.88/241.55 down(f(b)) 542.88/241.55 down(f(g(x0))) 542.88/241.55 down(f(c)) 542.88/241.55 down(f(fresh_constant)) 542.88/241.55 down(g(a)) 542.88/241.55 down(g(f(x0))) 542.88/241.55 down(g(b)) 542.88/241.55 down(g(c)) 542.88/241.55 down(g(fresh_constant)) 542.88/241.55 down(f(f(a))) 542.88/241.55 down(f(f(b))) 542.88/241.55 down(f(f(g(x0)))) 542.88/241.55 down(f(f(c))) 542.88/241.55 down(f(f(fresh_constant))) 542.88/241.55 down(g(g(a))) 542.88/241.55 down(g(g(f(x0)))) 542.88/241.55 down(g(g(b))) 542.88/241.55 down(g(g(c))) 542.88/241.55 down(g(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) 542.88/241.55 down(f(f(f(g(x0))))) 542.88/241.55 down(f(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) 542.88/241.55 down(g(g(g(f(x0))))) 542.88/241.55 down(g(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(x0)))))) 542.88/241.55 down(f(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(x0)))))) 542.88/241.55 down(g(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(x0))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(x0))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 f_flat(up(x0)) 542.88/241.55 g_flat(up(x0)) 542.88/241.55 542.88/241.55 We have to consider all minimal (P,Q,R)-chains. 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (375) TransformationProof (EQUIVALENT) 542.88/241.55 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(b))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.55 542.88/241.55 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 542.88/241.55 542.88/241.55 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (376) 542.88/241.55 Obligation: 542.88/241.55 Q DP problem: 542.88/241.55 The TRS P consists of the following rules: 542.88/241.55 542.88/241.55 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.55 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.55 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.55 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.55 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.55 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.55 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.55 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.55 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.55 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.55 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.55 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.55 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.55 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.55 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.55 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.55 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.55 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.55 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.55 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.55 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.55 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.55 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.55 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.55 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.55 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.55 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.55 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.55 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.55 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.55 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.55 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.55 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.55 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.55 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.55 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.88/241.55 542.88/241.55 The TRS R consists of the following rules: 542.88/241.55 542.88/241.55 down(a) -> up(f(a)) 542.88/241.55 down(b) -> up(g(b)) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.55 down(f(a)) -> f_flat(down(a)) 542.88/241.55 down(f(b)) -> f_flat(down(b)) 542.88/241.55 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.55 down(f(c)) -> f_flat(down(c)) 542.88/241.55 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.55 down(g(a)) -> g_flat(down(a)) 542.88/241.55 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.55 down(g(b)) -> g_flat(down(b)) 542.88/241.55 down(g(c)) -> g_flat(down(c)) 542.88/241.55 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.55 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.55 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.55 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.55 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.55 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.55 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.55 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.55 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.55 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.55 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.55 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.55 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.55 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.55 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.55 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.55 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.55 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.55 542.88/241.55 The set Q consists of the following terms: 542.88/241.55 542.88/241.55 down(a) 542.88/241.55 down(b) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.55 down(f(a)) 542.88/241.55 down(f(b)) 542.88/241.55 down(f(g(x0))) 542.88/241.55 down(f(c)) 542.88/241.55 down(f(fresh_constant)) 542.88/241.55 down(g(a)) 542.88/241.55 down(g(f(x0))) 542.88/241.55 down(g(b)) 542.88/241.55 down(g(c)) 542.88/241.55 down(g(fresh_constant)) 542.88/241.55 down(f(f(a))) 542.88/241.55 down(f(f(b))) 542.88/241.55 down(f(f(g(x0)))) 542.88/241.55 down(f(f(c))) 542.88/241.55 down(f(f(fresh_constant))) 542.88/241.55 down(g(g(a))) 542.88/241.55 down(g(g(f(x0)))) 542.88/241.55 down(g(g(b))) 542.88/241.55 down(g(g(c))) 542.88/241.55 down(g(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) 542.88/241.55 down(f(f(f(g(x0))))) 542.88/241.55 down(f(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) 542.88/241.55 down(g(g(g(f(x0))))) 542.88/241.55 down(g(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(x0)))))) 542.88/241.55 down(f(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(x0)))))) 542.88/241.55 down(g(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(x0))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(x0))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 f_flat(up(x0)) 542.88/241.55 g_flat(up(x0)) 542.88/241.55 542.88/241.55 We have to consider all minimal (P,Q,R)-chains. 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (377) TransformationProof (EQUIVALENT) 542.88/241.55 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(c))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.55 542.88/241.55 (TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))),TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 542.88/241.55 542.88/241.55 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (378) 542.88/241.55 Obligation: 542.88/241.55 Q DP problem: 542.88/241.55 The TRS P consists of the following rules: 542.88/241.55 542.88/241.55 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.55 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.55 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.55 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.55 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.55 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.55 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.55 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.55 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.55 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.55 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.55 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.55 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.55 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.55 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.55 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.55 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.55 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.55 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.55 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.55 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.55 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.55 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.55 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.55 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.55 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.55 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.55 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.55 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.55 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.55 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.55 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.55 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.55 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.55 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.55 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 542.88/241.55 542.88/241.55 The TRS R consists of the following rules: 542.88/241.55 542.88/241.55 down(a) -> up(f(a)) 542.88/241.55 down(b) -> up(g(b)) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.55 down(f(a)) -> f_flat(down(a)) 542.88/241.55 down(f(b)) -> f_flat(down(b)) 542.88/241.55 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.55 down(f(c)) -> f_flat(down(c)) 542.88/241.55 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.55 down(g(a)) -> g_flat(down(a)) 542.88/241.55 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.55 down(g(b)) -> g_flat(down(b)) 542.88/241.55 down(g(c)) -> g_flat(down(c)) 542.88/241.55 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.55 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.55 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.55 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.55 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.55 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.55 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.55 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.55 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.55 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.55 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.55 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.55 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.55 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.55 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.55 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.55 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.55 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.55 542.88/241.55 The set Q consists of the following terms: 542.88/241.55 542.88/241.55 down(a) 542.88/241.55 down(b) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.55 down(f(a)) 542.88/241.55 down(f(b)) 542.88/241.55 down(f(g(x0))) 542.88/241.55 down(f(c)) 542.88/241.55 down(f(fresh_constant)) 542.88/241.55 down(g(a)) 542.88/241.55 down(g(f(x0))) 542.88/241.55 down(g(b)) 542.88/241.55 down(g(c)) 542.88/241.55 down(g(fresh_constant)) 542.88/241.55 down(f(f(a))) 542.88/241.55 down(f(f(b))) 542.88/241.55 down(f(f(g(x0)))) 542.88/241.55 down(f(f(c))) 542.88/241.55 down(f(f(fresh_constant))) 542.88/241.55 down(g(g(a))) 542.88/241.55 down(g(g(f(x0)))) 542.88/241.55 down(g(g(b))) 542.88/241.55 down(g(g(c))) 542.88/241.55 down(g(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) 542.88/241.55 down(f(f(f(g(x0))))) 542.88/241.55 down(f(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) 542.88/241.55 down(g(g(g(f(x0))))) 542.88/241.55 down(g(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(x0)))))) 542.88/241.55 down(f(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(x0)))))) 542.88/241.55 down(g(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(x0))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(x0))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 f_flat(up(x0)) 542.88/241.55 g_flat(up(x0)) 542.88/241.55 542.88/241.55 We have to consider all minimal (P,Q,R)-chains. 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (379) TransformationProof (EQUIVALENT) 542.88/241.55 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.55 542.88/241.55 (TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))),TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 542.88/241.55 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (380) 542.88/241.55 Obligation: 542.88/241.55 Q DP problem: 542.88/241.55 The TRS P consists of the following rules: 542.88/241.55 542.88/241.55 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.55 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.55 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.55 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.55 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.55 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.55 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.55 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.55 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.55 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.55 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.55 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.55 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.55 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.55 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.55 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.55 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.55 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.55 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.55 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.55 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.55 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.55 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.55 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.55 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.55 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.55 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.55 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.55 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.55 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.55 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.55 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.55 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.55 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.55 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.55 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 542.88/241.55 542.88/241.55 The TRS R consists of the following rules: 542.88/241.55 542.88/241.55 down(a) -> up(f(a)) 542.88/241.55 down(b) -> up(g(b)) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.55 down(f(a)) -> f_flat(down(a)) 542.88/241.55 down(f(b)) -> f_flat(down(b)) 542.88/241.55 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.55 down(f(c)) -> f_flat(down(c)) 542.88/241.55 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.55 down(g(a)) -> g_flat(down(a)) 542.88/241.55 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.55 down(g(b)) -> g_flat(down(b)) 542.88/241.55 down(g(c)) -> g_flat(down(c)) 542.88/241.55 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.55 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.55 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.55 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.55 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.55 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.55 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.55 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.55 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.55 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.55 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.55 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.55 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.55 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.55 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.55 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.55 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.55 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.55 542.88/241.55 The set Q consists of the following terms: 542.88/241.55 542.88/241.55 down(a) 542.88/241.55 down(b) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.55 down(f(a)) 542.88/241.55 down(f(b)) 542.88/241.55 down(f(g(x0))) 542.88/241.55 down(f(c)) 542.88/241.55 down(f(fresh_constant)) 542.88/241.55 down(g(a)) 542.88/241.55 down(g(f(x0))) 542.88/241.55 down(g(b)) 542.88/241.55 down(g(c)) 542.88/241.55 down(g(fresh_constant)) 542.88/241.55 down(f(f(a))) 542.88/241.55 down(f(f(b))) 542.88/241.55 down(f(f(g(x0)))) 542.88/241.55 down(f(f(c))) 542.88/241.55 down(f(f(fresh_constant))) 542.88/241.55 down(g(g(a))) 542.88/241.55 down(g(g(f(x0)))) 542.88/241.55 down(g(g(b))) 542.88/241.55 down(g(g(c))) 542.88/241.55 down(g(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) 542.88/241.55 down(f(f(f(g(x0))))) 542.88/241.55 down(f(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) 542.88/241.55 down(g(g(g(f(x0))))) 542.88/241.55 down(g(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(x0)))))) 542.88/241.55 down(f(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(x0)))))) 542.88/241.55 down(g(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(x0))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(x0))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 f_flat(up(x0)) 542.88/241.55 g_flat(up(x0)) 542.88/241.55 542.88/241.55 We have to consider all minimal (P,Q,R)-chains. 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (381) TransformationProof (EQUIVALENT) 542.88/241.55 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.55 542.88/241.55 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 542.88/241.55 542.88/241.55 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (382) 542.88/241.55 Obligation: 542.88/241.55 Q DP problem: 542.88/241.55 The TRS P consists of the following rules: 542.88/241.55 542.88/241.55 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.55 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.55 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.55 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.55 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.55 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.55 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.55 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.55 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.55 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.55 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.55 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.55 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.55 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.55 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.55 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.55 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.55 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.55 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.55 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.55 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.55 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.55 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.55 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.55 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.55 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.55 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.55 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.55 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.55 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.55 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.55 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.55 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.55 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.55 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.55 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 542.88/241.55 542.88/241.55 The TRS R consists of the following rules: 542.88/241.55 542.88/241.55 down(a) -> up(f(a)) 542.88/241.55 down(b) -> up(g(b)) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.55 down(f(a)) -> f_flat(down(a)) 542.88/241.55 down(f(b)) -> f_flat(down(b)) 542.88/241.55 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.55 down(f(c)) -> f_flat(down(c)) 542.88/241.55 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.55 down(g(a)) -> g_flat(down(a)) 542.88/241.55 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.55 down(g(b)) -> g_flat(down(b)) 542.88/241.55 down(g(c)) -> g_flat(down(c)) 542.88/241.55 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.55 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.55 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.55 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.55 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.55 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.55 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.55 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.55 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.55 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.55 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.55 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.55 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.55 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.55 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.55 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.55 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.55 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.55 542.88/241.55 The set Q consists of the following terms: 542.88/241.55 542.88/241.55 down(a) 542.88/241.55 down(b) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.55 down(f(a)) 542.88/241.55 down(f(b)) 542.88/241.55 down(f(g(x0))) 542.88/241.55 down(f(c)) 542.88/241.55 down(f(fresh_constant)) 542.88/241.55 down(g(a)) 542.88/241.55 down(g(f(x0))) 542.88/241.55 down(g(b)) 542.88/241.55 down(g(c)) 542.88/241.55 down(g(fresh_constant)) 542.88/241.55 down(f(f(a))) 542.88/241.55 down(f(f(b))) 542.88/241.55 down(f(f(g(x0)))) 542.88/241.55 down(f(f(c))) 542.88/241.55 down(f(f(fresh_constant))) 542.88/241.55 down(g(g(a))) 542.88/241.55 down(g(g(f(x0)))) 542.88/241.55 down(g(g(b))) 542.88/241.55 down(g(g(c))) 542.88/241.55 down(g(g(fresh_constant))) 542.88/241.55 down(f(f(f(a)))) 542.88/241.55 down(f(f(f(b)))) 542.88/241.55 down(f(f(f(g(x0))))) 542.88/241.55 down(f(f(f(c)))) 542.88/241.55 down(f(f(f(fresh_constant)))) 542.88/241.55 down(g(g(g(a)))) 542.88/241.55 down(g(g(g(f(x0))))) 542.88/241.55 down(g(g(g(b)))) 542.88/241.55 down(g(g(g(c)))) 542.88/241.55 down(g(g(g(fresh_constant)))) 542.88/241.55 down(f(f(f(f(a))))) 542.88/241.55 down(f(f(f(f(b))))) 542.88/241.55 down(f(f(f(f(g(x0)))))) 542.88/241.55 down(f(f(f(f(c))))) 542.88/241.55 down(f(f(f(f(fresh_constant))))) 542.88/241.55 down(g(g(g(g(a))))) 542.88/241.55 down(g(g(g(g(f(x0)))))) 542.88/241.55 down(g(g(g(g(b))))) 542.88/241.55 down(g(g(g(g(c))))) 542.88/241.55 down(g(g(g(g(fresh_constant))))) 542.88/241.55 down(f(f(f(f(f(a)))))) 542.88/241.55 down(f(f(f(f(f(b)))))) 542.88/241.55 down(f(f(f(f(f(g(x0))))))) 542.88/241.55 down(f(f(f(f(f(c)))))) 542.88/241.55 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.55 down(g(g(g(g(g(a)))))) 542.88/241.55 down(g(g(g(g(g(f(x0))))))) 542.88/241.55 down(g(g(g(g(g(b)))))) 542.88/241.55 down(g(g(g(g(g(c)))))) 542.88/241.55 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.55 down(f(f(f(f(f(f(a))))))) 542.88/241.55 down(f(f(f(f(f(f(b))))))) 542.88/241.55 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.55 down(f(f(f(f(f(f(c))))))) 542.88/241.55 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.55 down(g(g(g(g(g(g(a))))))) 542.88/241.55 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.55 down(g(g(g(g(g(g(b))))))) 542.88/241.55 down(g(g(g(g(g(g(c))))))) 542.88/241.55 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.55 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.55 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.55 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.55 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 f_flat(up(x0)) 542.88/241.55 g_flat(up(x0)) 542.88/241.55 542.88/241.55 We have to consider all minimal (P,Q,R)-chains. 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (383) TransformationProof (EQUIVALENT) 542.88/241.55 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.55 542.88/241.55 (TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))),TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 542.88/241.55 542.88/241.55 542.88/241.55 ---------------------------------------- 542.88/241.55 542.88/241.55 (384) 542.88/241.55 Obligation: 542.88/241.55 Q DP problem: 542.88/241.55 The TRS P consists of the following rules: 542.88/241.55 542.88/241.55 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.55 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.55 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.55 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.55 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.55 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.55 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.55 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.55 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.55 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.55 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.55 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.55 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.55 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.55 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.55 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.55 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.55 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.55 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.55 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.55 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.55 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.55 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.55 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.55 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.55 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.55 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.55 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.55 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.56 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.56 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.56 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.56 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.56 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.56 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.56 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.56 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.56 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 542.88/241.56 The TRS R consists of the following rules: 542.88/241.56 542.88/241.56 down(a) -> up(f(a)) 542.88/241.56 down(b) -> up(g(b)) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.56 down(f(a)) -> f_flat(down(a)) 542.88/241.56 down(f(b)) -> f_flat(down(b)) 542.88/241.56 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.56 down(f(c)) -> f_flat(down(c)) 542.88/241.56 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.56 down(g(a)) -> g_flat(down(a)) 542.88/241.56 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.56 down(g(b)) -> g_flat(down(b)) 542.88/241.56 down(g(c)) -> g_flat(down(c)) 542.88/241.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.56 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.56 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.56 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.56 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.56 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.56 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.56 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.56 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.56 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.56 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.56 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.56 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.56 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.56 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.56 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.56 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.56 542.88/241.56 The set Q consists of the following terms: 542.88/241.56 542.88/241.56 down(a) 542.88/241.56 down(b) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.56 down(f(a)) 542.88/241.56 down(f(b)) 542.88/241.56 down(f(g(x0))) 542.88/241.56 down(f(c)) 542.88/241.56 down(f(fresh_constant)) 542.88/241.56 down(g(a)) 542.88/241.56 down(g(f(x0))) 542.88/241.56 down(g(b)) 542.88/241.56 down(g(c)) 542.88/241.56 down(g(fresh_constant)) 542.88/241.56 down(f(f(a))) 542.88/241.56 down(f(f(b))) 542.88/241.56 down(f(f(g(x0)))) 542.88/241.56 down(f(f(c))) 542.88/241.56 down(f(f(fresh_constant))) 542.88/241.56 down(g(g(a))) 542.88/241.56 down(g(g(f(x0)))) 542.88/241.56 down(g(g(b))) 542.88/241.56 down(g(g(c))) 542.88/241.56 down(g(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) 542.88/241.56 down(f(f(f(g(x0))))) 542.88/241.56 down(f(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) 542.88/241.56 down(g(g(g(f(x0))))) 542.88/241.56 down(g(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(x0)))))) 542.88/241.56 down(f(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(x0)))))) 542.88/241.56 down(g(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(x0))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(x0))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 f_flat(up(x0)) 542.88/241.56 g_flat(up(x0)) 542.88/241.56 542.88/241.56 We have to consider all minimal (P,Q,R)-chains. 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (385) TransformationProof (EQUIVALENT) 542.88/241.56 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.56 542.88/241.56 (TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))),TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 542.88/241.56 542.88/241.56 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (386) 542.88/241.56 Obligation: 542.88/241.56 Q DP problem: 542.88/241.56 The TRS P consists of the following rules: 542.88/241.56 542.88/241.56 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.56 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.56 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.56 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.56 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.56 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.56 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.56 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.56 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.56 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.56 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.56 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.56 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.56 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.56 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.56 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.56 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.56 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.56 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.56 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.56 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.56 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.56 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.56 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.56 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.56 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.56 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.56 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.56 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.56 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.56 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.56 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.56 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.56 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.56 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.56 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 542.88/241.56 542.88/241.56 The TRS R consists of the following rules: 542.88/241.56 542.88/241.56 down(a) -> up(f(a)) 542.88/241.56 down(b) -> up(g(b)) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.56 down(f(a)) -> f_flat(down(a)) 542.88/241.56 down(f(b)) -> f_flat(down(b)) 542.88/241.56 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.56 down(f(c)) -> f_flat(down(c)) 542.88/241.56 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.56 down(g(a)) -> g_flat(down(a)) 542.88/241.56 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.56 down(g(b)) -> g_flat(down(b)) 542.88/241.56 down(g(c)) -> g_flat(down(c)) 542.88/241.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.56 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.56 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.56 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.56 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.56 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.56 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.56 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.56 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.56 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.56 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.56 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.56 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.56 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.56 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.56 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.56 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.56 542.88/241.56 The set Q consists of the following terms: 542.88/241.56 542.88/241.56 down(a) 542.88/241.56 down(b) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.56 down(f(a)) 542.88/241.56 down(f(b)) 542.88/241.56 down(f(g(x0))) 542.88/241.56 down(f(c)) 542.88/241.56 down(f(fresh_constant)) 542.88/241.56 down(g(a)) 542.88/241.56 down(g(f(x0))) 542.88/241.56 down(g(b)) 542.88/241.56 down(g(c)) 542.88/241.56 down(g(fresh_constant)) 542.88/241.56 down(f(f(a))) 542.88/241.56 down(f(f(b))) 542.88/241.56 down(f(f(g(x0)))) 542.88/241.56 down(f(f(c))) 542.88/241.56 down(f(f(fresh_constant))) 542.88/241.56 down(g(g(a))) 542.88/241.56 down(g(g(f(x0)))) 542.88/241.56 down(g(g(b))) 542.88/241.56 down(g(g(c))) 542.88/241.56 down(g(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) 542.88/241.56 down(f(f(f(g(x0))))) 542.88/241.56 down(f(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) 542.88/241.56 down(g(g(g(f(x0))))) 542.88/241.56 down(g(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(x0)))))) 542.88/241.56 down(f(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(x0)))))) 542.88/241.56 down(g(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(x0))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(x0))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 f_flat(up(x0)) 542.88/241.56 g_flat(up(x0)) 542.88/241.56 542.88/241.56 We have to consider all minimal (P,Q,R)-chains. 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (387) TransformationProof (EQUIVALENT) 542.88/241.56 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.56 542.88/241.56 (TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))),TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.56 542.88/241.56 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (388) 542.88/241.56 Obligation: 542.88/241.56 Q DP problem: 542.88/241.56 The TRS P consists of the following rules: 542.88/241.56 542.88/241.56 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.56 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.56 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.56 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.56 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.56 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.56 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.56 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.56 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.56 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.56 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.56 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.56 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.56 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.56 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.56 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.56 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.56 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.56 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.56 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.56 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.56 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.56 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.56 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.56 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.56 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.56 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.56 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.56 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.56 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.56 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.56 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.56 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.56 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.56 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.56 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 542.88/241.56 The TRS R consists of the following rules: 542.88/241.56 542.88/241.56 down(a) -> up(f(a)) 542.88/241.56 down(b) -> up(g(b)) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.56 down(f(a)) -> f_flat(down(a)) 542.88/241.56 down(f(b)) -> f_flat(down(b)) 542.88/241.56 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.56 down(f(c)) -> f_flat(down(c)) 542.88/241.56 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.56 down(g(a)) -> g_flat(down(a)) 542.88/241.56 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.56 down(g(b)) -> g_flat(down(b)) 542.88/241.56 down(g(c)) -> g_flat(down(c)) 542.88/241.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.56 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.56 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.56 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.56 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.56 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.56 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.56 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.56 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.56 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.56 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.56 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.56 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.56 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.56 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.56 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.56 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.56 542.88/241.56 The set Q consists of the following terms: 542.88/241.56 542.88/241.56 down(a) 542.88/241.56 down(b) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.56 down(f(a)) 542.88/241.56 down(f(b)) 542.88/241.56 down(f(g(x0))) 542.88/241.56 down(f(c)) 542.88/241.56 down(f(fresh_constant)) 542.88/241.56 down(g(a)) 542.88/241.56 down(g(f(x0))) 542.88/241.56 down(g(b)) 542.88/241.56 down(g(c)) 542.88/241.56 down(g(fresh_constant)) 542.88/241.56 down(f(f(a))) 542.88/241.56 down(f(f(b))) 542.88/241.56 down(f(f(g(x0)))) 542.88/241.56 down(f(f(c))) 542.88/241.56 down(f(f(fresh_constant))) 542.88/241.56 down(g(g(a))) 542.88/241.56 down(g(g(f(x0)))) 542.88/241.56 down(g(g(b))) 542.88/241.56 down(g(g(c))) 542.88/241.56 down(g(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) 542.88/241.56 down(f(f(f(g(x0))))) 542.88/241.56 down(f(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) 542.88/241.56 down(g(g(g(f(x0))))) 542.88/241.56 down(g(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(x0)))))) 542.88/241.56 down(f(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(x0)))))) 542.88/241.56 down(g(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(x0))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(x0))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 f_flat(up(x0)) 542.88/241.56 g_flat(up(x0)) 542.88/241.56 542.88/241.56 We have to consider all minimal (P,Q,R)-chains. 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (389) TransformationProof (EQUIVALENT) 542.88/241.56 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(a))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.56 542.88/241.56 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a)))))))))))) 542.88/241.56 542.88/241.56 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (390) 542.88/241.56 Obligation: 542.88/241.56 Q DP problem: 542.88/241.56 The TRS P consists of the following rules: 542.88/241.56 542.88/241.56 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.56 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.56 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.56 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.56 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.56 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.56 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.56 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.56 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.56 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.56 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.56 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.56 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.56 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.56 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.56 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.56 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.56 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.56 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.56 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.56 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.56 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.56 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.56 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.56 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.56 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.56 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.56 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.56 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.56 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.56 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.56 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.56 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.56 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.56 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.56 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 542.88/241.56 542.88/241.56 The TRS R consists of the following rules: 542.88/241.56 542.88/241.56 down(a) -> up(f(a)) 542.88/241.56 down(b) -> up(g(b)) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.56 down(f(a)) -> f_flat(down(a)) 542.88/241.56 down(f(b)) -> f_flat(down(b)) 542.88/241.56 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.56 down(f(c)) -> f_flat(down(c)) 542.88/241.56 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.56 down(g(a)) -> g_flat(down(a)) 542.88/241.56 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.56 down(g(b)) -> g_flat(down(b)) 542.88/241.56 down(g(c)) -> g_flat(down(c)) 542.88/241.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.56 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.56 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.56 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.56 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.56 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.56 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.56 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.56 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.56 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.56 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.56 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.56 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.56 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.56 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.56 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.56 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.56 542.88/241.56 The set Q consists of the following terms: 542.88/241.56 542.88/241.56 down(a) 542.88/241.56 down(b) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.56 down(f(a)) 542.88/241.56 down(f(b)) 542.88/241.56 down(f(g(x0))) 542.88/241.56 down(f(c)) 542.88/241.56 down(f(fresh_constant)) 542.88/241.56 down(g(a)) 542.88/241.56 down(g(f(x0))) 542.88/241.56 down(g(b)) 542.88/241.56 down(g(c)) 542.88/241.56 down(g(fresh_constant)) 542.88/241.56 down(f(f(a))) 542.88/241.56 down(f(f(b))) 542.88/241.56 down(f(f(g(x0)))) 542.88/241.56 down(f(f(c))) 542.88/241.56 down(f(f(fresh_constant))) 542.88/241.56 down(g(g(a))) 542.88/241.56 down(g(g(f(x0)))) 542.88/241.56 down(g(g(b))) 542.88/241.56 down(g(g(c))) 542.88/241.56 down(g(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) 542.88/241.56 down(f(f(f(g(x0))))) 542.88/241.56 down(f(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) 542.88/241.56 down(g(g(g(f(x0))))) 542.88/241.56 down(g(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(x0)))))) 542.88/241.56 down(f(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(x0)))))) 542.88/241.56 down(g(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(x0))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(x0))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 f_flat(up(x0)) 542.88/241.56 g_flat(up(x0)) 542.88/241.56 542.88/241.56 We have to consider all minimal (P,Q,R)-chains. 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (391) TransformationProof (EQUIVALENT) 542.88/241.56 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(b))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.56 542.88/241.56 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b)))))))))))) 542.88/241.56 542.88/241.56 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (392) 542.88/241.56 Obligation: 542.88/241.56 Q DP problem: 542.88/241.56 The TRS P consists of the following rules: 542.88/241.56 542.88/241.56 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.56 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.56 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.56 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.56 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.56 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.56 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.56 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.56 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.56 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.56 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.56 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.56 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.56 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.56 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.56 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.56 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.56 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.56 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.56 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.56 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.56 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.56 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.56 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.56 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.56 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.56 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.56 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.56 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.56 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.56 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.56 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.56 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.56 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.56 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.56 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 542.88/241.56 542.88/241.56 The TRS R consists of the following rules: 542.88/241.56 542.88/241.56 down(a) -> up(f(a)) 542.88/241.56 down(b) -> up(g(b)) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 542.88/241.56 down(f(a)) -> f_flat(down(a)) 542.88/241.56 down(f(b)) -> f_flat(down(b)) 542.88/241.56 down(f(g(y4))) -> f_flat(down(g(y4))) 542.88/241.56 down(f(c)) -> f_flat(down(c)) 542.88/241.56 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 542.88/241.56 down(g(a)) -> g_flat(down(a)) 542.88/241.56 down(g(f(y6))) -> g_flat(down(f(y6))) 542.88/241.56 down(g(b)) -> g_flat(down(b)) 542.88/241.56 down(g(c)) -> g_flat(down(c)) 542.88/241.56 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 542.88/241.56 down(f(f(a))) -> f_flat(down(f(a))) 542.88/241.56 down(f(f(b))) -> f_flat(down(f(b))) 542.88/241.56 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 542.88/241.56 down(f(f(c))) -> f_flat(down(f(c))) 542.88/241.56 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 542.88/241.56 down(g(g(a))) -> g_flat(down(g(a))) 542.88/241.56 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 542.88/241.56 down(g(g(b))) -> g_flat(down(g(b))) 542.88/241.56 down(g(g(c))) -> g_flat(down(g(c))) 542.88/241.56 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 542.88/241.56 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 542.88/241.56 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 542.88/241.56 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 542.88/241.56 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 542.88/241.56 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 542.88/241.56 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 g_flat(up(x_1)) -> up(g(x_1)) 542.88/241.56 f_flat(up(x_1)) -> up(f(x_1)) 542.88/241.56 542.88/241.56 The set Q consists of the following terms: 542.88/241.56 542.88/241.56 down(a) 542.88/241.56 down(b) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 542.88/241.56 down(f(a)) 542.88/241.56 down(f(b)) 542.88/241.56 down(f(g(x0))) 542.88/241.56 down(f(c)) 542.88/241.56 down(f(fresh_constant)) 542.88/241.56 down(g(a)) 542.88/241.56 down(g(f(x0))) 542.88/241.56 down(g(b)) 542.88/241.56 down(g(c)) 542.88/241.56 down(g(fresh_constant)) 542.88/241.56 down(f(f(a))) 542.88/241.56 down(f(f(b))) 542.88/241.56 down(f(f(g(x0)))) 542.88/241.56 down(f(f(c))) 542.88/241.56 down(f(f(fresh_constant))) 542.88/241.56 down(g(g(a))) 542.88/241.56 down(g(g(f(x0)))) 542.88/241.56 down(g(g(b))) 542.88/241.56 down(g(g(c))) 542.88/241.56 down(g(g(fresh_constant))) 542.88/241.56 down(f(f(f(a)))) 542.88/241.56 down(f(f(f(b)))) 542.88/241.56 down(f(f(f(g(x0))))) 542.88/241.56 down(f(f(f(c)))) 542.88/241.56 down(f(f(f(fresh_constant)))) 542.88/241.56 down(g(g(g(a)))) 542.88/241.56 down(g(g(g(f(x0))))) 542.88/241.56 down(g(g(g(b)))) 542.88/241.56 down(g(g(g(c)))) 542.88/241.56 down(g(g(g(fresh_constant)))) 542.88/241.56 down(f(f(f(f(a))))) 542.88/241.56 down(f(f(f(f(b))))) 542.88/241.56 down(f(f(f(f(g(x0)))))) 542.88/241.56 down(f(f(f(f(c))))) 542.88/241.56 down(f(f(f(f(fresh_constant))))) 542.88/241.56 down(g(g(g(g(a))))) 542.88/241.56 down(g(g(g(g(f(x0)))))) 542.88/241.56 down(g(g(g(g(b))))) 542.88/241.56 down(g(g(g(g(c))))) 542.88/241.56 down(g(g(g(g(fresh_constant))))) 542.88/241.56 down(f(f(f(f(f(a)))))) 542.88/241.56 down(f(f(f(f(f(b)))))) 542.88/241.56 down(f(f(f(f(f(g(x0))))))) 542.88/241.56 down(f(f(f(f(f(c)))))) 542.88/241.56 down(f(f(f(f(f(fresh_constant)))))) 542.88/241.56 down(g(g(g(g(g(a)))))) 542.88/241.56 down(g(g(g(g(g(f(x0))))))) 542.88/241.56 down(g(g(g(g(g(b)))))) 542.88/241.56 down(g(g(g(g(g(c)))))) 542.88/241.56 down(g(g(g(g(g(fresh_constant)))))) 542.88/241.56 down(f(f(f(f(f(f(a))))))) 542.88/241.56 down(f(f(f(f(f(f(b))))))) 542.88/241.56 down(f(f(f(f(f(f(g(x0)))))))) 542.88/241.56 down(f(f(f(f(f(f(c))))))) 542.88/241.56 down(f(f(f(f(f(f(fresh_constant))))))) 542.88/241.56 down(g(g(g(g(g(g(a))))))) 542.88/241.56 down(g(g(g(g(g(g(f(x0)))))))) 542.88/241.56 down(g(g(g(g(g(g(b))))))) 542.88/241.56 down(g(g(g(g(g(g(c))))))) 542.88/241.56 down(g(g(g(g(g(g(fresh_constant))))))) 542.88/241.56 down(f(f(f(f(f(f(f(a)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(b)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(g(x0))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(c)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(fresh_constant)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(a)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(f(x0))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(b)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(c)))))))) 542.88/241.56 down(g(g(g(g(g(g(g(fresh_constant)))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(a))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(b))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(c))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(a))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(b))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(c))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(a)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(b)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(c)))))))))) 542.88/241.56 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(a)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(b)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(c)))))))))) 542.88/241.56 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 f_flat(up(x0)) 542.88/241.56 g_flat(up(x0)) 542.88/241.56 542.88/241.56 We have to consider all minimal (P,Q,R)-chains. 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (393) TransformationProof (EQUIVALENT) 542.88/241.56 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(g(x0)))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 542.88/241.56 542.88/241.56 (TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0))))))))))))) 542.88/241.56 542.88/241.56 542.88/241.56 ---------------------------------------- 542.88/241.56 542.88/241.56 (394) 542.88/241.56 Obligation: 542.88/241.56 Q DP problem: 542.88/241.56 The TRS P consists of the following rules: 542.88/241.56 542.88/241.56 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 542.88/241.56 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 542.88/241.56 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 542.88/241.56 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 542.88/241.56 TOP(up(f(a))) -> TOP(up(f(f(a)))) 542.88/241.56 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 542.88/241.56 TOP(up(f(b))) -> TOP(up(f(g(b)))) 542.88/241.56 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 542.88/241.56 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 542.88/241.56 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 542.88/241.56 TOP(up(g(b))) -> TOP(up(g(g(b)))) 542.88/241.56 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 542.88/241.56 TOP(up(g(a))) -> TOP(up(g(f(a)))) 542.88/241.56 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 542.88/241.56 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 542.88/241.56 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 542.88/241.56 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 542.88/241.56 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 542.88/241.56 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 542.88/241.56 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 542.88/241.56 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 542.88/241.56 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 542.88/241.56 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 542.88/241.56 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 542.88/241.56 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 542.88/241.56 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 542.88/241.56 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 542.88/241.56 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 542.88/241.56 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 542.88/241.56 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 542.88/241.56 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 542.88/241.56 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 542.88/241.56 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 542.88/241.56 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 542.88/241.56 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 542.88/241.56 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 542.88/241.56 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 542.88/241.56 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.63 543.11/241.63 The TRS R consists of the following rules: 543.11/241.63 543.11/241.63 down(a) -> up(f(a)) 543.11/241.63 down(b) -> up(g(b)) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.63 down(f(a)) -> f_flat(down(a)) 543.11/241.63 down(f(b)) -> f_flat(down(b)) 543.11/241.63 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.63 down(f(c)) -> f_flat(down(c)) 543.11/241.63 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.63 down(g(a)) -> g_flat(down(a)) 543.11/241.63 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.63 down(g(b)) -> g_flat(down(b)) 543.11/241.63 down(g(c)) -> g_flat(down(c)) 543.11/241.63 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.63 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.63 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.63 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.63 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.63 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.63 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.63 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.63 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.63 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.63 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.63 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.63 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.63 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.63 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.63 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.63 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.63 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.63 543.11/241.63 The set Q consists of the following terms: 543.11/241.63 543.11/241.63 down(a) 543.11/241.63 down(b) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.63 down(f(a)) 543.11/241.63 down(f(b)) 543.11/241.63 down(f(g(x0))) 543.11/241.63 down(f(c)) 543.11/241.63 down(f(fresh_constant)) 543.11/241.63 down(g(a)) 543.11/241.63 down(g(f(x0))) 543.11/241.63 down(g(b)) 543.11/241.63 down(g(c)) 543.11/241.63 down(g(fresh_constant)) 543.11/241.63 down(f(f(a))) 543.11/241.63 down(f(f(b))) 543.11/241.63 down(f(f(g(x0)))) 543.11/241.63 down(f(f(c))) 543.11/241.63 down(f(f(fresh_constant))) 543.11/241.63 down(g(g(a))) 543.11/241.63 down(g(g(f(x0)))) 543.11/241.63 down(g(g(b))) 543.11/241.63 down(g(g(c))) 543.11/241.63 down(g(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) 543.11/241.63 down(f(f(f(g(x0))))) 543.11/241.63 down(f(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) 543.11/241.63 down(g(g(g(f(x0))))) 543.11/241.63 down(g(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(x0)))))) 543.11/241.63 down(f(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(x0)))))) 543.11/241.63 down(g(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(x0))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(x0))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 f_flat(up(x0)) 543.11/241.63 g_flat(up(x0)) 543.11/241.63 543.11/241.63 We have to consider all minimal (P,Q,R)-chains. 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (395) TransformationProof (EQUIVALENT) 543.11/241.63 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.11/241.63 543.11/241.63 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.11/241.63 543.11/241.63 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (396) 543.11/241.63 Obligation: 543.11/241.63 Q DP problem: 543.11/241.63 The TRS P consists of the following rules: 543.11/241.63 543.11/241.63 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.63 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.63 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.63 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.63 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.63 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 543.11/241.63 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.63 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 543.11/241.63 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 543.11/241.63 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.63 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.63 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.63 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.63 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.63 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.63 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.63 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.63 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.63 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.63 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.63 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.63 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.63 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.63 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.63 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.63 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.63 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.63 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.63 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.63 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.63 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.63 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.63 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.63 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.63 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.63 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.63 543.11/241.63 The TRS R consists of the following rules: 543.11/241.63 543.11/241.63 down(a) -> up(f(a)) 543.11/241.63 down(b) -> up(g(b)) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.63 down(f(a)) -> f_flat(down(a)) 543.11/241.63 down(f(b)) -> f_flat(down(b)) 543.11/241.63 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.63 down(f(c)) -> f_flat(down(c)) 543.11/241.63 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.63 down(g(a)) -> g_flat(down(a)) 543.11/241.63 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.63 down(g(b)) -> g_flat(down(b)) 543.11/241.63 down(g(c)) -> g_flat(down(c)) 543.11/241.63 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.63 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.63 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.63 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.63 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.63 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.63 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.63 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.63 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.63 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.63 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.63 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.63 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.63 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.63 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.63 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.63 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.63 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.63 543.11/241.63 The set Q consists of the following terms: 543.11/241.63 543.11/241.63 down(a) 543.11/241.63 down(b) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.63 down(f(a)) 543.11/241.63 down(f(b)) 543.11/241.63 down(f(g(x0))) 543.11/241.63 down(f(c)) 543.11/241.63 down(f(fresh_constant)) 543.11/241.63 down(g(a)) 543.11/241.63 down(g(f(x0))) 543.11/241.63 down(g(b)) 543.11/241.63 down(g(c)) 543.11/241.63 down(g(fresh_constant)) 543.11/241.63 down(f(f(a))) 543.11/241.63 down(f(f(b))) 543.11/241.63 down(f(f(g(x0)))) 543.11/241.63 down(f(f(c))) 543.11/241.63 down(f(f(fresh_constant))) 543.11/241.63 down(g(g(a))) 543.11/241.63 down(g(g(f(x0)))) 543.11/241.63 down(g(g(b))) 543.11/241.63 down(g(g(c))) 543.11/241.63 down(g(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) 543.11/241.63 down(f(f(f(g(x0))))) 543.11/241.63 down(f(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) 543.11/241.63 down(g(g(g(f(x0))))) 543.11/241.63 down(g(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(x0)))))) 543.11/241.63 down(f(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(x0)))))) 543.11/241.63 down(g(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(x0))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(x0))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 f_flat(up(x0)) 543.11/241.63 g_flat(up(x0)) 543.11/241.63 543.11/241.63 We have to consider all minimal (P,Q,R)-chains. 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (397) TransformationProof (EQUIVALENT) 543.11/241.63 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.11/241.63 543.11/241.63 (TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))),TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.11/241.63 543.11/241.63 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (398) 543.11/241.63 Obligation: 543.11/241.63 Q DP problem: 543.11/241.63 The TRS P consists of the following rules: 543.11/241.63 543.11/241.63 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.63 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.63 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.63 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.63 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.63 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 543.11/241.63 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.63 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 543.11/241.63 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 543.11/241.63 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.63 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.63 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.63 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.63 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.63 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.63 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.63 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.63 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.63 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.63 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.63 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.63 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.63 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.63 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.63 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.63 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.63 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.63 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.63 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.63 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.63 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.63 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.63 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.63 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.63 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.63 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.11/241.63 543.11/241.63 The TRS R consists of the following rules: 543.11/241.63 543.11/241.63 down(a) -> up(f(a)) 543.11/241.63 down(b) -> up(g(b)) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.63 down(f(a)) -> f_flat(down(a)) 543.11/241.63 down(f(b)) -> f_flat(down(b)) 543.11/241.63 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.63 down(f(c)) -> f_flat(down(c)) 543.11/241.63 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.63 down(g(a)) -> g_flat(down(a)) 543.11/241.63 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.63 down(g(b)) -> g_flat(down(b)) 543.11/241.63 down(g(c)) -> g_flat(down(c)) 543.11/241.63 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.63 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.63 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.63 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.63 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.63 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.63 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.63 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.63 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.63 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.63 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.63 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.63 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.63 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.63 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.63 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.63 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.63 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.63 543.11/241.63 The set Q consists of the following terms: 543.11/241.63 543.11/241.63 down(a) 543.11/241.63 down(b) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.63 down(f(a)) 543.11/241.63 down(f(b)) 543.11/241.63 down(f(g(x0))) 543.11/241.63 down(f(c)) 543.11/241.63 down(f(fresh_constant)) 543.11/241.63 down(g(a)) 543.11/241.63 down(g(f(x0))) 543.11/241.63 down(g(b)) 543.11/241.63 down(g(c)) 543.11/241.63 down(g(fresh_constant)) 543.11/241.63 down(f(f(a))) 543.11/241.63 down(f(f(b))) 543.11/241.63 down(f(f(g(x0)))) 543.11/241.63 down(f(f(c))) 543.11/241.63 down(f(f(fresh_constant))) 543.11/241.63 down(g(g(a))) 543.11/241.63 down(g(g(f(x0)))) 543.11/241.63 down(g(g(b))) 543.11/241.63 down(g(g(c))) 543.11/241.63 down(g(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) 543.11/241.63 down(f(f(f(g(x0))))) 543.11/241.63 down(f(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) 543.11/241.63 down(g(g(g(f(x0))))) 543.11/241.63 down(g(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(x0)))))) 543.11/241.63 down(f(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(x0)))))) 543.11/241.63 down(g(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(x0))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(x0))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 f_flat(up(x0)) 543.11/241.63 g_flat(up(x0)) 543.11/241.63 543.11/241.63 We have to consider all minimal (P,Q,R)-chains. 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (399) TransformationProof (EQUIVALENT) 543.11/241.63 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.11/241.63 543.11/241.63 (TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))),TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.63 543.11/241.63 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (400) 543.11/241.63 Obligation: 543.11/241.63 Q DP problem: 543.11/241.63 The TRS P consists of the following rules: 543.11/241.63 543.11/241.63 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.63 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.63 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.63 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.63 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.63 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 543.11/241.63 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.63 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 543.11/241.63 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 543.11/241.63 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.63 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.63 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.63 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.63 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.63 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.63 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.63 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.63 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.63 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.63 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.63 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.63 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.63 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.63 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.63 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.63 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.63 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.63 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.63 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.63 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.63 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.63 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.63 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.63 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.63 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.63 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 543.11/241.63 The TRS R consists of the following rules: 543.11/241.63 543.11/241.63 down(a) -> up(f(a)) 543.11/241.63 down(b) -> up(g(b)) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.63 down(f(a)) -> f_flat(down(a)) 543.11/241.63 down(f(b)) -> f_flat(down(b)) 543.11/241.63 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.63 down(f(c)) -> f_flat(down(c)) 543.11/241.63 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.63 down(g(a)) -> g_flat(down(a)) 543.11/241.63 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.63 down(g(b)) -> g_flat(down(b)) 543.11/241.63 down(g(c)) -> g_flat(down(c)) 543.11/241.63 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.63 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.63 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.63 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.63 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.63 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.63 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.63 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.63 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.63 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.63 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.63 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.63 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.63 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.63 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.63 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.63 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.63 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.63 543.11/241.63 The set Q consists of the following terms: 543.11/241.63 543.11/241.63 down(a) 543.11/241.63 down(b) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.63 down(f(a)) 543.11/241.63 down(f(b)) 543.11/241.63 down(f(g(x0))) 543.11/241.63 down(f(c)) 543.11/241.63 down(f(fresh_constant)) 543.11/241.63 down(g(a)) 543.11/241.63 down(g(f(x0))) 543.11/241.63 down(g(b)) 543.11/241.63 down(g(c)) 543.11/241.63 down(g(fresh_constant)) 543.11/241.63 down(f(f(a))) 543.11/241.63 down(f(f(b))) 543.11/241.63 down(f(f(g(x0)))) 543.11/241.63 down(f(f(c))) 543.11/241.63 down(f(f(fresh_constant))) 543.11/241.63 down(g(g(a))) 543.11/241.63 down(g(g(f(x0)))) 543.11/241.63 down(g(g(b))) 543.11/241.63 down(g(g(c))) 543.11/241.63 down(g(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) 543.11/241.63 down(f(f(f(g(x0))))) 543.11/241.63 down(f(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) 543.11/241.63 down(g(g(g(f(x0))))) 543.11/241.63 down(g(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(x0)))))) 543.11/241.63 down(f(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(x0)))))) 543.11/241.63 down(g(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(x0))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(x0))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 f_flat(up(x0)) 543.11/241.63 g_flat(up(x0)) 543.11/241.63 543.11/241.63 We have to consider all minimal (P,Q,R)-chains. 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (401) TransformationProof (EQUIVALENT) 543.11/241.63 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(a))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.11/241.63 543.11/241.63 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a)))))))))))) 543.11/241.63 543.11/241.63 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (402) 543.11/241.63 Obligation: 543.11/241.63 Q DP problem: 543.11/241.63 The TRS P consists of the following rules: 543.11/241.63 543.11/241.63 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.63 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.63 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.63 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.63 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.63 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 543.11/241.63 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.63 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 543.11/241.63 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 543.11/241.63 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.63 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.63 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.63 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.63 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.63 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.63 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.63 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.63 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.63 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.63 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.63 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.63 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.63 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.63 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.63 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.63 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.63 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.63 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.63 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.63 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.63 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.63 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.63 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.63 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.63 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.63 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.11/241.63 543.11/241.63 The TRS R consists of the following rules: 543.11/241.63 543.11/241.63 down(a) -> up(f(a)) 543.11/241.63 down(b) -> up(g(b)) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.63 down(f(a)) -> f_flat(down(a)) 543.11/241.63 down(f(b)) -> f_flat(down(b)) 543.11/241.63 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.63 down(f(c)) -> f_flat(down(c)) 543.11/241.63 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.63 down(g(a)) -> g_flat(down(a)) 543.11/241.63 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.63 down(g(b)) -> g_flat(down(b)) 543.11/241.63 down(g(c)) -> g_flat(down(c)) 543.11/241.63 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.63 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.63 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.63 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.63 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.63 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.63 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.63 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.63 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.63 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.63 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.63 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.63 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.63 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.63 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.63 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.63 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.63 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.63 543.11/241.63 The set Q consists of the following terms: 543.11/241.63 543.11/241.63 down(a) 543.11/241.63 down(b) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.63 down(f(a)) 543.11/241.63 down(f(b)) 543.11/241.63 down(f(g(x0))) 543.11/241.63 down(f(c)) 543.11/241.63 down(f(fresh_constant)) 543.11/241.63 down(g(a)) 543.11/241.63 down(g(f(x0))) 543.11/241.63 down(g(b)) 543.11/241.63 down(g(c)) 543.11/241.63 down(g(fresh_constant)) 543.11/241.63 down(f(f(a))) 543.11/241.63 down(f(f(b))) 543.11/241.63 down(f(f(g(x0)))) 543.11/241.63 down(f(f(c))) 543.11/241.63 down(f(f(fresh_constant))) 543.11/241.63 down(g(g(a))) 543.11/241.63 down(g(g(f(x0)))) 543.11/241.63 down(g(g(b))) 543.11/241.63 down(g(g(c))) 543.11/241.63 down(g(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) 543.11/241.63 down(f(f(f(g(x0))))) 543.11/241.63 down(f(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) 543.11/241.63 down(g(g(g(f(x0))))) 543.11/241.63 down(g(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(x0)))))) 543.11/241.63 down(f(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(x0)))))) 543.11/241.63 down(g(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(x0))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(x0))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 f_flat(up(x0)) 543.11/241.63 g_flat(up(x0)) 543.11/241.63 543.11/241.63 We have to consider all minimal (P,Q,R)-chains. 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (403) TransformationProof (EQUIVALENT) 543.11/241.63 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(f(x0)))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.11/241.63 543.11/241.63 (TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0))))))))))))) 543.11/241.63 543.11/241.63 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (404) 543.11/241.63 Obligation: 543.11/241.63 Q DP problem: 543.11/241.63 The TRS P consists of the following rules: 543.11/241.63 543.11/241.63 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.63 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.63 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.63 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.63 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.63 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 543.11/241.63 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.63 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 543.11/241.63 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 543.11/241.63 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.63 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.63 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.63 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.63 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.63 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.63 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.63 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.63 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.63 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.63 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.63 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.63 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.63 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.63 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.63 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.63 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.63 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.63 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.63 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.63 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.63 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.63 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.63 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.63 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.63 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.63 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.63 543.11/241.63 The TRS R consists of the following rules: 543.11/241.63 543.11/241.63 down(a) -> up(f(a)) 543.11/241.63 down(b) -> up(g(b)) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.63 down(f(a)) -> f_flat(down(a)) 543.11/241.63 down(f(b)) -> f_flat(down(b)) 543.11/241.63 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.63 down(f(c)) -> f_flat(down(c)) 543.11/241.63 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.63 down(g(a)) -> g_flat(down(a)) 543.11/241.63 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.63 down(g(b)) -> g_flat(down(b)) 543.11/241.63 down(g(c)) -> g_flat(down(c)) 543.11/241.63 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.63 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.63 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.63 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.63 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.63 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.63 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.63 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.63 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.63 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.63 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.63 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.63 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.63 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.63 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.63 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.63 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.63 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.63 543.11/241.63 The set Q consists of the following terms: 543.11/241.63 543.11/241.63 down(a) 543.11/241.63 down(b) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.63 down(f(a)) 543.11/241.63 down(f(b)) 543.11/241.63 down(f(g(x0))) 543.11/241.63 down(f(c)) 543.11/241.63 down(f(fresh_constant)) 543.11/241.63 down(g(a)) 543.11/241.63 down(g(f(x0))) 543.11/241.63 down(g(b)) 543.11/241.63 down(g(c)) 543.11/241.63 down(g(fresh_constant)) 543.11/241.63 down(f(f(a))) 543.11/241.63 down(f(f(b))) 543.11/241.63 down(f(f(g(x0)))) 543.11/241.63 down(f(f(c))) 543.11/241.63 down(f(f(fresh_constant))) 543.11/241.63 down(g(g(a))) 543.11/241.63 down(g(g(f(x0)))) 543.11/241.63 down(g(g(b))) 543.11/241.63 down(g(g(c))) 543.11/241.63 down(g(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) 543.11/241.63 down(f(f(f(g(x0))))) 543.11/241.63 down(f(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) 543.11/241.63 down(g(g(g(f(x0))))) 543.11/241.63 down(g(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(x0)))))) 543.11/241.63 down(f(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(x0)))))) 543.11/241.63 down(g(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(x0))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(x0))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 f_flat(up(x0)) 543.11/241.63 g_flat(up(x0)) 543.11/241.63 543.11/241.63 We have to consider all minimal (P,Q,R)-chains. 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (405) TransformationProof (EQUIVALENT) 543.11/241.63 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(c))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.11/241.63 543.11/241.63 (TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c)))))))))))) 543.11/241.63 543.11/241.63 543.11/241.63 ---------------------------------------- 543.11/241.63 543.11/241.63 (406) 543.11/241.63 Obligation: 543.11/241.63 Q DP problem: 543.11/241.63 The TRS P consists of the following rules: 543.11/241.63 543.11/241.63 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.63 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.63 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.63 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.63 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.63 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 543.11/241.63 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.63 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 543.11/241.63 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 543.11/241.63 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.63 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.63 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.63 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.63 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.63 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.63 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.63 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.63 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.63 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.63 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.63 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.63 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.63 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.63 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.63 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.63 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.63 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.63 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.63 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.63 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.63 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.63 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.63 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.63 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.63 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.63 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.11/241.63 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.63 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.11/241.63 543.11/241.63 The TRS R consists of the following rules: 543.11/241.63 543.11/241.63 down(a) -> up(f(a)) 543.11/241.63 down(b) -> up(g(b)) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.63 down(f(a)) -> f_flat(down(a)) 543.11/241.63 down(f(b)) -> f_flat(down(b)) 543.11/241.63 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.63 down(f(c)) -> f_flat(down(c)) 543.11/241.63 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.63 down(g(a)) -> g_flat(down(a)) 543.11/241.63 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.63 down(g(b)) -> g_flat(down(b)) 543.11/241.63 down(g(c)) -> g_flat(down(c)) 543.11/241.63 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.63 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.63 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.63 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.63 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.63 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.63 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.63 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.63 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.63 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.63 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.63 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.63 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.63 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.63 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.63 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.63 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.63 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.63 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.63 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.63 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.63 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.63 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.63 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.63 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.63 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.63 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.63 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.63 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.63 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.63 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.63 543.11/241.63 The set Q consists of the following terms: 543.11/241.63 543.11/241.63 down(a) 543.11/241.63 down(b) 543.11/241.63 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.63 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.63 down(f(a)) 543.11/241.63 down(f(b)) 543.11/241.63 down(f(g(x0))) 543.11/241.63 down(f(c)) 543.11/241.63 down(f(fresh_constant)) 543.11/241.63 down(g(a)) 543.11/241.63 down(g(f(x0))) 543.11/241.63 down(g(b)) 543.11/241.63 down(g(c)) 543.11/241.63 down(g(fresh_constant)) 543.11/241.63 down(f(f(a))) 543.11/241.63 down(f(f(b))) 543.11/241.63 down(f(f(g(x0)))) 543.11/241.63 down(f(f(c))) 543.11/241.63 down(f(f(fresh_constant))) 543.11/241.63 down(g(g(a))) 543.11/241.63 down(g(g(f(x0)))) 543.11/241.63 down(g(g(b))) 543.11/241.63 down(g(g(c))) 543.11/241.63 down(g(g(fresh_constant))) 543.11/241.63 down(f(f(f(a)))) 543.11/241.63 down(f(f(f(b)))) 543.11/241.63 down(f(f(f(g(x0))))) 543.11/241.63 down(f(f(f(c)))) 543.11/241.63 down(f(f(f(fresh_constant)))) 543.11/241.63 down(g(g(g(a)))) 543.11/241.63 down(g(g(g(f(x0))))) 543.11/241.63 down(g(g(g(b)))) 543.11/241.63 down(g(g(g(c)))) 543.11/241.63 down(g(g(g(fresh_constant)))) 543.11/241.63 down(f(f(f(f(a))))) 543.11/241.63 down(f(f(f(f(b))))) 543.11/241.63 down(f(f(f(f(g(x0)))))) 543.11/241.63 down(f(f(f(f(c))))) 543.11/241.63 down(f(f(f(f(fresh_constant))))) 543.11/241.63 down(g(g(g(g(a))))) 543.11/241.63 down(g(g(g(g(f(x0)))))) 543.11/241.63 down(g(g(g(g(b))))) 543.11/241.63 down(g(g(g(g(c))))) 543.11/241.63 down(g(g(g(g(fresh_constant))))) 543.11/241.63 down(f(f(f(f(f(a)))))) 543.11/241.63 down(f(f(f(f(f(b)))))) 543.11/241.63 down(f(f(f(f(f(g(x0))))))) 543.11/241.63 down(f(f(f(f(f(c)))))) 543.11/241.63 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.63 down(g(g(g(g(g(a)))))) 543.11/241.63 down(g(g(g(g(g(f(x0))))))) 543.11/241.63 down(g(g(g(g(g(b)))))) 543.11/241.63 down(g(g(g(g(g(c)))))) 543.11/241.63 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.64 down(f(f(f(f(f(f(a))))))) 543.11/241.64 down(f(f(f(f(f(f(b))))))) 543.11/241.64 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.64 down(f(f(f(f(f(f(c))))))) 543.11/241.64 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.64 down(g(g(g(g(g(g(a))))))) 543.11/241.64 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.64 down(g(g(g(g(g(g(b))))))) 543.11/241.64 down(g(g(g(g(g(g(c))))))) 543.11/241.64 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.64 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.64 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.64 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.64 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.64 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.64 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.64 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.64 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.64 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.64 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.64 f_flat(up(x0)) 543.11/241.64 g_flat(up(x0)) 543.11/241.64 543.11/241.64 We have to consider all minimal (P,Q,R)-chains. 543.11/241.64 ---------------------------------------- 543.11/241.64 543.11/241.64 (407) TransformationProof (EQUIVALENT) 543.11/241.64 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.11/241.64 543.11/241.64 (TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant)))))))))))) 543.11/241.65 543.11/241.65 543.11/241.65 ---------------------------------------- 543.11/241.65 543.11/241.65 (408) 543.11/241.65 Obligation: 543.11/241.65 Q DP problem: 543.11/241.65 The TRS P consists of the following rules: 543.11/241.65 543.11/241.65 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.65 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.65 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.65 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.65 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.65 TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) 543.11/241.65 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.65 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 543.11/241.65 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 543.11/241.65 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.65 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.65 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.65 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.65 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.65 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.65 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.65 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.65 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.65 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.65 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.65 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.65 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.65 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.65 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.65 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.65 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.65 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.65 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.65 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.65 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.65 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.65 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.65 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.65 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.65 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.65 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.65 543.11/241.65 The TRS R consists of the following rules: 543.11/241.65 543.11/241.65 down(a) -> up(f(a)) 543.11/241.65 down(b) -> up(g(b)) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.65 down(f(a)) -> f_flat(down(a)) 543.11/241.65 down(f(b)) -> f_flat(down(b)) 543.11/241.65 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.65 down(f(c)) -> f_flat(down(c)) 543.11/241.65 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.65 down(g(a)) -> g_flat(down(a)) 543.11/241.65 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.65 down(g(b)) -> g_flat(down(b)) 543.11/241.65 down(g(c)) -> g_flat(down(c)) 543.11/241.65 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.65 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.65 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.65 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.65 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.65 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.65 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.65 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.65 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.65 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.65 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.65 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.65 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.65 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.65 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.65 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.65 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.65 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.65 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.65 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.65 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.65 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.65 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.65 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.65 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.65 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.65 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.65 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.65 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.65 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.65 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.65 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.65 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.65 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.65 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.65 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.65 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.65 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.65 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.65 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.65 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.65 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.65 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.65 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.65 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.65 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.65 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.65 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.65 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.65 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.65 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.65 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.65 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.65 543.11/241.65 The set Q consists of the following terms: 543.11/241.65 543.11/241.65 down(a) 543.11/241.65 down(b) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.65 down(f(a)) 543.11/241.65 down(f(b)) 543.11/241.65 down(f(g(x0))) 543.11/241.65 down(f(c)) 543.11/241.65 down(f(fresh_constant)) 543.11/241.65 down(g(a)) 543.11/241.65 down(g(f(x0))) 543.11/241.65 down(g(b)) 543.11/241.65 down(g(c)) 543.11/241.65 down(g(fresh_constant)) 543.11/241.65 down(f(f(a))) 543.11/241.65 down(f(f(b))) 543.11/241.65 down(f(f(g(x0)))) 543.11/241.65 down(f(f(c))) 543.11/241.65 down(f(f(fresh_constant))) 543.11/241.65 down(g(g(a))) 543.11/241.65 down(g(g(f(x0)))) 543.11/241.65 down(g(g(b))) 543.11/241.65 down(g(g(c))) 543.11/241.65 down(g(g(fresh_constant))) 543.11/241.65 down(f(f(f(a)))) 543.11/241.65 down(f(f(f(b)))) 543.11/241.65 down(f(f(f(g(x0))))) 543.11/241.65 down(f(f(f(c)))) 543.11/241.65 down(f(f(f(fresh_constant)))) 543.11/241.65 down(g(g(g(a)))) 543.11/241.65 down(g(g(g(f(x0))))) 543.11/241.65 down(g(g(g(b)))) 543.11/241.65 down(g(g(g(c)))) 543.11/241.65 down(g(g(g(fresh_constant)))) 543.11/241.65 down(f(f(f(f(a))))) 543.11/241.65 down(f(f(f(f(b))))) 543.11/241.65 down(f(f(f(f(g(x0)))))) 543.11/241.65 down(f(f(f(f(c))))) 543.11/241.65 down(f(f(f(f(fresh_constant))))) 543.11/241.65 down(g(g(g(g(a))))) 543.11/241.65 down(g(g(g(g(f(x0)))))) 543.11/241.65 down(g(g(g(g(b))))) 543.11/241.65 down(g(g(g(g(c))))) 543.11/241.65 down(g(g(g(g(fresh_constant))))) 543.11/241.65 down(f(f(f(f(f(a)))))) 543.11/241.65 down(f(f(f(f(f(b)))))) 543.11/241.65 down(f(f(f(f(f(g(x0))))))) 543.11/241.65 down(f(f(f(f(f(c)))))) 543.11/241.65 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.65 down(g(g(g(g(g(a)))))) 543.11/241.65 down(g(g(g(g(g(f(x0))))))) 543.11/241.65 down(g(g(g(g(g(b)))))) 543.11/241.65 down(g(g(g(g(g(c)))))) 543.11/241.65 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.65 down(f(f(f(f(f(f(a))))))) 543.11/241.65 down(f(f(f(f(f(f(b))))))) 543.11/241.65 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.65 down(f(f(f(f(f(f(c))))))) 543.11/241.65 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.65 down(g(g(g(g(g(g(a))))))) 543.11/241.65 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.65 down(g(g(g(g(g(g(b))))))) 543.11/241.65 down(g(g(g(g(g(g(c))))))) 543.11/241.65 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.65 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 f_flat(up(x0)) 543.11/241.65 g_flat(up(x0)) 543.11/241.65 543.11/241.65 We have to consider all minimal (P,Q,R)-chains. 543.11/241.65 ---------------------------------------- 543.11/241.65 543.11/241.65 (409) TransformationProof (EQUIVALENT) 543.11/241.65 By rewriting [LPAR04] the rule TOP(up(f(f(a)))) -> TOP(f_flat(f_flat(up(f(a))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.11/241.65 543.11/241.65 (TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))),TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a)))))) 543.11/241.65 543.11/241.65 543.11/241.65 ---------------------------------------- 543.11/241.65 543.11/241.65 (410) 543.11/241.65 Obligation: 543.11/241.65 Q DP problem: 543.11/241.65 The TRS P consists of the following rules: 543.11/241.65 543.11/241.65 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.65 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.65 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.65 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.65 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.65 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.65 TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) 543.11/241.65 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 543.11/241.65 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.65 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.65 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.65 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.65 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.65 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.65 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.65 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.65 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.65 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.65 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.65 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.65 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.65 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.65 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.65 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.65 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.65 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.65 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.65 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.65 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.65 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.65 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.65 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.65 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.65 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.65 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.65 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.11/241.65 543.11/241.65 The TRS R consists of the following rules: 543.11/241.65 543.11/241.65 down(a) -> up(f(a)) 543.11/241.65 down(b) -> up(g(b)) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.65 down(f(a)) -> f_flat(down(a)) 543.11/241.65 down(f(b)) -> f_flat(down(b)) 543.11/241.65 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.65 down(f(c)) -> f_flat(down(c)) 543.11/241.65 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.65 down(g(a)) -> g_flat(down(a)) 543.11/241.65 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.65 down(g(b)) -> g_flat(down(b)) 543.11/241.65 down(g(c)) -> g_flat(down(c)) 543.11/241.65 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.65 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.65 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.65 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.65 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.65 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.65 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.65 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.65 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.65 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.65 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.65 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.65 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.65 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.65 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.65 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.65 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.65 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.65 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.65 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.65 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.65 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.65 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.65 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.65 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.65 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.65 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.65 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.65 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.65 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.65 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.65 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.65 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.65 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.65 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.65 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.65 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.65 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.65 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.65 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.65 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.65 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.65 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.65 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.65 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.65 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.65 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.65 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.65 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.65 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.65 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.65 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.65 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.65 543.11/241.65 The set Q consists of the following terms: 543.11/241.65 543.11/241.65 down(a) 543.11/241.65 down(b) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.65 down(f(a)) 543.11/241.65 down(f(b)) 543.11/241.65 down(f(g(x0))) 543.11/241.65 down(f(c)) 543.11/241.65 down(f(fresh_constant)) 543.11/241.65 down(g(a)) 543.11/241.65 down(g(f(x0))) 543.11/241.65 down(g(b)) 543.11/241.65 down(g(c)) 543.11/241.65 down(g(fresh_constant)) 543.11/241.65 down(f(f(a))) 543.11/241.65 down(f(f(b))) 543.11/241.65 down(f(f(g(x0)))) 543.11/241.65 down(f(f(c))) 543.11/241.65 down(f(f(fresh_constant))) 543.11/241.65 down(g(g(a))) 543.11/241.65 down(g(g(f(x0)))) 543.11/241.65 down(g(g(b))) 543.11/241.65 down(g(g(c))) 543.11/241.65 down(g(g(fresh_constant))) 543.11/241.65 down(f(f(f(a)))) 543.11/241.65 down(f(f(f(b)))) 543.11/241.65 down(f(f(f(g(x0))))) 543.11/241.65 down(f(f(f(c)))) 543.11/241.65 down(f(f(f(fresh_constant)))) 543.11/241.65 down(g(g(g(a)))) 543.11/241.65 down(g(g(g(f(x0))))) 543.11/241.65 down(g(g(g(b)))) 543.11/241.65 down(g(g(g(c)))) 543.11/241.65 down(g(g(g(fresh_constant)))) 543.11/241.65 down(f(f(f(f(a))))) 543.11/241.65 down(f(f(f(f(b))))) 543.11/241.65 down(f(f(f(f(g(x0)))))) 543.11/241.65 down(f(f(f(f(c))))) 543.11/241.65 down(f(f(f(f(fresh_constant))))) 543.11/241.65 down(g(g(g(g(a))))) 543.11/241.65 down(g(g(g(g(f(x0)))))) 543.11/241.65 down(g(g(g(g(b))))) 543.11/241.65 down(g(g(g(g(c))))) 543.11/241.65 down(g(g(g(g(fresh_constant))))) 543.11/241.65 down(f(f(f(f(f(a)))))) 543.11/241.65 down(f(f(f(f(f(b)))))) 543.11/241.65 down(f(f(f(f(f(g(x0))))))) 543.11/241.65 down(f(f(f(f(f(c)))))) 543.11/241.65 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.65 down(g(g(g(g(g(a)))))) 543.11/241.65 down(g(g(g(g(g(f(x0))))))) 543.11/241.65 down(g(g(g(g(g(b)))))) 543.11/241.65 down(g(g(g(g(g(c)))))) 543.11/241.65 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.65 down(f(f(f(f(f(f(a))))))) 543.11/241.65 down(f(f(f(f(f(f(b))))))) 543.11/241.65 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.65 down(f(f(f(f(f(f(c))))))) 543.11/241.65 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.65 down(g(g(g(g(g(g(a))))))) 543.11/241.65 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.65 down(g(g(g(g(g(g(b))))))) 543.11/241.65 down(g(g(g(g(g(g(c))))))) 543.11/241.65 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.65 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 f_flat(up(x0)) 543.11/241.65 g_flat(up(x0)) 543.11/241.65 543.11/241.65 We have to consider all minimal (P,Q,R)-chains. 543.11/241.65 ---------------------------------------- 543.11/241.65 543.11/241.65 (411) TransformationProof (EQUIVALENT) 543.11/241.65 By rewriting [LPAR04] the rule TOP(up(f(f(b)))) -> TOP(f_flat(f_flat(up(g(b))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.11/241.65 543.11/241.65 (TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))),TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b)))))) 543.11/241.65 543.11/241.65 543.11/241.65 ---------------------------------------- 543.11/241.65 543.11/241.65 (412) 543.11/241.65 Obligation: 543.11/241.65 Q DP problem: 543.11/241.65 The TRS P consists of the following rules: 543.11/241.65 543.11/241.65 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.65 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.65 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.65 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.65 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.65 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.65 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) 543.11/241.65 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.65 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.65 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.65 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.65 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.65 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.65 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.65 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.65 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.65 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.65 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.65 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.65 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.65 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.65 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.65 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.65 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.65 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.65 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.65 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.65 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.65 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.65 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.65 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.65 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.65 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.65 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.65 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.11/241.65 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.11/241.65 543.11/241.65 The TRS R consists of the following rules: 543.11/241.65 543.11/241.65 down(a) -> up(f(a)) 543.11/241.65 down(b) -> up(g(b)) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.65 down(f(a)) -> f_flat(down(a)) 543.11/241.65 down(f(b)) -> f_flat(down(b)) 543.11/241.65 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.65 down(f(c)) -> f_flat(down(c)) 543.11/241.65 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.65 down(g(a)) -> g_flat(down(a)) 543.11/241.65 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.65 down(g(b)) -> g_flat(down(b)) 543.11/241.65 down(g(c)) -> g_flat(down(c)) 543.11/241.65 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.65 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.65 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.65 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.65 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.65 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.65 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.65 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.65 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.65 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.65 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.65 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.65 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.65 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.65 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.65 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.65 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.65 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.65 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.65 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.65 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.65 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.65 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.65 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.65 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.65 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.65 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.65 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.65 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.65 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.65 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.65 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.65 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.65 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.65 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.65 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.65 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.65 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.65 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.65 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.65 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.65 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.65 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.65 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.65 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.65 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.65 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.65 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.65 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.65 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.65 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.65 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.65 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.65 543.11/241.65 The set Q consists of the following terms: 543.11/241.65 543.11/241.65 down(a) 543.11/241.65 down(b) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.65 down(f(a)) 543.11/241.65 down(f(b)) 543.11/241.65 down(f(g(x0))) 543.11/241.65 down(f(c)) 543.11/241.65 down(f(fresh_constant)) 543.11/241.65 down(g(a)) 543.11/241.65 down(g(f(x0))) 543.11/241.65 down(g(b)) 543.11/241.65 down(g(c)) 543.11/241.65 down(g(fresh_constant)) 543.11/241.65 down(f(f(a))) 543.11/241.65 down(f(f(b))) 543.11/241.65 down(f(f(g(x0)))) 543.11/241.65 down(f(f(c))) 543.11/241.65 down(f(f(fresh_constant))) 543.11/241.65 down(g(g(a))) 543.11/241.65 down(g(g(f(x0)))) 543.11/241.65 down(g(g(b))) 543.11/241.65 down(g(g(c))) 543.11/241.65 down(g(g(fresh_constant))) 543.11/241.65 down(f(f(f(a)))) 543.11/241.65 down(f(f(f(b)))) 543.11/241.65 down(f(f(f(g(x0))))) 543.11/241.65 down(f(f(f(c)))) 543.11/241.65 down(f(f(f(fresh_constant)))) 543.11/241.65 down(g(g(g(a)))) 543.11/241.65 down(g(g(g(f(x0))))) 543.11/241.65 down(g(g(g(b)))) 543.11/241.65 down(g(g(g(c)))) 543.11/241.65 down(g(g(g(fresh_constant)))) 543.11/241.65 down(f(f(f(f(a))))) 543.11/241.65 down(f(f(f(f(b))))) 543.11/241.65 down(f(f(f(f(g(x0)))))) 543.11/241.65 down(f(f(f(f(c))))) 543.11/241.65 down(f(f(f(f(fresh_constant))))) 543.11/241.65 down(g(g(g(g(a))))) 543.11/241.65 down(g(g(g(g(f(x0)))))) 543.11/241.65 down(g(g(g(g(b))))) 543.11/241.65 down(g(g(g(g(c))))) 543.11/241.65 down(g(g(g(g(fresh_constant))))) 543.11/241.65 down(f(f(f(f(f(a)))))) 543.11/241.65 down(f(f(f(f(f(b)))))) 543.11/241.65 down(f(f(f(f(f(g(x0))))))) 543.11/241.65 down(f(f(f(f(f(c)))))) 543.11/241.65 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.65 down(g(g(g(g(g(a)))))) 543.11/241.65 down(g(g(g(g(g(f(x0))))))) 543.11/241.65 down(g(g(g(g(g(b)))))) 543.11/241.65 down(g(g(g(g(g(c)))))) 543.11/241.65 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.65 down(f(f(f(f(f(f(a))))))) 543.11/241.65 down(f(f(f(f(f(f(b))))))) 543.11/241.65 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.65 down(f(f(f(f(f(f(c))))))) 543.11/241.65 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.65 down(g(g(g(g(g(g(a))))))) 543.11/241.65 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.65 down(g(g(g(g(g(g(b))))))) 543.11/241.65 down(g(g(g(g(g(g(c))))))) 543.11/241.65 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.65 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 f_flat(up(x0)) 543.11/241.65 g_flat(up(x0)) 543.11/241.65 543.11/241.65 We have to consider all minimal (P,Q,R)-chains. 543.11/241.65 ---------------------------------------- 543.11/241.65 543.11/241.65 (413) TransformationProof (EQUIVALENT) 543.11/241.65 By rewriting [LPAR04] the rule TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(down(a))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.11/241.65 543.11/241.65 (TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))),TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a))))))) 543.11/241.65 543.11/241.65 543.11/241.65 ---------------------------------------- 543.11/241.65 543.11/241.65 (414) 543.11/241.65 Obligation: 543.11/241.65 Q DP problem: 543.11/241.65 The TRS P consists of the following rules: 543.11/241.65 543.11/241.65 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.65 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.65 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.65 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.65 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.65 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.65 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) 543.11/241.65 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.65 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.65 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.65 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.65 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.65 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.65 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.65 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.65 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.65 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.65 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.65 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.65 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.65 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.65 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.65 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.65 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.65 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.65 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.65 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.65 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.65 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.65 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.11/241.65 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.11/241.65 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.11/241.65 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.11/241.65 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.11/241.65 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.11/241.65 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.11/241.65 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.11/241.65 543.11/241.65 The TRS R consists of the following rules: 543.11/241.65 543.11/241.65 down(a) -> up(f(a)) 543.11/241.65 down(b) -> up(g(b)) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.11/241.65 down(f(a)) -> f_flat(down(a)) 543.11/241.65 down(f(b)) -> f_flat(down(b)) 543.11/241.65 down(f(g(y4))) -> f_flat(down(g(y4))) 543.11/241.65 down(f(c)) -> f_flat(down(c)) 543.11/241.65 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.11/241.65 down(g(a)) -> g_flat(down(a)) 543.11/241.65 down(g(f(y6))) -> g_flat(down(f(y6))) 543.11/241.65 down(g(b)) -> g_flat(down(b)) 543.11/241.65 down(g(c)) -> g_flat(down(c)) 543.11/241.65 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.11/241.65 down(f(f(a))) -> f_flat(down(f(a))) 543.11/241.65 down(f(f(b))) -> f_flat(down(f(b))) 543.11/241.65 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.11/241.65 down(f(f(c))) -> f_flat(down(f(c))) 543.11/241.65 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.11/241.65 down(g(g(a))) -> g_flat(down(g(a))) 543.11/241.65 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.11/241.65 down(g(g(b))) -> g_flat(down(g(b))) 543.11/241.65 down(g(g(c))) -> g_flat(down(g(c))) 543.11/241.65 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.11/241.65 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.11/241.65 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.11/241.65 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.11/241.65 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.11/241.65 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.11/241.65 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.11/241.65 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.11/241.65 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.11/241.65 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.11/241.65 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.11/241.65 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.11/241.65 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.11/241.65 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.11/241.65 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.11/241.65 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.11/241.65 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.11/241.65 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.11/241.65 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.11/241.65 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.11/241.65 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.11/241.65 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.11/241.65 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.11/241.65 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.11/241.65 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.11/241.65 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.11/241.65 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.11/241.65 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.11/241.65 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.11/241.65 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.11/241.65 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.11/241.65 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.11/241.65 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.11/241.65 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.11/241.65 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.11/241.65 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.11/241.65 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.11/241.65 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.11/241.65 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.11/241.65 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.11/241.65 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.11/241.65 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 g_flat(up(x_1)) -> up(g(x_1)) 543.11/241.65 f_flat(up(x_1)) -> up(f(x_1)) 543.11/241.65 543.11/241.65 The set Q consists of the following terms: 543.11/241.65 543.11/241.65 down(a) 543.11/241.65 down(b) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.11/241.65 down(f(a)) 543.11/241.65 down(f(b)) 543.11/241.65 down(f(g(x0))) 543.11/241.65 down(f(c)) 543.11/241.65 down(f(fresh_constant)) 543.11/241.65 down(g(a)) 543.11/241.65 down(g(f(x0))) 543.11/241.65 down(g(b)) 543.11/241.65 down(g(c)) 543.11/241.65 down(g(fresh_constant)) 543.11/241.65 down(f(f(a))) 543.11/241.65 down(f(f(b))) 543.11/241.65 down(f(f(g(x0)))) 543.11/241.65 down(f(f(c))) 543.11/241.65 down(f(f(fresh_constant))) 543.11/241.65 down(g(g(a))) 543.11/241.65 down(g(g(f(x0)))) 543.11/241.65 down(g(g(b))) 543.11/241.65 down(g(g(c))) 543.11/241.65 down(g(g(fresh_constant))) 543.11/241.65 down(f(f(f(a)))) 543.11/241.65 down(f(f(f(b)))) 543.11/241.65 down(f(f(f(g(x0))))) 543.11/241.65 down(f(f(f(c)))) 543.11/241.65 down(f(f(f(fresh_constant)))) 543.11/241.65 down(g(g(g(a)))) 543.11/241.65 down(g(g(g(f(x0))))) 543.11/241.65 down(g(g(g(b)))) 543.11/241.65 down(g(g(g(c)))) 543.11/241.65 down(g(g(g(fresh_constant)))) 543.11/241.65 down(f(f(f(f(a))))) 543.11/241.65 down(f(f(f(f(b))))) 543.11/241.65 down(f(f(f(f(g(x0)))))) 543.11/241.65 down(f(f(f(f(c))))) 543.11/241.65 down(f(f(f(f(fresh_constant))))) 543.11/241.65 down(g(g(g(g(a))))) 543.11/241.65 down(g(g(g(g(f(x0)))))) 543.11/241.65 down(g(g(g(g(b))))) 543.11/241.65 down(g(g(g(g(c))))) 543.11/241.65 down(g(g(g(g(fresh_constant))))) 543.11/241.65 down(f(f(f(f(f(a)))))) 543.11/241.65 down(f(f(f(f(f(b)))))) 543.11/241.65 down(f(f(f(f(f(g(x0))))))) 543.11/241.65 down(f(f(f(f(f(c)))))) 543.11/241.65 down(f(f(f(f(f(fresh_constant)))))) 543.11/241.65 down(g(g(g(g(g(a)))))) 543.11/241.65 down(g(g(g(g(g(f(x0))))))) 543.11/241.65 down(g(g(g(g(g(b)))))) 543.11/241.65 down(g(g(g(g(g(c)))))) 543.11/241.65 down(g(g(g(g(g(fresh_constant)))))) 543.11/241.65 down(f(f(f(f(f(f(a))))))) 543.11/241.65 down(f(f(f(f(f(f(b))))))) 543.11/241.65 down(f(f(f(f(f(f(g(x0)))))))) 543.11/241.65 down(f(f(f(f(f(f(c))))))) 543.11/241.65 down(f(f(f(f(f(f(fresh_constant))))))) 543.11/241.65 down(g(g(g(g(g(g(a))))))) 543.11/241.65 down(g(g(g(g(g(g(f(x0)))))))) 543.11/241.65 down(g(g(g(g(g(g(b))))))) 543.11/241.65 down(g(g(g(g(g(g(c))))))) 543.11/241.65 down(g(g(g(g(g(g(fresh_constant))))))) 543.11/241.65 down(f(f(f(f(f(f(f(a)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(b)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(g(x0))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(c)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(a)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(f(x0))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(b)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(c)))))))) 543.11/241.65 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(a))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(b))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(c))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(a))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(b))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(c))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.11/241.65 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.11/241.65 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.11/241.65 f_flat(up(x0)) 543.11/241.65 g_flat(up(x0)) 543.11/241.65 543.11/241.65 We have to consider all minimal (P,Q,R)-chains. 543.11/241.65 ---------------------------------------- 543.11/241.65 543.11/241.65 (415) TransformationProof (EQUIVALENT) 543.11/241.65 By rewriting [LPAR04] the rule TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(down(b))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.11/241.65 543.11/241.65 (TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))),TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b))))))) 543.11/241.65 543.11/241.65 543.11/241.65 ---------------------------------------- 543.11/241.65 543.11/241.65 (416) 543.11/241.65 Obligation: 543.11/241.65 Q DP problem: 543.11/241.65 The TRS P consists of the following rules: 543.11/241.65 543.11/241.65 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.11/241.65 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.11/241.65 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.11/241.65 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.11/241.65 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.11/241.65 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.11/241.65 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.11/241.65 TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.11/241.65 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.11/241.65 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.11/241.65 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.11/241.65 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.11/241.65 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.11/241.65 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.11/241.65 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.11/241.65 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.11/241.65 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.11/241.65 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.11/241.65 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.11/241.65 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.11/241.65 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.11/241.65 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.11/241.65 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.11/241.65 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.11/241.65 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.11/241.65 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.11/241.65 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.11/241.65 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.11/241.65 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.11/241.65 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.11/241.65 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.67 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.67 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.67 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.67 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.67 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.67 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.67 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.67 543.34/241.67 The TRS R consists of the following rules: 543.34/241.67 543.34/241.67 down(a) -> up(f(a)) 543.34/241.67 down(b) -> up(g(b)) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.67 down(f(a)) -> f_flat(down(a)) 543.34/241.67 down(f(b)) -> f_flat(down(b)) 543.34/241.67 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.67 down(f(c)) -> f_flat(down(c)) 543.34/241.67 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.67 down(g(a)) -> g_flat(down(a)) 543.34/241.67 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.67 down(g(b)) -> g_flat(down(b)) 543.34/241.67 down(g(c)) -> g_flat(down(c)) 543.34/241.67 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.67 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.67 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.67 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.67 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.67 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.67 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.67 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.67 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.67 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.67 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.67 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.67 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.67 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.67 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.67 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.67 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.67 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.67 543.34/241.67 The set Q consists of the following terms: 543.34/241.67 543.34/241.67 down(a) 543.34/241.67 down(b) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.67 down(f(a)) 543.34/241.67 down(f(b)) 543.34/241.67 down(f(g(x0))) 543.34/241.67 down(f(c)) 543.34/241.67 down(f(fresh_constant)) 543.34/241.67 down(g(a)) 543.34/241.67 down(g(f(x0))) 543.34/241.67 down(g(b)) 543.34/241.67 down(g(c)) 543.34/241.67 down(g(fresh_constant)) 543.34/241.67 down(f(f(a))) 543.34/241.67 down(f(f(b))) 543.34/241.67 down(f(f(g(x0)))) 543.34/241.67 down(f(f(c))) 543.34/241.67 down(f(f(fresh_constant))) 543.34/241.67 down(g(g(a))) 543.34/241.67 down(g(g(f(x0)))) 543.34/241.67 down(g(g(b))) 543.34/241.67 down(g(g(c))) 543.34/241.67 down(g(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) 543.34/241.67 down(f(f(f(g(x0))))) 543.34/241.67 down(f(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) 543.34/241.67 down(g(g(g(f(x0))))) 543.34/241.67 down(g(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(x0)))))) 543.34/241.67 down(f(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(x0)))))) 543.34/241.67 down(g(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(x0))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(x0))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 f_flat(up(x0)) 543.34/241.67 g_flat(up(x0)) 543.34/241.67 543.34/241.67 We have to consider all minimal (P,Q,R)-chains. 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (417) TransformationProof (EQUIVALENT) 543.34/241.67 By rewriting [LPAR04] the rule TOP(up(g(g(b)))) -> TOP(g_flat(g_flat(up(g(b))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.34/241.67 543.34/241.67 (TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))),TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b)))))) 543.34/241.67 543.34/241.67 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (418) 543.34/241.67 Obligation: 543.34/241.67 Q DP problem: 543.34/241.67 The TRS P consists of the following rules: 543.34/241.67 543.34/241.67 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.67 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.67 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.67 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.67 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.67 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.67 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.67 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.67 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.34/241.67 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.34/241.67 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.67 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.67 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.34/241.67 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.34/241.67 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.34/241.67 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.34/241.67 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.67 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.67 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.67 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.67 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.67 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.67 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.67 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.67 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.67 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.67 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.67 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.67 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.67 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.67 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.67 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.67 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.67 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.67 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.67 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.67 543.34/241.67 The TRS R consists of the following rules: 543.34/241.67 543.34/241.67 down(a) -> up(f(a)) 543.34/241.67 down(b) -> up(g(b)) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.67 down(f(a)) -> f_flat(down(a)) 543.34/241.67 down(f(b)) -> f_flat(down(b)) 543.34/241.67 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.67 down(f(c)) -> f_flat(down(c)) 543.34/241.67 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.67 down(g(a)) -> g_flat(down(a)) 543.34/241.67 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.67 down(g(b)) -> g_flat(down(b)) 543.34/241.67 down(g(c)) -> g_flat(down(c)) 543.34/241.67 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.67 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.67 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.67 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.67 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.67 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.67 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.67 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.67 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.67 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.67 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.67 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.67 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.67 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.67 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.67 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.67 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.67 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.67 543.34/241.67 The set Q consists of the following terms: 543.34/241.67 543.34/241.67 down(a) 543.34/241.67 down(b) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.67 down(f(a)) 543.34/241.67 down(f(b)) 543.34/241.67 down(f(g(x0))) 543.34/241.67 down(f(c)) 543.34/241.67 down(f(fresh_constant)) 543.34/241.67 down(g(a)) 543.34/241.67 down(g(f(x0))) 543.34/241.67 down(g(b)) 543.34/241.67 down(g(c)) 543.34/241.67 down(g(fresh_constant)) 543.34/241.67 down(f(f(a))) 543.34/241.67 down(f(f(b))) 543.34/241.67 down(f(f(g(x0)))) 543.34/241.67 down(f(f(c))) 543.34/241.67 down(f(f(fresh_constant))) 543.34/241.67 down(g(g(a))) 543.34/241.67 down(g(g(f(x0)))) 543.34/241.67 down(g(g(b))) 543.34/241.67 down(g(g(c))) 543.34/241.67 down(g(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) 543.34/241.67 down(f(f(f(g(x0))))) 543.34/241.67 down(f(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) 543.34/241.67 down(g(g(g(f(x0))))) 543.34/241.67 down(g(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(x0)))))) 543.34/241.67 down(f(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(x0)))))) 543.34/241.67 down(g(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(x0))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(x0))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 f_flat(up(x0)) 543.34/241.67 g_flat(up(x0)) 543.34/241.67 543.34/241.67 We have to consider all minimal (P,Q,R)-chains. 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (419) TransformationProof (EQUIVALENT) 543.34/241.67 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(b))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.67 543.34/241.67 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b)))))))))))) 543.34/241.67 543.34/241.67 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (420) 543.34/241.67 Obligation: 543.34/241.67 Q DP problem: 543.34/241.67 The TRS P consists of the following rules: 543.34/241.67 543.34/241.67 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.67 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.67 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.67 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.67 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.67 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.67 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.67 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.67 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.34/241.67 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.34/241.67 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.67 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.67 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.34/241.67 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.34/241.67 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.34/241.67 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.34/241.67 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.67 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.67 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.67 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.67 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.67 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.67 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.67 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.67 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.67 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.67 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.67 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.67 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.67 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.67 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.67 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.67 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.67 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.67 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.67 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.67 543.34/241.67 The TRS R consists of the following rules: 543.34/241.67 543.34/241.67 down(a) -> up(f(a)) 543.34/241.67 down(b) -> up(g(b)) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.67 down(f(a)) -> f_flat(down(a)) 543.34/241.67 down(f(b)) -> f_flat(down(b)) 543.34/241.67 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.67 down(f(c)) -> f_flat(down(c)) 543.34/241.67 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.67 down(g(a)) -> g_flat(down(a)) 543.34/241.67 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.67 down(g(b)) -> g_flat(down(b)) 543.34/241.67 down(g(c)) -> g_flat(down(c)) 543.34/241.67 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.67 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.67 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.67 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.67 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.67 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.67 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.67 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.67 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.67 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.67 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.67 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.67 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.67 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.67 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.67 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.67 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.67 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.67 543.34/241.67 The set Q consists of the following terms: 543.34/241.67 543.34/241.67 down(a) 543.34/241.67 down(b) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.67 down(f(a)) 543.34/241.67 down(f(b)) 543.34/241.67 down(f(g(x0))) 543.34/241.67 down(f(c)) 543.34/241.67 down(f(fresh_constant)) 543.34/241.67 down(g(a)) 543.34/241.67 down(g(f(x0))) 543.34/241.67 down(g(b)) 543.34/241.67 down(g(c)) 543.34/241.67 down(g(fresh_constant)) 543.34/241.67 down(f(f(a))) 543.34/241.67 down(f(f(b))) 543.34/241.67 down(f(f(g(x0)))) 543.34/241.67 down(f(f(c))) 543.34/241.67 down(f(f(fresh_constant))) 543.34/241.67 down(g(g(a))) 543.34/241.67 down(g(g(f(x0)))) 543.34/241.67 down(g(g(b))) 543.34/241.67 down(g(g(c))) 543.34/241.67 down(g(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) 543.34/241.67 down(f(f(f(g(x0))))) 543.34/241.67 down(f(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) 543.34/241.67 down(g(g(g(f(x0))))) 543.34/241.67 down(g(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(x0)))))) 543.34/241.67 down(f(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(x0)))))) 543.34/241.67 down(g(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(x0))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(x0))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 f_flat(up(x0)) 543.34/241.67 g_flat(up(x0)) 543.34/241.67 543.34/241.67 We have to consider all minimal (P,Q,R)-chains. 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (421) TransformationProof (EQUIVALENT) 543.34/241.67 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(c))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.67 543.34/241.67 (TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c)))))))))))) 543.34/241.67 543.34/241.67 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (422) 543.34/241.67 Obligation: 543.34/241.67 Q DP problem: 543.34/241.67 The TRS P consists of the following rules: 543.34/241.67 543.34/241.67 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.67 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.67 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.67 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.67 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.67 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.67 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.67 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.67 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.34/241.67 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.34/241.67 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.67 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.67 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.34/241.67 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.34/241.67 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.34/241.67 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.34/241.67 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.67 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.67 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.67 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.67 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.67 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.67 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.67 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.67 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.67 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.67 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.67 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.67 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.67 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.67 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.67 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.67 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.67 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.67 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.67 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.67 543.34/241.67 The TRS R consists of the following rules: 543.34/241.67 543.34/241.67 down(a) -> up(f(a)) 543.34/241.67 down(b) -> up(g(b)) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.67 down(f(a)) -> f_flat(down(a)) 543.34/241.67 down(f(b)) -> f_flat(down(b)) 543.34/241.67 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.67 down(f(c)) -> f_flat(down(c)) 543.34/241.67 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.67 down(g(a)) -> g_flat(down(a)) 543.34/241.67 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.67 down(g(b)) -> g_flat(down(b)) 543.34/241.67 down(g(c)) -> g_flat(down(c)) 543.34/241.67 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.67 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.67 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.67 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.67 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.67 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.67 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.67 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.67 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.67 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.67 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.67 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.67 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.67 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.67 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.67 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.67 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.67 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.67 543.34/241.67 The set Q consists of the following terms: 543.34/241.67 543.34/241.67 down(a) 543.34/241.67 down(b) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.67 down(f(a)) 543.34/241.67 down(f(b)) 543.34/241.67 down(f(g(x0))) 543.34/241.67 down(f(c)) 543.34/241.67 down(f(fresh_constant)) 543.34/241.67 down(g(a)) 543.34/241.67 down(g(f(x0))) 543.34/241.67 down(g(b)) 543.34/241.67 down(g(c)) 543.34/241.67 down(g(fresh_constant)) 543.34/241.67 down(f(f(a))) 543.34/241.67 down(f(f(b))) 543.34/241.67 down(f(f(g(x0)))) 543.34/241.67 down(f(f(c))) 543.34/241.67 down(f(f(fresh_constant))) 543.34/241.67 down(g(g(a))) 543.34/241.67 down(g(g(f(x0)))) 543.34/241.67 down(g(g(b))) 543.34/241.67 down(g(g(c))) 543.34/241.67 down(g(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) 543.34/241.67 down(f(f(f(g(x0))))) 543.34/241.67 down(f(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) 543.34/241.67 down(g(g(g(f(x0))))) 543.34/241.67 down(g(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(x0)))))) 543.34/241.67 down(f(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(x0)))))) 543.34/241.67 down(g(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(x0))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(x0))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 f_flat(up(x0)) 543.34/241.67 g_flat(up(x0)) 543.34/241.67 543.34/241.67 We have to consider all minimal (P,Q,R)-chains. 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (423) TransformationProof (EQUIVALENT) 543.34/241.67 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.67 543.34/241.67 (TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant)))))))))))) 543.34/241.67 543.34/241.67 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (424) 543.34/241.67 Obligation: 543.34/241.67 Q DP problem: 543.34/241.67 The TRS P consists of the following rules: 543.34/241.67 543.34/241.67 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.67 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.67 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.67 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.67 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.67 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.67 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.67 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.67 TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) 543.34/241.67 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.34/241.67 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.67 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.67 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.34/241.67 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.34/241.67 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.34/241.67 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.34/241.67 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.67 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.67 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.67 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.67 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.67 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.67 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.67 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.67 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.67 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.67 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.67 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.67 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.67 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.67 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.67 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.67 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.67 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.67 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.67 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.67 543.34/241.67 The TRS R consists of the following rules: 543.34/241.67 543.34/241.67 down(a) -> up(f(a)) 543.34/241.67 down(b) -> up(g(b)) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.67 down(f(a)) -> f_flat(down(a)) 543.34/241.67 down(f(b)) -> f_flat(down(b)) 543.34/241.67 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.67 down(f(c)) -> f_flat(down(c)) 543.34/241.67 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.67 down(g(a)) -> g_flat(down(a)) 543.34/241.67 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.67 down(g(b)) -> g_flat(down(b)) 543.34/241.67 down(g(c)) -> g_flat(down(c)) 543.34/241.67 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.67 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.67 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.67 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.67 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.67 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.67 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.67 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.67 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.67 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.67 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.67 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.67 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.67 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.67 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.67 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.67 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.67 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.67 543.34/241.67 The set Q consists of the following terms: 543.34/241.67 543.34/241.67 down(a) 543.34/241.67 down(b) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.67 down(f(a)) 543.34/241.67 down(f(b)) 543.34/241.67 down(f(g(x0))) 543.34/241.67 down(f(c)) 543.34/241.67 down(f(fresh_constant)) 543.34/241.67 down(g(a)) 543.34/241.67 down(g(f(x0))) 543.34/241.67 down(g(b)) 543.34/241.67 down(g(c)) 543.34/241.67 down(g(fresh_constant)) 543.34/241.67 down(f(f(a))) 543.34/241.67 down(f(f(b))) 543.34/241.67 down(f(f(g(x0)))) 543.34/241.67 down(f(f(c))) 543.34/241.67 down(f(f(fresh_constant))) 543.34/241.67 down(g(g(a))) 543.34/241.67 down(g(g(f(x0)))) 543.34/241.67 down(g(g(b))) 543.34/241.67 down(g(g(c))) 543.34/241.67 down(g(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) 543.34/241.67 down(f(f(f(g(x0))))) 543.34/241.67 down(f(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) 543.34/241.67 down(g(g(g(f(x0))))) 543.34/241.67 down(g(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(x0)))))) 543.34/241.67 down(f(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(x0)))))) 543.34/241.67 down(g(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(x0))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(x0))))))) 543.34/241.67 down(g(g(g(g(g(b)))))) 543.34/241.67 down(g(g(g(g(g(c)))))) 543.34/241.67 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.67 down(f(f(f(f(f(f(a))))))) 543.34/241.67 down(f(f(f(f(f(f(b))))))) 543.34/241.67 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.67 down(f(f(f(f(f(f(c))))))) 543.34/241.67 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.67 down(g(g(g(g(g(g(a))))))) 543.34/241.67 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.67 down(g(g(g(g(g(g(b))))))) 543.34/241.67 down(g(g(g(g(g(g(c))))))) 543.34/241.67 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.67 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.67 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 f_flat(up(x0)) 543.34/241.67 g_flat(up(x0)) 543.34/241.67 543.34/241.67 We have to consider all minimal (P,Q,R)-chains. 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (425) TransformationProof (EQUIVALENT) 543.34/241.67 By rewriting [LPAR04] the rule TOP(up(g(g(a)))) -> TOP(g_flat(g_flat(up(f(a))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.34/241.67 543.34/241.67 (TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))),TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a)))))) 543.34/241.67 543.34/241.67 543.34/241.67 ---------------------------------------- 543.34/241.67 543.34/241.67 (426) 543.34/241.67 Obligation: 543.34/241.67 Q DP problem: 543.34/241.67 The TRS P consists of the following rules: 543.34/241.67 543.34/241.67 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.67 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.67 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.67 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.67 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.67 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.67 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.67 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.67 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) 543.34/241.67 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.67 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.67 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.34/241.67 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.34/241.67 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.34/241.67 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.34/241.67 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.67 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.67 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.67 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.67 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.67 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.67 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.67 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.67 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.67 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.67 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.67 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.67 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.67 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.67 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.67 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.67 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.67 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.67 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.67 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.67 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.67 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.67 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.67 543.34/241.67 The TRS R consists of the following rules: 543.34/241.67 543.34/241.67 down(a) -> up(f(a)) 543.34/241.67 down(b) -> up(g(b)) 543.34/241.67 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.67 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.67 down(f(a)) -> f_flat(down(a)) 543.34/241.67 down(f(b)) -> f_flat(down(b)) 543.34/241.67 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.67 down(f(c)) -> f_flat(down(c)) 543.34/241.67 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.67 down(g(a)) -> g_flat(down(a)) 543.34/241.67 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.67 down(g(b)) -> g_flat(down(b)) 543.34/241.67 down(g(c)) -> g_flat(down(c)) 543.34/241.67 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.67 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.67 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.67 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.67 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.67 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.67 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.67 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.67 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.67 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.67 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.67 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.67 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.67 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.67 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.67 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.67 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.67 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.67 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.67 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.67 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.67 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.67 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.67 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.67 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.67 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.67 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.67 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.67 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.67 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.67 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.67 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.67 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.67 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.67 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.67 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.67 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.67 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.68 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.68 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.68 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.68 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.68 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.68 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.68 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.68 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.68 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.68 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.68 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.68 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.68 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.68 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.68 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.68 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.68 543.34/241.68 The set Q consists of the following terms: 543.34/241.68 543.34/241.68 down(a) 543.34/241.68 down(b) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.68 down(f(a)) 543.34/241.68 down(f(b)) 543.34/241.68 down(f(g(x0))) 543.34/241.68 down(f(c)) 543.34/241.68 down(f(fresh_constant)) 543.34/241.68 down(g(a)) 543.34/241.68 down(g(f(x0))) 543.34/241.68 down(g(b)) 543.34/241.68 down(g(c)) 543.34/241.68 down(g(fresh_constant)) 543.34/241.68 down(f(f(a))) 543.34/241.68 down(f(f(b))) 543.34/241.68 down(f(f(g(x0)))) 543.34/241.68 down(f(f(c))) 543.34/241.68 down(f(f(fresh_constant))) 543.34/241.68 down(g(g(a))) 543.34/241.68 down(g(g(f(x0)))) 543.34/241.68 down(g(g(b))) 543.34/241.68 down(g(g(c))) 543.34/241.68 down(g(g(fresh_constant))) 543.34/241.68 down(f(f(f(a)))) 543.34/241.68 down(f(f(f(b)))) 543.34/241.68 down(f(f(f(g(x0))))) 543.34/241.68 down(f(f(f(c)))) 543.34/241.68 down(f(f(f(fresh_constant)))) 543.34/241.68 down(g(g(g(a)))) 543.34/241.68 down(g(g(g(f(x0))))) 543.34/241.68 down(g(g(g(b)))) 543.34/241.68 down(g(g(g(c)))) 543.34/241.68 down(g(g(g(fresh_constant)))) 543.34/241.68 down(f(f(f(f(a))))) 543.34/241.68 down(f(f(f(f(b))))) 543.34/241.68 down(f(f(f(f(g(x0)))))) 543.34/241.68 down(f(f(f(f(c))))) 543.34/241.68 down(f(f(f(f(fresh_constant))))) 543.34/241.68 down(g(g(g(g(a))))) 543.34/241.68 down(g(g(g(g(f(x0)))))) 543.34/241.68 down(g(g(g(g(b))))) 543.34/241.68 down(g(g(g(g(c))))) 543.34/241.68 down(g(g(g(g(fresh_constant))))) 543.34/241.68 down(f(f(f(f(f(a)))))) 543.34/241.68 down(f(f(f(f(f(b)))))) 543.34/241.68 down(f(f(f(f(f(g(x0))))))) 543.34/241.68 down(f(f(f(f(f(c)))))) 543.34/241.68 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.68 down(g(g(g(g(g(a)))))) 543.34/241.68 down(g(g(g(g(g(f(x0))))))) 543.34/241.68 down(g(g(g(g(g(b)))))) 543.34/241.68 down(g(g(g(g(g(c)))))) 543.34/241.68 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.68 down(f(f(f(f(f(f(a))))))) 543.34/241.68 down(f(f(f(f(f(f(b))))))) 543.34/241.68 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.68 down(f(f(f(f(f(f(c))))))) 543.34/241.68 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.68 down(g(g(g(g(g(g(a))))))) 543.34/241.68 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.68 down(g(g(g(g(g(g(b))))))) 543.34/241.68 down(g(g(g(g(g(g(c))))))) 543.34/241.68 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.68 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.68 f_flat(up(x0)) 543.34/241.68 g_flat(up(x0)) 543.34/241.68 543.34/241.68 We have to consider all minimal (P,Q,R)-chains. 543.34/241.68 ---------------------------------------- 543.34/241.68 543.34/241.68 (427) TransformationProof (EQUIVALENT) 543.34/241.68 By rewriting [LPAR04] the rule TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(down(a))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.68 543.34/241.68 (TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))),TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a))))))) 543.34/241.68 543.34/241.68 543.34/241.68 ---------------------------------------- 543.34/241.68 543.34/241.68 (428) 543.34/241.68 Obligation: 543.34/241.68 Q DP problem: 543.34/241.68 The TRS P consists of the following rules: 543.34/241.68 543.34/241.68 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.68 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.68 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.68 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.68 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.68 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.68 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.68 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.68 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.68 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.68 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) 543.34/241.68 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.34/241.68 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.34/241.68 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.34/241.68 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.68 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.68 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.68 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.68 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.68 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.68 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.68 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.68 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.68 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.68 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.68 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.68 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.68 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.68 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.68 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.68 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.68 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.68 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.68 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.68 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.68 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.68 543.34/241.68 The TRS R consists of the following rules: 543.34/241.68 543.34/241.68 down(a) -> up(f(a)) 543.34/241.68 down(b) -> up(g(b)) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.68 down(f(a)) -> f_flat(down(a)) 543.34/241.68 down(f(b)) -> f_flat(down(b)) 543.34/241.68 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.68 down(f(c)) -> f_flat(down(c)) 543.34/241.68 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.68 down(g(a)) -> g_flat(down(a)) 543.34/241.68 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.68 down(g(b)) -> g_flat(down(b)) 543.34/241.68 down(g(c)) -> g_flat(down(c)) 543.34/241.68 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.68 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.68 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.68 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.68 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.68 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.68 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.68 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.68 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.68 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.68 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.68 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.68 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.68 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.68 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.68 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.68 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.68 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.68 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.68 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.68 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.68 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.68 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.68 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.68 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.68 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.68 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.68 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.68 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.68 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.68 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.68 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.68 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.68 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.68 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.68 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.68 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.68 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.68 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.68 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.68 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.68 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.68 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.68 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.68 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.68 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.68 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.68 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.68 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.68 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.68 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.68 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.68 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.68 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.68 543.34/241.68 The set Q consists of the following terms: 543.34/241.68 543.34/241.68 down(a) 543.34/241.68 down(b) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.68 down(f(a)) 543.34/241.68 down(f(b)) 543.34/241.68 down(f(g(x0))) 543.34/241.68 down(f(c)) 543.34/241.68 down(f(fresh_constant)) 543.34/241.68 down(g(a)) 543.34/241.68 down(g(f(x0))) 543.34/241.68 down(g(b)) 543.34/241.68 down(g(c)) 543.34/241.68 down(g(fresh_constant)) 543.34/241.68 down(f(f(a))) 543.34/241.68 down(f(f(b))) 543.34/241.68 down(f(f(g(x0)))) 543.34/241.68 down(f(f(c))) 543.34/241.68 down(f(f(fresh_constant))) 543.34/241.68 down(g(g(a))) 543.34/241.68 down(g(g(f(x0)))) 543.34/241.68 down(g(g(b))) 543.34/241.68 down(g(g(c))) 543.34/241.68 down(g(g(fresh_constant))) 543.34/241.68 down(f(f(f(a)))) 543.34/241.68 down(f(f(f(b)))) 543.34/241.68 down(f(f(f(g(x0))))) 543.34/241.68 down(f(f(f(c)))) 543.34/241.68 down(f(f(f(fresh_constant)))) 543.34/241.68 down(g(g(g(a)))) 543.34/241.68 down(g(g(g(f(x0))))) 543.34/241.68 down(g(g(g(b)))) 543.34/241.68 down(g(g(g(c)))) 543.34/241.68 down(g(g(g(fresh_constant)))) 543.34/241.68 down(f(f(f(f(a))))) 543.34/241.68 down(f(f(f(f(b))))) 543.34/241.68 down(f(f(f(f(g(x0)))))) 543.34/241.68 down(f(f(f(f(c))))) 543.34/241.68 down(f(f(f(f(fresh_constant))))) 543.34/241.68 down(g(g(g(g(a))))) 543.34/241.68 down(g(g(g(g(f(x0)))))) 543.34/241.68 down(g(g(g(g(b))))) 543.34/241.68 down(g(g(g(g(c))))) 543.34/241.68 down(g(g(g(g(fresh_constant))))) 543.34/241.68 down(f(f(f(f(f(a)))))) 543.34/241.68 down(f(f(f(f(f(b)))))) 543.34/241.68 down(f(f(f(f(f(g(x0))))))) 543.34/241.68 down(f(f(f(f(f(c)))))) 543.34/241.68 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.68 down(g(g(g(g(g(a)))))) 543.34/241.68 down(g(g(g(g(g(f(x0))))))) 543.34/241.68 down(g(g(g(g(g(b)))))) 543.34/241.68 down(g(g(g(g(g(c)))))) 543.34/241.68 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.68 down(f(f(f(f(f(f(a))))))) 543.34/241.68 down(f(f(f(f(f(f(b))))))) 543.34/241.68 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.68 down(f(f(f(f(f(f(c))))))) 543.34/241.68 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.68 down(g(g(g(g(g(g(a))))))) 543.34/241.68 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.68 down(g(g(g(g(g(g(b))))))) 543.34/241.68 down(g(g(g(g(g(g(c))))))) 543.34/241.68 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.68 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.68 f_flat(up(x0)) 543.34/241.68 g_flat(up(x0)) 543.34/241.68 543.34/241.68 We have to consider all minimal (P,Q,R)-chains. 543.34/241.68 ---------------------------------------- 543.34/241.68 543.34/241.68 (429) TransformationProof (EQUIVALENT) 543.34/241.68 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(down(f(a)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.68 543.34/241.68 (TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))),TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.34/241.68 543.34/241.68 543.34/241.68 ---------------------------------------- 543.34/241.68 543.34/241.68 (430) 543.34/241.68 Obligation: 543.34/241.68 Q DP problem: 543.34/241.68 The TRS P consists of the following rules: 543.34/241.68 543.34/241.68 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.68 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.68 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.68 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.68 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.68 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.68 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.68 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.68 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.68 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.68 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) 543.34/241.68 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.34/241.68 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.34/241.68 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.68 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.68 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.68 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.68 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.68 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.68 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.68 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.68 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.68 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.68 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.68 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.68 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.68 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.68 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.68 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.68 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.68 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.68 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.68 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.68 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.68 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.68 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.68 543.34/241.68 The TRS R consists of the following rules: 543.34/241.68 543.34/241.68 down(a) -> up(f(a)) 543.34/241.68 down(b) -> up(g(b)) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.68 down(f(a)) -> f_flat(down(a)) 543.34/241.68 down(f(b)) -> f_flat(down(b)) 543.34/241.68 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.68 down(f(c)) -> f_flat(down(c)) 543.34/241.68 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.68 down(g(a)) -> g_flat(down(a)) 543.34/241.68 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.68 down(g(b)) -> g_flat(down(b)) 543.34/241.68 down(g(c)) -> g_flat(down(c)) 543.34/241.68 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.68 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.68 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.68 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.68 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.68 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.68 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.68 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.68 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.68 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.68 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.68 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.68 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.68 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.68 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.68 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.68 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.68 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.68 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.68 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.68 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.68 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.68 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.68 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.68 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.68 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.68 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.68 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.68 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.68 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.68 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.68 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.68 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.68 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.68 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.68 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.68 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.68 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.68 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.68 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.68 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.68 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.68 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.68 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.68 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.68 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.68 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.68 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.68 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.68 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.68 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.68 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.68 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.68 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.68 543.34/241.68 The set Q consists of the following terms: 543.34/241.68 543.34/241.68 down(a) 543.34/241.68 down(b) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.68 down(f(a)) 543.34/241.68 down(f(b)) 543.34/241.68 down(f(g(x0))) 543.34/241.68 down(f(c)) 543.34/241.68 down(f(fresh_constant)) 543.34/241.68 down(g(a)) 543.34/241.68 down(g(f(x0))) 543.34/241.68 down(g(b)) 543.34/241.68 down(g(c)) 543.34/241.68 down(g(fresh_constant)) 543.34/241.68 down(f(f(a))) 543.34/241.68 down(f(f(b))) 543.34/241.68 down(f(f(g(x0)))) 543.34/241.68 down(f(f(c))) 543.34/241.68 down(f(f(fresh_constant))) 543.34/241.68 down(g(g(a))) 543.34/241.68 down(g(g(f(x0)))) 543.34/241.68 down(g(g(b))) 543.34/241.68 down(g(g(c))) 543.34/241.68 down(g(g(fresh_constant))) 543.34/241.68 down(f(f(f(a)))) 543.34/241.68 down(f(f(f(b)))) 543.34/241.68 down(f(f(f(g(x0))))) 543.34/241.68 down(f(f(f(c)))) 543.34/241.68 down(f(f(f(fresh_constant)))) 543.34/241.68 down(g(g(g(a)))) 543.34/241.68 down(g(g(g(f(x0))))) 543.34/241.68 down(g(g(g(b)))) 543.34/241.68 down(g(g(g(c)))) 543.34/241.68 down(g(g(g(fresh_constant)))) 543.34/241.68 down(f(f(f(f(a))))) 543.34/241.68 down(f(f(f(f(b))))) 543.34/241.68 down(f(f(f(f(g(x0)))))) 543.34/241.68 down(f(f(f(f(c))))) 543.34/241.68 down(f(f(f(f(fresh_constant))))) 543.34/241.68 down(g(g(g(g(a))))) 543.34/241.68 down(g(g(g(g(f(x0)))))) 543.34/241.68 down(g(g(g(g(b))))) 543.34/241.68 down(g(g(g(g(c))))) 543.34/241.68 down(g(g(g(g(fresh_constant))))) 543.34/241.68 down(f(f(f(f(f(a)))))) 543.34/241.68 down(f(f(f(f(f(b)))))) 543.34/241.68 down(f(f(f(f(f(g(x0))))))) 543.34/241.68 down(f(f(f(f(f(c)))))) 543.34/241.68 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.68 down(g(g(g(g(g(a)))))) 543.34/241.68 down(g(g(g(g(g(f(x0))))))) 543.34/241.68 down(g(g(g(g(g(b)))))) 543.34/241.68 down(g(g(g(g(g(c)))))) 543.34/241.68 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.68 down(f(f(f(f(f(f(a))))))) 543.34/241.68 down(f(f(f(f(f(f(b))))))) 543.34/241.68 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.68 down(f(f(f(f(f(f(c))))))) 543.34/241.68 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.68 down(g(g(g(g(g(g(a))))))) 543.34/241.68 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.68 down(g(g(g(g(g(g(b))))))) 543.34/241.68 down(g(g(g(g(g(g(c))))))) 543.34/241.68 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.68 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.68 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.68 f_flat(up(x0)) 543.34/241.68 g_flat(up(x0)) 543.34/241.68 543.34/241.68 We have to consider all minimal (P,Q,R)-chains. 543.34/241.68 ---------------------------------------- 543.34/241.68 543.34/241.68 (431) TransformationProof (EQUIVALENT) 543.34/241.68 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(down(f(b)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.68 543.34/241.68 (TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))),TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.34/241.68 543.34/241.68 543.34/241.68 ---------------------------------------- 543.34/241.68 543.34/241.68 (432) 543.34/241.68 Obligation: 543.34/241.68 Q DP problem: 543.34/241.68 The TRS P consists of the following rules: 543.34/241.68 543.34/241.68 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.68 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.68 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.68 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.68 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.68 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.68 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.68 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.68 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.68 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.68 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) 543.34/241.68 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.34/241.68 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.68 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.68 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.68 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.68 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.68 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.68 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.68 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.68 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.68 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.68 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.68 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.68 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.68 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.68 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.68 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.68 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.68 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.68 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.68 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.68 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.68 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.68 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.68 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.68 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.68 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.68 543.34/241.68 The TRS R consists of the following rules: 543.34/241.68 543.34/241.68 down(a) -> up(f(a)) 543.34/241.68 down(b) -> up(g(b)) 543.34/241.68 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.68 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.69 down(f(a)) -> f_flat(down(a)) 543.34/241.69 down(f(b)) -> f_flat(down(b)) 543.34/241.69 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.69 down(f(c)) -> f_flat(down(c)) 543.34/241.69 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.69 down(g(a)) -> g_flat(down(a)) 543.34/241.69 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.69 down(g(b)) -> g_flat(down(b)) 543.34/241.69 down(g(c)) -> g_flat(down(c)) 543.34/241.69 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.69 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.69 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.69 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.69 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.69 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.69 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.69 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.69 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.69 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.69 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.69 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.69 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.69 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.69 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.69 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.69 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.69 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.69 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.69 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.69 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.69 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.69 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.69 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.69 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.69 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.69 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.69 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.69 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.69 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.69 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.69 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.69 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.69 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.69 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.69 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.69 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.69 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.69 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.69 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.69 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.69 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.69 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.69 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.69 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.69 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.69 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.69 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.69 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.69 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.69 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.69 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.69 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.69 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.69 543.34/241.69 The set Q consists of the following terms: 543.34/241.69 543.34/241.69 down(a) 543.34/241.69 down(b) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.69 down(f(a)) 543.34/241.69 down(f(b)) 543.34/241.69 down(f(g(x0))) 543.34/241.69 down(f(c)) 543.34/241.69 down(f(fresh_constant)) 543.34/241.69 down(g(a)) 543.34/241.69 down(g(f(x0))) 543.34/241.69 down(g(b)) 543.34/241.69 down(g(c)) 543.34/241.69 down(g(fresh_constant)) 543.34/241.69 down(f(f(a))) 543.34/241.69 down(f(f(b))) 543.34/241.69 down(f(f(g(x0)))) 543.34/241.69 down(f(f(c))) 543.34/241.69 down(f(f(fresh_constant))) 543.34/241.69 down(g(g(a))) 543.34/241.69 down(g(g(f(x0)))) 543.34/241.69 down(g(g(b))) 543.34/241.69 down(g(g(c))) 543.34/241.69 down(g(g(fresh_constant))) 543.34/241.69 down(f(f(f(a)))) 543.34/241.69 down(f(f(f(b)))) 543.34/241.69 down(f(f(f(g(x0))))) 543.34/241.69 down(f(f(f(c)))) 543.34/241.69 down(f(f(f(fresh_constant)))) 543.34/241.69 down(g(g(g(a)))) 543.34/241.69 down(g(g(g(f(x0))))) 543.34/241.69 down(g(g(g(b)))) 543.34/241.69 down(g(g(g(c)))) 543.34/241.69 down(g(g(g(fresh_constant)))) 543.34/241.69 down(f(f(f(f(a))))) 543.34/241.69 down(f(f(f(f(b))))) 543.34/241.69 down(f(f(f(f(g(x0)))))) 543.34/241.69 down(f(f(f(f(c))))) 543.34/241.69 down(f(f(f(f(fresh_constant))))) 543.34/241.69 down(g(g(g(g(a))))) 543.34/241.69 down(g(g(g(g(f(x0)))))) 543.34/241.69 down(g(g(g(g(b))))) 543.34/241.69 down(g(g(g(g(c))))) 543.34/241.69 down(g(g(g(g(fresh_constant))))) 543.34/241.69 down(f(f(f(f(f(a)))))) 543.34/241.69 down(f(f(f(f(f(b)))))) 543.34/241.69 down(f(f(f(f(f(g(x0))))))) 543.34/241.69 down(f(f(f(f(f(c)))))) 543.34/241.69 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.69 down(g(g(g(g(g(a)))))) 543.34/241.69 down(g(g(g(g(g(f(x0))))))) 543.34/241.69 down(g(g(g(g(g(b)))))) 543.34/241.69 down(g(g(g(g(g(c)))))) 543.34/241.69 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.69 down(f(f(f(f(f(f(a))))))) 543.34/241.69 down(f(f(f(f(f(f(b))))))) 543.34/241.69 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.69 down(f(f(f(f(f(f(c))))))) 543.34/241.69 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.69 down(g(g(g(g(g(g(a))))))) 543.34/241.69 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.69 down(g(g(g(g(g(g(b))))))) 543.34/241.69 down(g(g(g(g(g(g(c))))))) 543.34/241.69 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.69 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.69 f_flat(up(x0)) 543.34/241.69 g_flat(up(x0)) 543.34/241.69 543.34/241.69 We have to consider all minimal (P,Q,R)-chains. 543.34/241.69 ---------------------------------------- 543.34/241.69 543.34/241.69 (433) TransformationProof (EQUIVALENT) 543.34/241.69 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(down(f(g(x0))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.69 543.34/241.69 (TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))),TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.34/241.69 543.34/241.69 543.34/241.69 ---------------------------------------- 543.34/241.69 543.34/241.69 (434) 543.34/241.69 Obligation: 543.34/241.69 Q DP problem: 543.34/241.69 The TRS P consists of the following rules: 543.34/241.69 543.34/241.69 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.69 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.69 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.69 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.69 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.69 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.69 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.69 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.69 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.69 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.69 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) 543.34/241.69 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.69 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.69 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.69 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.69 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.69 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.69 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.69 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.69 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.69 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.69 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.69 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.69 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.69 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.69 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.69 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.69 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.69 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.69 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.69 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.69 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.69 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.69 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.69 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.69 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.69 543.34/241.69 The TRS R consists of the following rules: 543.34/241.69 543.34/241.69 down(a) -> up(f(a)) 543.34/241.69 down(b) -> up(g(b)) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.69 down(f(a)) -> f_flat(down(a)) 543.34/241.69 down(f(b)) -> f_flat(down(b)) 543.34/241.69 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.69 down(f(c)) -> f_flat(down(c)) 543.34/241.69 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.69 down(g(a)) -> g_flat(down(a)) 543.34/241.69 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.69 down(g(b)) -> g_flat(down(b)) 543.34/241.69 down(g(c)) -> g_flat(down(c)) 543.34/241.69 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.69 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.69 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.69 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.69 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.69 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.69 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.69 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.69 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.69 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.69 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.69 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.69 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.69 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.69 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.69 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.69 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.69 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.69 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.69 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.69 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.69 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.69 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.69 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.69 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.69 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.69 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.69 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.69 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.69 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.69 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.69 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.69 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.69 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.69 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.69 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.69 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.69 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.69 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.69 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.69 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.69 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.69 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.69 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.69 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.69 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.69 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.69 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.69 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.69 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.69 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.69 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.69 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.69 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.69 543.34/241.69 The set Q consists of the following terms: 543.34/241.69 543.34/241.69 down(a) 543.34/241.69 down(b) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.69 down(f(a)) 543.34/241.69 down(f(b)) 543.34/241.69 down(f(g(x0))) 543.34/241.69 down(f(c)) 543.34/241.69 down(f(fresh_constant)) 543.34/241.69 down(g(a)) 543.34/241.69 down(g(f(x0))) 543.34/241.69 down(g(b)) 543.34/241.69 down(g(c)) 543.34/241.69 down(g(fresh_constant)) 543.34/241.69 down(f(f(a))) 543.34/241.69 down(f(f(b))) 543.34/241.69 down(f(f(g(x0)))) 543.34/241.69 down(f(f(c))) 543.34/241.69 down(f(f(fresh_constant))) 543.34/241.69 down(g(g(a))) 543.34/241.69 down(g(g(f(x0)))) 543.34/241.69 down(g(g(b))) 543.34/241.69 down(g(g(c))) 543.34/241.69 down(g(g(fresh_constant))) 543.34/241.69 down(f(f(f(a)))) 543.34/241.69 down(f(f(f(b)))) 543.34/241.69 down(f(f(f(g(x0))))) 543.34/241.69 down(f(f(f(c)))) 543.34/241.69 down(f(f(f(fresh_constant)))) 543.34/241.69 down(g(g(g(a)))) 543.34/241.69 down(g(g(g(f(x0))))) 543.34/241.69 down(g(g(g(b)))) 543.34/241.69 down(g(g(g(c)))) 543.34/241.69 down(g(g(g(fresh_constant)))) 543.34/241.69 down(f(f(f(f(a))))) 543.34/241.69 down(f(f(f(f(b))))) 543.34/241.69 down(f(f(f(f(g(x0)))))) 543.34/241.69 down(f(f(f(f(c))))) 543.34/241.69 down(f(f(f(f(fresh_constant))))) 543.34/241.69 down(g(g(g(g(a))))) 543.34/241.69 down(g(g(g(g(f(x0)))))) 543.34/241.69 down(g(g(g(g(b))))) 543.34/241.69 down(g(g(g(g(c))))) 543.34/241.69 down(g(g(g(g(fresh_constant))))) 543.34/241.69 down(f(f(f(f(f(a)))))) 543.34/241.69 down(f(f(f(f(f(b)))))) 543.34/241.69 down(f(f(f(f(f(g(x0))))))) 543.34/241.69 down(f(f(f(f(f(c)))))) 543.34/241.69 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.69 down(g(g(g(g(g(a)))))) 543.34/241.69 down(g(g(g(g(g(f(x0))))))) 543.34/241.69 down(g(g(g(g(g(b)))))) 543.34/241.69 down(g(g(g(g(g(c)))))) 543.34/241.69 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.69 down(f(f(f(f(f(f(a))))))) 543.34/241.69 down(f(f(f(f(f(f(b))))))) 543.34/241.69 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.69 down(f(f(f(f(f(f(c))))))) 543.34/241.69 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.69 down(g(g(g(g(g(g(a))))))) 543.34/241.69 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.69 down(g(g(g(g(g(g(b))))))) 543.34/241.69 down(g(g(g(g(g(g(c))))))) 543.34/241.69 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.69 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.69 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.69 f_flat(up(x0)) 543.34/241.69 g_flat(up(x0)) 543.34/241.69 543.34/241.69 We have to consider all minimal (P,Q,R)-chains. 543.34/241.69 ---------------------------------------- 543.34/241.69 543.34/241.69 (435) TransformationProof (EQUIVALENT) 543.34/241.69 By rewriting [LPAR04] the rule TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(down(b))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.69 543.34/241.69 (TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))),TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b))))))) 543.34/241.69 543.34/241.69 543.34/241.69 ---------------------------------------- 543.34/241.69 543.34/241.69 (436) 543.34/241.69 Obligation: 543.34/241.69 Q DP problem: 543.34/241.69 The TRS P consists of the following rules: 543.34/241.69 543.34/241.69 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.69 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.69 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.69 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.69 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.69 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.69 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.69 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.69 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.69 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.69 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) 543.34/241.69 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.69 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.69 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.69 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.69 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.69 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.69 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.69 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.69 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.69 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.69 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.69 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.69 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.69 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.69 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.69 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.69 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.69 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.69 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.69 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.69 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.69 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.69 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.69 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.69 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.69 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.69 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.69 543.34/241.69 The TRS R consists of the following rules: 543.34/241.69 543.34/241.69 down(a) -> up(f(a)) 543.34/241.69 down(b) -> up(g(b)) 543.34/241.69 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.69 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.69 down(f(a)) -> f_flat(down(a)) 543.34/241.69 down(f(b)) -> f_flat(down(b)) 543.34/241.69 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.69 down(f(c)) -> f_flat(down(c)) 543.34/241.69 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.69 down(g(a)) -> g_flat(down(a)) 543.34/241.69 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.69 down(g(b)) -> g_flat(down(b)) 543.34/241.69 down(g(c)) -> g_flat(down(c)) 543.34/241.69 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.69 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.69 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.69 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.69 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.69 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.69 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.69 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.69 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.69 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.69 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.69 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.69 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.69 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.69 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.70 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.70 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.70 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.70 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.70 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.70 543.34/241.70 The set Q consists of the following terms: 543.34/241.70 543.34/241.70 down(a) 543.34/241.70 down(b) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.70 down(f(a)) 543.34/241.70 down(f(b)) 543.34/241.70 down(f(g(x0))) 543.34/241.70 down(f(c)) 543.34/241.70 down(f(fresh_constant)) 543.34/241.70 down(g(a)) 543.34/241.70 down(g(f(x0))) 543.34/241.70 down(g(b)) 543.34/241.70 down(g(c)) 543.34/241.70 down(g(fresh_constant)) 543.34/241.70 down(f(f(a))) 543.34/241.70 down(f(f(b))) 543.34/241.70 down(f(f(g(x0)))) 543.34/241.70 down(f(f(c))) 543.34/241.70 down(f(f(fresh_constant))) 543.34/241.70 down(g(g(a))) 543.34/241.70 down(g(g(f(x0)))) 543.34/241.70 down(g(g(b))) 543.34/241.70 down(g(g(c))) 543.34/241.70 down(g(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) 543.34/241.70 down(f(f(f(g(x0))))) 543.34/241.70 down(f(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) 543.34/241.70 down(g(g(g(f(x0))))) 543.34/241.70 down(g(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(x0)))))) 543.34/241.70 down(f(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(x0)))))) 543.34/241.70 down(g(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(x0))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(x0))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 f_flat(up(x0)) 543.34/241.70 g_flat(up(x0)) 543.34/241.70 543.34/241.70 We have to consider all minimal (P,Q,R)-chains. 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (437) TransformationProof (EQUIVALENT) 543.34/241.70 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(down(g(a)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.70 543.34/241.70 (TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))),TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.34/241.70 543.34/241.70 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (438) 543.34/241.70 Obligation: 543.34/241.70 Q DP problem: 543.34/241.70 The TRS P consists of the following rules: 543.34/241.70 543.34/241.70 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.70 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.70 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.70 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.70 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.70 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.70 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.70 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.70 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.70 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.70 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) 543.34/241.70 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.70 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.70 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.70 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.70 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.70 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.70 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.70 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.70 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.70 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.70 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.70 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.70 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.70 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.70 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.70 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.70 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.70 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.70 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.70 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.70 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.70 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.70 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.70 543.34/241.70 The TRS R consists of the following rules: 543.34/241.70 543.34/241.70 down(a) -> up(f(a)) 543.34/241.70 down(b) -> up(g(b)) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.70 down(f(a)) -> f_flat(down(a)) 543.34/241.70 down(f(b)) -> f_flat(down(b)) 543.34/241.70 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.70 down(f(c)) -> f_flat(down(c)) 543.34/241.70 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.70 down(g(a)) -> g_flat(down(a)) 543.34/241.70 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.70 down(g(b)) -> g_flat(down(b)) 543.34/241.70 down(g(c)) -> g_flat(down(c)) 543.34/241.70 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.70 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.70 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.70 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.70 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.70 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.70 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.70 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.70 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.70 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.70 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.70 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.70 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.70 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.70 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.70 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.70 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.70 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.70 543.34/241.70 The set Q consists of the following terms: 543.34/241.70 543.34/241.70 down(a) 543.34/241.70 down(b) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.70 down(f(a)) 543.34/241.70 down(f(b)) 543.34/241.70 down(f(g(x0))) 543.34/241.70 down(f(c)) 543.34/241.70 down(f(fresh_constant)) 543.34/241.70 down(g(a)) 543.34/241.70 down(g(f(x0))) 543.34/241.70 down(g(b)) 543.34/241.70 down(g(c)) 543.34/241.70 down(g(fresh_constant)) 543.34/241.70 down(f(f(a))) 543.34/241.70 down(f(f(b))) 543.34/241.70 down(f(f(g(x0)))) 543.34/241.70 down(f(f(c))) 543.34/241.70 down(f(f(fresh_constant))) 543.34/241.70 down(g(g(a))) 543.34/241.70 down(g(g(f(x0)))) 543.34/241.70 down(g(g(b))) 543.34/241.70 down(g(g(c))) 543.34/241.70 down(g(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) 543.34/241.70 down(f(f(f(g(x0))))) 543.34/241.70 down(f(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) 543.34/241.70 down(g(g(g(f(x0))))) 543.34/241.70 down(g(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(x0)))))) 543.34/241.70 down(f(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(x0)))))) 543.34/241.70 down(g(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(x0))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(x0))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 f_flat(up(x0)) 543.34/241.70 g_flat(up(x0)) 543.34/241.70 543.34/241.70 We have to consider all minimal (P,Q,R)-chains. 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (439) TransformationProof (EQUIVALENT) 543.34/241.70 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(down(g(f(x0))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.70 543.34/241.70 (TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))),TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.34/241.70 543.34/241.70 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (440) 543.34/241.70 Obligation: 543.34/241.70 Q DP problem: 543.34/241.70 The TRS P consists of the following rules: 543.34/241.70 543.34/241.70 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.70 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.70 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.70 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.70 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.70 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.70 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.70 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.70 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.70 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.70 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) 543.34/241.70 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.70 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.70 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.70 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.70 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.70 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.70 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.70 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.70 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.70 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.70 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.70 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.70 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.70 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.70 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.70 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.70 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.70 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.70 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.70 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.70 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.70 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.70 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.70 543.34/241.70 The TRS R consists of the following rules: 543.34/241.70 543.34/241.70 down(a) -> up(f(a)) 543.34/241.70 down(b) -> up(g(b)) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.70 down(f(a)) -> f_flat(down(a)) 543.34/241.70 down(f(b)) -> f_flat(down(b)) 543.34/241.70 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.70 down(f(c)) -> f_flat(down(c)) 543.34/241.70 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.70 down(g(a)) -> g_flat(down(a)) 543.34/241.70 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.70 down(g(b)) -> g_flat(down(b)) 543.34/241.70 down(g(c)) -> g_flat(down(c)) 543.34/241.70 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.70 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.70 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.70 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.70 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.70 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.70 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.70 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.70 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.70 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.70 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.70 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.70 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.70 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.70 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.70 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.70 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.70 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.70 543.34/241.70 The set Q consists of the following terms: 543.34/241.70 543.34/241.70 down(a) 543.34/241.70 down(b) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.70 down(f(a)) 543.34/241.70 down(f(b)) 543.34/241.70 down(f(g(x0))) 543.34/241.70 down(f(c)) 543.34/241.70 down(f(fresh_constant)) 543.34/241.70 down(g(a)) 543.34/241.70 down(g(f(x0))) 543.34/241.70 down(g(b)) 543.34/241.70 down(g(c)) 543.34/241.70 down(g(fresh_constant)) 543.34/241.70 down(f(f(a))) 543.34/241.70 down(f(f(b))) 543.34/241.70 down(f(f(g(x0)))) 543.34/241.70 down(f(f(c))) 543.34/241.70 down(f(f(fresh_constant))) 543.34/241.70 down(g(g(a))) 543.34/241.70 down(g(g(f(x0)))) 543.34/241.70 down(g(g(b))) 543.34/241.70 down(g(g(c))) 543.34/241.70 down(g(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) 543.34/241.70 down(f(f(f(g(x0))))) 543.34/241.70 down(f(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) 543.34/241.70 down(g(g(g(f(x0))))) 543.34/241.70 down(g(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(x0)))))) 543.34/241.70 down(f(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(x0)))))) 543.34/241.70 down(g(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(x0))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(x0))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 f_flat(up(x0)) 543.34/241.70 g_flat(up(x0)) 543.34/241.70 543.34/241.70 We have to consider all minimal (P,Q,R)-chains. 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (441) TransformationProof (EQUIVALENT) 543.34/241.70 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(down(f(c)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.70 543.34/241.70 (TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(c)))))),TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(c))))))) 543.34/241.70 543.34/241.70 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (442) 543.34/241.70 Obligation: 543.34/241.70 Q DP problem: 543.34/241.70 The TRS P consists of the following rules: 543.34/241.70 543.34/241.70 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.70 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.70 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.70 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.70 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.70 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.70 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.70 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.70 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.70 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.70 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.70 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.70 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.70 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.70 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.70 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.70 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.70 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.70 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.70 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.70 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.70 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.70 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.70 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.70 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.70 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.70 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.70 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.70 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.70 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.70 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.70 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.70 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.70 TOP(up(f(f(f(f(c)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(c)))))) 543.34/241.70 543.34/241.70 The TRS R consists of the following rules: 543.34/241.70 543.34/241.70 down(a) -> up(f(a)) 543.34/241.70 down(b) -> up(g(b)) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.70 down(f(a)) -> f_flat(down(a)) 543.34/241.70 down(f(b)) -> f_flat(down(b)) 543.34/241.70 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.70 down(f(c)) -> f_flat(down(c)) 543.34/241.70 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.70 down(g(a)) -> g_flat(down(a)) 543.34/241.70 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.70 down(g(b)) -> g_flat(down(b)) 543.34/241.70 down(g(c)) -> g_flat(down(c)) 543.34/241.70 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.70 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.70 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.70 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.70 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.70 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.70 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.70 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.70 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.70 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.70 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.70 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.70 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.70 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.70 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.70 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.70 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.70 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.70 543.34/241.70 The set Q consists of the following terms: 543.34/241.70 543.34/241.70 down(a) 543.34/241.70 down(b) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.70 down(f(a)) 543.34/241.70 down(f(b)) 543.34/241.70 down(f(g(x0))) 543.34/241.70 down(f(c)) 543.34/241.70 down(f(fresh_constant)) 543.34/241.70 down(g(a)) 543.34/241.70 down(g(f(x0))) 543.34/241.70 down(g(b)) 543.34/241.70 down(g(c)) 543.34/241.70 down(g(fresh_constant)) 543.34/241.70 down(f(f(a))) 543.34/241.70 down(f(f(b))) 543.34/241.70 down(f(f(g(x0)))) 543.34/241.70 down(f(f(c))) 543.34/241.70 down(f(f(fresh_constant))) 543.34/241.70 down(g(g(a))) 543.34/241.70 down(g(g(f(x0)))) 543.34/241.70 down(g(g(b))) 543.34/241.70 down(g(g(c))) 543.34/241.70 down(g(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) 543.34/241.70 down(f(f(f(g(x0))))) 543.34/241.70 down(f(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) 543.34/241.70 down(g(g(g(f(x0))))) 543.34/241.70 down(g(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(x0)))))) 543.34/241.70 down(f(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(x0)))))) 543.34/241.70 down(g(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(x0))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(x0))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 f_flat(up(x0)) 543.34/241.70 g_flat(up(x0)) 543.34/241.70 543.34/241.70 We have to consider all minimal (P,Q,R)-chains. 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (443) DependencyGraphProof (EQUIVALENT) 543.34/241.70 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (444) 543.34/241.70 Obligation: 543.34/241.70 Q DP problem: 543.34/241.70 The TRS P consists of the following rules: 543.34/241.70 543.34/241.70 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.70 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.70 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.70 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.70 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.70 TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) 543.34/241.70 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.70 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.70 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.70 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.70 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.70 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.70 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.70 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.70 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.70 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.70 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.70 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.70 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.70 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.70 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.70 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.70 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.70 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.70 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.70 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.70 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.70 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.70 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.70 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.70 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.70 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.70 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.70 543.34/241.70 The TRS R consists of the following rules: 543.34/241.70 543.34/241.70 down(a) -> up(f(a)) 543.34/241.70 down(b) -> up(g(b)) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.70 down(f(a)) -> f_flat(down(a)) 543.34/241.70 down(f(b)) -> f_flat(down(b)) 543.34/241.70 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.70 down(f(c)) -> f_flat(down(c)) 543.34/241.70 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.70 down(g(a)) -> g_flat(down(a)) 543.34/241.70 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.70 down(g(b)) -> g_flat(down(b)) 543.34/241.70 down(g(c)) -> g_flat(down(c)) 543.34/241.70 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.70 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.70 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.70 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.70 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.70 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.70 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.70 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.70 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.70 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.70 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.70 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.70 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.70 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.70 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.70 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.70 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.70 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.70 543.34/241.70 The set Q consists of the following terms: 543.34/241.70 543.34/241.70 down(a) 543.34/241.70 down(b) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.70 down(f(a)) 543.34/241.70 down(f(b)) 543.34/241.70 down(f(g(x0))) 543.34/241.70 down(f(c)) 543.34/241.70 down(f(fresh_constant)) 543.34/241.70 down(g(a)) 543.34/241.70 down(g(f(x0))) 543.34/241.70 down(g(b)) 543.34/241.70 down(g(c)) 543.34/241.70 down(g(fresh_constant)) 543.34/241.70 down(f(f(a))) 543.34/241.70 down(f(f(b))) 543.34/241.70 down(f(f(g(x0)))) 543.34/241.70 down(f(f(c))) 543.34/241.70 down(f(f(fresh_constant))) 543.34/241.70 down(g(g(a))) 543.34/241.70 down(g(g(f(x0)))) 543.34/241.70 down(g(g(b))) 543.34/241.70 down(g(g(c))) 543.34/241.70 down(g(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) 543.34/241.70 down(f(f(f(g(x0))))) 543.34/241.70 down(f(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) 543.34/241.70 down(g(g(g(f(x0))))) 543.34/241.70 down(g(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(x0)))))) 543.34/241.70 down(f(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(x0)))))) 543.34/241.70 down(g(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(x0))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(x0))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 f_flat(up(x0)) 543.34/241.70 g_flat(up(x0)) 543.34/241.70 543.34/241.70 We have to consider all minimal (P,Q,R)-chains. 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (445) TransformationProof (EQUIVALENT) 543.34/241.70 By rewriting [LPAR04] the rule TOP(up(f(f(a)))) -> TOP(f_flat(up(f(f(a))))) at position [0] we obtained the following new rules [LPAR04]: 543.34/241.70 543.34/241.70 (TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))),TOP(up(f(f(a)))) -> TOP(up(f(f(f(a)))))) 543.34/241.70 543.34/241.70 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (446) 543.34/241.70 Obligation: 543.34/241.70 Q DP problem: 543.34/241.70 The TRS P consists of the following rules: 543.34/241.70 543.34/241.70 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.70 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.70 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.70 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.70 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.70 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.70 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.70 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.70 TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) 543.34/241.70 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.70 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.70 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.70 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.70 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.70 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.70 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.70 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.70 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.70 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.70 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.70 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.70 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.70 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.70 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.70 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.70 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.70 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.70 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.70 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.70 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.70 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.70 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.70 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.70 543.34/241.70 The TRS R consists of the following rules: 543.34/241.70 543.34/241.70 down(a) -> up(f(a)) 543.34/241.70 down(b) -> up(g(b)) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.70 down(f(a)) -> f_flat(down(a)) 543.34/241.70 down(f(b)) -> f_flat(down(b)) 543.34/241.70 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.70 down(f(c)) -> f_flat(down(c)) 543.34/241.70 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.70 down(g(a)) -> g_flat(down(a)) 543.34/241.70 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.70 down(g(b)) -> g_flat(down(b)) 543.34/241.70 down(g(c)) -> g_flat(down(c)) 543.34/241.70 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.70 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.70 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.70 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.70 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.70 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.70 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.70 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.70 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.70 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.70 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.70 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.70 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.70 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.70 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.70 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.70 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.70 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.70 543.34/241.70 The set Q consists of the following terms: 543.34/241.70 543.34/241.70 down(a) 543.34/241.70 down(b) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.70 down(f(a)) 543.34/241.70 down(f(b)) 543.34/241.70 down(f(g(x0))) 543.34/241.70 down(f(c)) 543.34/241.70 down(f(fresh_constant)) 543.34/241.70 down(g(a)) 543.34/241.70 down(g(f(x0))) 543.34/241.70 down(g(b)) 543.34/241.70 down(g(c)) 543.34/241.70 down(g(fresh_constant)) 543.34/241.70 down(f(f(a))) 543.34/241.70 down(f(f(b))) 543.34/241.70 down(f(f(g(x0)))) 543.34/241.70 down(f(f(c))) 543.34/241.70 down(f(f(fresh_constant))) 543.34/241.70 down(g(g(a))) 543.34/241.70 down(g(g(f(x0)))) 543.34/241.70 down(g(g(b))) 543.34/241.70 down(g(g(c))) 543.34/241.70 down(g(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) 543.34/241.70 down(f(f(f(g(x0))))) 543.34/241.70 down(f(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) 543.34/241.70 down(g(g(g(f(x0))))) 543.34/241.70 down(g(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(x0)))))) 543.34/241.70 down(f(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(x0)))))) 543.34/241.70 down(g(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(x0))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(x0))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 f_flat(up(x0)) 543.34/241.70 g_flat(up(x0)) 543.34/241.70 543.34/241.70 We have to consider all minimal (P,Q,R)-chains. 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (447) TransformationProof (EQUIVALENT) 543.34/241.70 By rewriting [LPAR04] the rule TOP(up(g(g(b)))) -> TOP(g_flat(up(g(g(b))))) at position [0] we obtained the following new rules [LPAR04]: 543.34/241.70 543.34/241.70 (TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))),TOP(up(g(g(b)))) -> TOP(up(g(g(g(b)))))) 543.34/241.70 543.34/241.70 543.34/241.70 ---------------------------------------- 543.34/241.70 543.34/241.70 (448) 543.34/241.70 Obligation: 543.34/241.70 Q DP problem: 543.34/241.70 The TRS P consists of the following rules: 543.34/241.70 543.34/241.70 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.70 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.70 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.70 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.70 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.70 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.70 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.70 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.70 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.70 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.70 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) 543.34/241.70 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.70 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.70 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.70 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.70 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.70 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.70 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.70 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.70 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.70 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.70 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.70 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.70 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.70 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.70 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.70 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.70 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.70 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.70 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.70 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.70 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.70 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.70 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.70 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.70 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.70 543.34/241.70 The TRS R consists of the following rules: 543.34/241.70 543.34/241.70 down(a) -> up(f(a)) 543.34/241.70 down(b) -> up(g(b)) 543.34/241.70 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.70 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.70 down(f(a)) -> f_flat(down(a)) 543.34/241.70 down(f(b)) -> f_flat(down(b)) 543.34/241.70 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.70 down(f(c)) -> f_flat(down(c)) 543.34/241.70 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.70 down(g(a)) -> g_flat(down(a)) 543.34/241.70 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.70 down(g(b)) -> g_flat(down(b)) 543.34/241.70 down(g(c)) -> g_flat(down(c)) 543.34/241.70 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.70 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.70 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.70 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.70 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.70 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.70 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.70 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.70 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.70 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.70 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.70 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.70 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.70 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.70 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.70 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.70 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.70 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.70 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.70 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.70 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.70 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.70 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.70 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.70 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.70 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.70 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.70 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.70 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.70 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.70 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.70 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.70 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.70 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.70 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.70 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.70 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.70 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.70 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.70 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.70 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.70 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.70 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.70 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.70 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.70 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.70 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.70 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.70 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.70 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.70 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.70 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.70 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.70 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.70 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.71 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.71 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.71 543.34/241.71 The set Q consists of the following terms: 543.34/241.71 543.34/241.71 down(a) 543.34/241.71 down(b) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.71 down(f(a)) 543.34/241.71 down(f(b)) 543.34/241.71 down(f(g(x0))) 543.34/241.71 down(f(c)) 543.34/241.71 down(f(fresh_constant)) 543.34/241.71 down(g(a)) 543.34/241.71 down(g(f(x0))) 543.34/241.71 down(g(b)) 543.34/241.71 down(g(c)) 543.34/241.71 down(g(fresh_constant)) 543.34/241.71 down(f(f(a))) 543.34/241.71 down(f(f(b))) 543.34/241.71 down(f(f(g(x0)))) 543.34/241.71 down(f(f(c))) 543.34/241.71 down(f(f(fresh_constant))) 543.34/241.71 down(g(g(a))) 543.34/241.71 down(g(g(f(x0)))) 543.34/241.71 down(g(g(b))) 543.34/241.71 down(g(g(c))) 543.34/241.71 down(g(g(fresh_constant))) 543.34/241.71 down(f(f(f(a)))) 543.34/241.71 down(f(f(f(b)))) 543.34/241.71 down(f(f(f(g(x0))))) 543.34/241.71 down(f(f(f(c)))) 543.34/241.71 down(f(f(f(fresh_constant)))) 543.34/241.71 down(g(g(g(a)))) 543.34/241.71 down(g(g(g(f(x0))))) 543.34/241.71 down(g(g(g(b)))) 543.34/241.71 down(g(g(g(c)))) 543.34/241.71 down(g(g(g(fresh_constant)))) 543.34/241.71 down(f(f(f(f(a))))) 543.34/241.71 down(f(f(f(f(b))))) 543.34/241.71 down(f(f(f(f(g(x0)))))) 543.34/241.71 down(f(f(f(f(c))))) 543.34/241.71 down(f(f(f(f(fresh_constant))))) 543.34/241.71 down(g(g(g(g(a))))) 543.34/241.71 down(g(g(g(g(f(x0)))))) 543.34/241.71 down(g(g(g(g(b))))) 543.34/241.71 down(g(g(g(g(c))))) 543.34/241.71 down(g(g(g(g(fresh_constant))))) 543.34/241.71 down(f(f(f(f(f(a)))))) 543.34/241.71 down(f(f(f(f(f(b)))))) 543.34/241.71 down(f(f(f(f(f(g(x0))))))) 543.34/241.71 down(f(f(f(f(f(c)))))) 543.34/241.71 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.71 down(g(g(g(g(g(a)))))) 543.34/241.71 down(g(g(g(g(g(f(x0))))))) 543.34/241.71 down(g(g(g(g(g(b)))))) 543.34/241.71 down(g(g(g(g(g(c)))))) 543.34/241.71 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.71 down(f(f(f(f(f(f(a))))))) 543.34/241.71 down(f(f(f(f(f(f(b))))))) 543.34/241.71 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.71 down(f(f(f(f(f(f(c))))))) 543.34/241.71 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.71 down(g(g(g(g(g(g(a))))))) 543.34/241.71 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.71 down(g(g(g(g(g(g(b))))))) 543.34/241.71 down(g(g(g(g(g(g(c))))))) 543.34/241.71 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.71 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.71 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.71 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.71 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.71 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.71 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.71 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.71 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.71 f_flat(up(x0)) 543.34/241.71 g_flat(up(x0)) 543.34/241.71 543.34/241.71 We have to consider all minimal (P,Q,R)-chains. 543.34/241.71 ---------------------------------------- 543.34/241.71 543.34/241.71 (449) TransformationProof (EQUIVALENT) 543.34/241.71 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(down(f(fresh_constant)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.71 543.34/241.71 (TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(fresh_constant)))))),TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(fresh_constant))))))) 543.34/241.71 543.34/241.71 543.34/241.71 ---------------------------------------- 543.34/241.71 543.34/241.71 (450) 543.34/241.71 Obligation: 543.34/241.71 Q DP problem: 543.34/241.71 The TRS P consists of the following rules: 543.34/241.71 543.34/241.71 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.71 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.71 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.71 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.71 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.71 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.71 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.71 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.71 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.71 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.71 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.71 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.71 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.71 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.71 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.71 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.71 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.71 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.71 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.71 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.71 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.71 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.71 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.71 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.71 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.71 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.71 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.71 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.71 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.71 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.71 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.71 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.71 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.71 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.71 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.71 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.71 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.71 TOP(up(f(f(f(f(fresh_constant)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(fresh_constant)))))) 543.34/241.71 543.34/241.71 The TRS R consists of the following rules: 543.34/241.71 543.34/241.71 down(a) -> up(f(a)) 543.34/241.71 down(b) -> up(g(b)) 543.34/241.71 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.71 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.71 down(f(a)) -> f_flat(down(a)) 543.34/241.71 down(f(b)) -> f_flat(down(b)) 543.34/241.71 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.71 down(f(c)) -> f_flat(down(c)) 543.34/241.71 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.71 down(g(a)) -> g_flat(down(a)) 543.34/241.71 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.71 down(g(b)) -> g_flat(down(b)) 543.34/241.71 down(g(c)) -> g_flat(down(c)) 543.34/241.71 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.71 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.71 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.71 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.71 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.71 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.71 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.71 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.71 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.71 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.71 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.71 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.71 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.71 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.71 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.71 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.71 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.71 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.71 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.71 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.71 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.71 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.71 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.71 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.71 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.71 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.71 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.71 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.71 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.71 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.71 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.71 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.71 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.71 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.71 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.71 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.72 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.72 543.34/241.72 The set Q consists of the following terms: 543.34/241.72 543.34/241.72 down(a) 543.34/241.72 down(b) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.72 down(f(a)) 543.34/241.72 down(f(b)) 543.34/241.72 down(f(g(x0))) 543.34/241.72 down(f(c)) 543.34/241.72 down(f(fresh_constant)) 543.34/241.72 down(g(a)) 543.34/241.72 down(g(f(x0))) 543.34/241.72 down(g(b)) 543.34/241.72 down(g(c)) 543.34/241.72 down(g(fresh_constant)) 543.34/241.72 down(f(f(a))) 543.34/241.72 down(f(f(b))) 543.34/241.72 down(f(f(g(x0)))) 543.34/241.72 down(f(f(c))) 543.34/241.72 down(f(f(fresh_constant))) 543.34/241.72 down(g(g(a))) 543.34/241.72 down(g(g(f(x0)))) 543.34/241.72 down(g(g(b))) 543.34/241.72 down(g(g(c))) 543.34/241.72 down(g(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) 543.34/241.72 down(f(f(f(g(x0))))) 543.34/241.72 down(f(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) 543.34/241.72 down(g(g(g(f(x0))))) 543.34/241.72 down(g(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(x0)))))) 543.34/241.72 down(f(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(x0)))))) 543.34/241.72 down(g(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(x0))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(x0))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 f_flat(up(x0)) 543.34/241.72 g_flat(up(x0)) 543.34/241.72 543.34/241.72 We have to consider all minimal (P,Q,R)-chains. 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (451) DependencyGraphProof (EQUIVALENT) 543.34/241.72 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (452) 543.34/241.72 Obligation: 543.34/241.72 Q DP problem: 543.34/241.72 The TRS P consists of the following rules: 543.34/241.72 543.34/241.72 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.72 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.72 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.72 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.72 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.72 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.72 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) 543.34/241.72 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.72 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.72 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.72 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.72 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.72 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.72 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.72 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.72 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.72 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.72 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.72 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.72 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.72 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.72 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.72 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.72 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.72 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.72 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.72 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.72 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.72 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.72 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.72 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.72 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.72 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.72 543.34/241.72 The TRS R consists of the following rules: 543.34/241.72 543.34/241.72 down(a) -> up(f(a)) 543.34/241.72 down(b) -> up(g(b)) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.72 down(f(a)) -> f_flat(down(a)) 543.34/241.72 down(f(b)) -> f_flat(down(b)) 543.34/241.72 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.72 down(f(c)) -> f_flat(down(c)) 543.34/241.72 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.72 down(g(a)) -> g_flat(down(a)) 543.34/241.72 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.72 down(g(b)) -> g_flat(down(b)) 543.34/241.72 down(g(c)) -> g_flat(down(c)) 543.34/241.72 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.72 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.72 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.72 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.72 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.72 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.72 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.72 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.72 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.72 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.72 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.72 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.72 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.72 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.72 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.72 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.72 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.72 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.72 543.34/241.72 The set Q consists of the following terms: 543.34/241.72 543.34/241.72 down(a) 543.34/241.72 down(b) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.72 down(f(a)) 543.34/241.72 down(f(b)) 543.34/241.72 down(f(g(x0))) 543.34/241.72 down(f(c)) 543.34/241.72 down(f(fresh_constant)) 543.34/241.72 down(g(a)) 543.34/241.72 down(g(f(x0))) 543.34/241.72 down(g(b)) 543.34/241.72 down(g(c)) 543.34/241.72 down(g(fresh_constant)) 543.34/241.72 down(f(f(a))) 543.34/241.72 down(f(f(b))) 543.34/241.72 down(f(f(g(x0)))) 543.34/241.72 down(f(f(c))) 543.34/241.72 down(f(f(fresh_constant))) 543.34/241.72 down(g(g(a))) 543.34/241.72 down(g(g(f(x0)))) 543.34/241.72 down(g(g(b))) 543.34/241.72 down(g(g(c))) 543.34/241.72 down(g(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) 543.34/241.72 down(f(f(f(g(x0))))) 543.34/241.72 down(f(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) 543.34/241.72 down(g(g(g(f(x0))))) 543.34/241.72 down(g(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(x0)))))) 543.34/241.72 down(f(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(x0)))))) 543.34/241.72 down(g(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(x0))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(x0))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 f_flat(up(x0)) 543.34/241.72 g_flat(up(x0)) 543.34/241.72 543.34/241.72 We have to consider all minimal (P,Q,R)-chains. 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (453) TransformationProof (EQUIVALENT) 543.34/241.72 By rewriting [LPAR04] the rule TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(f_flat(up(f(a)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.72 543.34/241.72 (TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))),TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a))))))) 543.34/241.72 543.34/241.72 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (454) 543.34/241.72 Obligation: 543.34/241.72 Q DP problem: 543.34/241.72 The TRS P consists of the following rules: 543.34/241.72 543.34/241.72 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.72 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.72 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.72 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.72 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.72 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.72 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.72 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.72 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.72 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.72 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) 543.34/241.72 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.72 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.72 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.72 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.72 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.72 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.72 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.72 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.72 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.72 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.72 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.72 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.72 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.72 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.72 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.72 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.72 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.72 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.72 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.72 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.72 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.72 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))) 543.34/241.72 543.34/241.72 The TRS R consists of the following rules: 543.34/241.72 543.34/241.72 down(a) -> up(f(a)) 543.34/241.72 down(b) -> up(g(b)) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.72 down(f(a)) -> f_flat(down(a)) 543.34/241.72 down(f(b)) -> f_flat(down(b)) 543.34/241.72 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.72 down(f(c)) -> f_flat(down(c)) 543.34/241.72 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.72 down(g(a)) -> g_flat(down(a)) 543.34/241.72 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.72 down(g(b)) -> g_flat(down(b)) 543.34/241.72 down(g(c)) -> g_flat(down(c)) 543.34/241.72 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.72 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.72 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.72 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.72 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.72 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.72 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.72 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.72 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.72 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.72 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.72 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.72 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.72 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.72 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.72 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.72 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.72 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.72 543.34/241.72 The set Q consists of the following terms: 543.34/241.72 543.34/241.72 down(a) 543.34/241.72 down(b) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.72 down(f(a)) 543.34/241.72 down(f(b)) 543.34/241.72 down(f(g(x0))) 543.34/241.72 down(f(c)) 543.34/241.72 down(f(fresh_constant)) 543.34/241.72 down(g(a)) 543.34/241.72 down(g(f(x0))) 543.34/241.72 down(g(b)) 543.34/241.72 down(g(c)) 543.34/241.72 down(g(fresh_constant)) 543.34/241.72 down(f(f(a))) 543.34/241.72 down(f(f(b))) 543.34/241.72 down(f(f(g(x0)))) 543.34/241.72 down(f(f(c))) 543.34/241.72 down(f(f(fresh_constant))) 543.34/241.72 down(g(g(a))) 543.34/241.72 down(g(g(f(x0)))) 543.34/241.72 down(g(g(b))) 543.34/241.72 down(g(g(c))) 543.34/241.72 down(g(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) 543.34/241.72 down(f(f(f(g(x0))))) 543.34/241.72 down(f(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) 543.34/241.72 down(g(g(g(f(x0))))) 543.34/241.72 down(g(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(x0)))))) 543.34/241.72 down(f(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(x0)))))) 543.34/241.72 down(g(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(x0))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(x0))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 f_flat(up(x0)) 543.34/241.72 g_flat(up(x0)) 543.34/241.72 543.34/241.72 We have to consider all minimal (P,Q,R)-chains. 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (455) TransformationProof (EQUIVALENT) 543.34/241.72 By rewriting [LPAR04] the rule TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(g_flat(up(g(b)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.72 543.34/241.72 (TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))),TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b))))))) 543.34/241.72 543.34/241.72 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (456) 543.34/241.72 Obligation: 543.34/241.72 Q DP problem: 543.34/241.72 The TRS P consists of the following rules: 543.34/241.72 543.34/241.72 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.72 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.72 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.72 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.72 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.72 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.72 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.72 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.72 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.72 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.72 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.72 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.72 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) 543.34/241.72 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.72 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.72 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.72 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.72 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.72 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.72 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.72 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.72 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.72 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.72 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.72 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.72 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.72 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.72 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.72 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.72 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.72 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.72 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))) 543.34/241.72 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))) 543.34/241.72 543.34/241.72 The TRS R consists of the following rules: 543.34/241.72 543.34/241.72 down(a) -> up(f(a)) 543.34/241.72 down(b) -> up(g(b)) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.72 down(f(a)) -> f_flat(down(a)) 543.34/241.72 down(f(b)) -> f_flat(down(b)) 543.34/241.72 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.72 down(f(c)) -> f_flat(down(c)) 543.34/241.72 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.72 down(g(a)) -> g_flat(down(a)) 543.34/241.72 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.72 down(g(b)) -> g_flat(down(b)) 543.34/241.72 down(g(c)) -> g_flat(down(c)) 543.34/241.72 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.72 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.72 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.72 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.72 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.72 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.72 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.72 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.72 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.72 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.72 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.72 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.72 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.72 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.72 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.72 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.72 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.72 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.72 543.34/241.72 The set Q consists of the following terms: 543.34/241.72 543.34/241.72 down(a) 543.34/241.72 down(b) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.72 down(f(a)) 543.34/241.72 down(f(b)) 543.34/241.72 down(f(g(x0))) 543.34/241.72 down(f(c)) 543.34/241.72 down(f(fresh_constant)) 543.34/241.72 down(g(a)) 543.34/241.72 down(g(f(x0))) 543.34/241.72 down(g(b)) 543.34/241.72 down(g(c)) 543.34/241.72 down(g(fresh_constant)) 543.34/241.72 down(f(f(a))) 543.34/241.72 down(f(f(b))) 543.34/241.72 down(f(f(g(x0)))) 543.34/241.72 down(f(f(c))) 543.34/241.72 down(f(f(fresh_constant))) 543.34/241.72 down(g(g(a))) 543.34/241.72 down(g(g(f(x0)))) 543.34/241.72 down(g(g(b))) 543.34/241.72 down(g(g(c))) 543.34/241.72 down(g(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) 543.34/241.72 down(f(f(f(g(x0))))) 543.34/241.72 down(f(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) 543.34/241.72 down(g(g(g(f(x0))))) 543.34/241.72 down(g(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(x0)))))) 543.34/241.72 down(f(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(x0)))))) 543.34/241.72 down(g(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(x0))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(x0))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 f_flat(up(x0)) 543.34/241.72 g_flat(up(x0)) 543.34/241.72 543.34/241.72 We have to consider all minimal (P,Q,R)-chains. 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (457) TransformationProof (EQUIVALENT) 543.34/241.72 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(a))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.72 543.34/241.72 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.34/241.72 543.34/241.72 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (458) 543.34/241.72 Obligation: 543.34/241.72 Q DP problem: 543.34/241.72 The TRS P consists of the following rules: 543.34/241.72 543.34/241.72 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.72 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.72 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.72 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.72 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.72 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.72 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.72 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.72 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.72 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.72 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.72 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.72 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) 543.34/241.72 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.72 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.72 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.72 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.72 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.72 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.72 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.72 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.72 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.72 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.72 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.72 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.72 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.72 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.72 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.72 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.72 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.72 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))) 543.34/241.72 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.72 543.34/241.72 The TRS R consists of the following rules: 543.34/241.72 543.34/241.72 down(a) -> up(f(a)) 543.34/241.72 down(b) -> up(g(b)) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.72 down(f(a)) -> f_flat(down(a)) 543.34/241.72 down(f(b)) -> f_flat(down(b)) 543.34/241.72 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.72 down(f(c)) -> f_flat(down(c)) 543.34/241.72 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.72 down(g(a)) -> g_flat(down(a)) 543.34/241.72 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.72 down(g(b)) -> g_flat(down(b)) 543.34/241.72 down(g(c)) -> g_flat(down(c)) 543.34/241.72 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.72 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.72 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.72 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.72 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.72 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.72 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.72 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.72 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.72 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.72 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.72 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.72 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.72 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.72 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.72 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.72 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.72 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.72 543.34/241.72 The set Q consists of the following terms: 543.34/241.72 543.34/241.72 down(a) 543.34/241.72 down(b) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.72 down(f(a)) 543.34/241.72 down(f(b)) 543.34/241.72 down(f(g(x0))) 543.34/241.72 down(f(c)) 543.34/241.72 down(f(fresh_constant)) 543.34/241.72 down(g(a)) 543.34/241.72 down(g(f(x0))) 543.34/241.72 down(g(b)) 543.34/241.72 down(g(c)) 543.34/241.72 down(g(fresh_constant)) 543.34/241.72 down(f(f(a))) 543.34/241.72 down(f(f(b))) 543.34/241.72 down(f(f(g(x0)))) 543.34/241.72 down(f(f(c))) 543.34/241.72 down(f(f(fresh_constant))) 543.34/241.72 down(g(g(a))) 543.34/241.72 down(g(g(f(x0)))) 543.34/241.72 down(g(g(b))) 543.34/241.72 down(g(g(c))) 543.34/241.72 down(g(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) 543.34/241.72 down(f(f(f(g(x0))))) 543.34/241.72 down(f(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) 543.34/241.72 down(g(g(g(f(x0))))) 543.34/241.72 down(g(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(x0)))))) 543.34/241.72 down(f(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(x0)))))) 543.34/241.72 down(g(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(x0))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(x0))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 f_flat(up(x0)) 543.34/241.72 g_flat(up(x0)) 543.34/241.72 543.34/241.72 We have to consider all minimal (P,Q,R)-chains. 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (459) TransformationProof (EQUIVALENT) 543.34/241.72 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(b))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.72 543.34/241.72 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.34/241.72 543.34/241.72 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (460) 543.34/241.72 Obligation: 543.34/241.72 Q DP problem: 543.34/241.72 The TRS P consists of the following rules: 543.34/241.72 543.34/241.72 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.72 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.72 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.72 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.72 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.72 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.72 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.72 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.72 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.72 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.72 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.72 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.72 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) 543.34/241.72 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.72 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.72 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.72 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.72 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.72 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.72 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.72 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.72 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.72 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.72 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.72 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.72 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.72 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.72 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.72 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.72 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))) 543.34/241.72 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.72 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.72 543.34/241.72 The TRS R consists of the following rules: 543.34/241.72 543.34/241.72 down(a) -> up(f(a)) 543.34/241.72 down(b) -> up(g(b)) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.72 down(f(a)) -> f_flat(down(a)) 543.34/241.72 down(f(b)) -> f_flat(down(b)) 543.34/241.72 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.72 down(f(c)) -> f_flat(down(c)) 543.34/241.72 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.72 down(g(a)) -> g_flat(down(a)) 543.34/241.72 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.72 down(g(b)) -> g_flat(down(b)) 543.34/241.72 down(g(c)) -> g_flat(down(c)) 543.34/241.72 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.72 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.72 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.72 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.72 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.72 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.72 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.72 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.72 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.72 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.72 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.72 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.72 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.72 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.72 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.72 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.72 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.72 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.72 543.34/241.72 The set Q consists of the following terms: 543.34/241.72 543.34/241.72 down(a) 543.34/241.72 down(b) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.72 down(f(a)) 543.34/241.72 down(f(b)) 543.34/241.72 down(f(g(x0))) 543.34/241.72 down(f(c)) 543.34/241.72 down(f(fresh_constant)) 543.34/241.72 down(g(a)) 543.34/241.72 down(g(f(x0))) 543.34/241.72 down(g(b)) 543.34/241.72 down(g(c)) 543.34/241.72 down(g(fresh_constant)) 543.34/241.72 down(f(f(a))) 543.34/241.72 down(f(f(b))) 543.34/241.72 down(f(f(g(x0)))) 543.34/241.72 down(f(f(c))) 543.34/241.72 down(f(f(fresh_constant))) 543.34/241.72 down(g(g(a))) 543.34/241.72 down(g(g(f(x0)))) 543.34/241.72 down(g(g(b))) 543.34/241.72 down(g(g(c))) 543.34/241.72 down(g(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) 543.34/241.72 down(f(f(f(g(x0))))) 543.34/241.72 down(f(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) 543.34/241.72 down(g(g(g(f(x0))))) 543.34/241.72 down(g(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(x0)))))) 543.34/241.72 down(f(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(x0)))))) 543.34/241.72 down(g(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(x0))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(x0))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 f_flat(up(x0)) 543.34/241.72 g_flat(up(x0)) 543.34/241.72 543.34/241.72 We have to consider all minimal (P,Q,R)-chains. 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (461) TransformationProof (EQUIVALENT) 543.34/241.72 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.72 543.34/241.72 (TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))),TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.34/241.72 543.34/241.72 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (462) 543.34/241.72 Obligation: 543.34/241.72 Q DP problem: 543.34/241.72 The TRS P consists of the following rules: 543.34/241.72 543.34/241.72 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.72 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.72 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.72 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.72 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.72 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.72 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.72 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.72 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.72 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.72 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.72 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.72 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) 543.34/241.72 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.72 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.72 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.72 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.72 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.72 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.72 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.72 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.72 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.72 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.72 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.72 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.72 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.72 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.72 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.72 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))) 543.34/241.72 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.72 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.72 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.72 543.34/241.72 The TRS R consists of the following rules: 543.34/241.72 543.34/241.72 down(a) -> up(f(a)) 543.34/241.72 down(b) -> up(g(b)) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.72 down(f(a)) -> f_flat(down(a)) 543.34/241.72 down(f(b)) -> f_flat(down(b)) 543.34/241.72 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.72 down(f(c)) -> f_flat(down(c)) 543.34/241.72 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.72 down(g(a)) -> g_flat(down(a)) 543.34/241.72 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.72 down(g(b)) -> g_flat(down(b)) 543.34/241.72 down(g(c)) -> g_flat(down(c)) 543.34/241.72 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.72 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.72 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.72 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.72 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.72 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.72 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.72 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.72 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.72 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.72 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.72 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.72 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.72 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.72 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.72 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.72 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.72 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.72 543.34/241.72 The set Q consists of the following terms: 543.34/241.72 543.34/241.72 down(a) 543.34/241.72 down(b) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.72 down(f(a)) 543.34/241.72 down(f(b)) 543.34/241.72 down(f(g(x0))) 543.34/241.72 down(f(c)) 543.34/241.72 down(f(fresh_constant)) 543.34/241.72 down(g(a)) 543.34/241.72 down(g(f(x0))) 543.34/241.72 down(g(b)) 543.34/241.72 down(g(c)) 543.34/241.72 down(g(fresh_constant)) 543.34/241.72 down(f(f(a))) 543.34/241.72 down(f(f(b))) 543.34/241.72 down(f(f(g(x0)))) 543.34/241.72 down(f(f(c))) 543.34/241.72 down(f(f(fresh_constant))) 543.34/241.72 down(g(g(a))) 543.34/241.72 down(g(g(f(x0)))) 543.34/241.72 down(g(g(b))) 543.34/241.72 down(g(g(c))) 543.34/241.72 down(g(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) 543.34/241.72 down(f(f(f(g(x0))))) 543.34/241.72 down(f(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) 543.34/241.72 down(g(g(g(f(x0))))) 543.34/241.72 down(g(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(x0)))))) 543.34/241.72 down(f(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(x0)))))) 543.34/241.72 down(g(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(x0))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(x0))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 f_flat(up(x0)) 543.34/241.72 g_flat(up(x0)) 543.34/241.72 543.34/241.72 We have to consider all minimal (P,Q,R)-chains. 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (463) TransformationProof (EQUIVALENT) 543.34/241.72 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(down(g(b)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.72 543.34/241.72 (TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))),TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.34/241.72 543.34/241.72 543.34/241.72 ---------------------------------------- 543.34/241.72 543.34/241.72 (464) 543.34/241.72 Obligation: 543.34/241.72 Q DP problem: 543.34/241.72 The TRS P consists of the following rules: 543.34/241.72 543.34/241.72 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.72 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.72 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.72 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.72 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.72 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.72 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.72 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.72 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.72 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.72 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.72 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.72 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) 543.34/241.72 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.72 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.72 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.72 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.72 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.72 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.72 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.72 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.72 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.72 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.72 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.72 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.72 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.72 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.72 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.72 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.72 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))) 543.34/241.72 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))) 543.34/241.72 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.72 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.72 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.72 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.72 543.34/241.72 The TRS R consists of the following rules: 543.34/241.72 543.34/241.72 down(a) -> up(f(a)) 543.34/241.72 down(b) -> up(g(b)) 543.34/241.72 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.72 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.72 down(f(a)) -> f_flat(down(a)) 543.34/241.72 down(f(b)) -> f_flat(down(b)) 543.34/241.72 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.72 down(f(c)) -> f_flat(down(c)) 543.34/241.72 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.72 down(g(a)) -> g_flat(down(a)) 543.34/241.72 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.72 down(g(b)) -> g_flat(down(b)) 543.34/241.72 down(g(c)) -> g_flat(down(c)) 543.34/241.72 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.72 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.72 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.72 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.72 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.72 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.72 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.72 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.72 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.72 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.72 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.72 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.72 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.72 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.72 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.72 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.72 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.72 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.72 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.72 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.72 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.72 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.72 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.72 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.72 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.72 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.72 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.72 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.72 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.72 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.72 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.72 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.72 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.72 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.72 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.72 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.72 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.72 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.72 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.72 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.72 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.72 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.72 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.72 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.72 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.72 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.72 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.72 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.72 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.72 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.72 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.72 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.72 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.72 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.72 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.73 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.73 543.34/241.73 The set Q consists of the following terms: 543.34/241.73 543.34/241.73 down(a) 543.34/241.73 down(b) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.73 down(f(a)) 543.34/241.73 down(f(b)) 543.34/241.73 down(f(g(x0))) 543.34/241.73 down(f(c)) 543.34/241.73 down(f(fresh_constant)) 543.34/241.73 down(g(a)) 543.34/241.73 down(g(f(x0))) 543.34/241.73 down(g(b)) 543.34/241.73 down(g(c)) 543.34/241.73 down(g(fresh_constant)) 543.34/241.73 down(f(f(a))) 543.34/241.73 down(f(f(b))) 543.34/241.73 down(f(f(g(x0)))) 543.34/241.73 down(f(f(c))) 543.34/241.73 down(f(f(fresh_constant))) 543.34/241.73 down(g(g(a))) 543.34/241.73 down(g(g(f(x0)))) 543.34/241.73 down(g(g(b))) 543.34/241.73 down(g(g(c))) 543.34/241.73 down(g(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) 543.34/241.73 down(f(f(f(g(x0))))) 543.34/241.73 down(f(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) 543.34/241.73 down(g(g(g(f(x0))))) 543.34/241.73 down(g(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(x0)))))) 543.34/241.73 down(f(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(x0)))))) 543.34/241.73 down(g(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(x0))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(x0))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 f_flat(up(x0)) 543.34/241.73 g_flat(up(x0)) 543.34/241.73 543.34/241.73 We have to consider all minimal (P,Q,R)-chains. 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (465) TransformationProof (EQUIVALENT) 543.34/241.73 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(down(g(c)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.73 543.34/241.73 (TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(c)))))),TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(c))))))) 543.34/241.73 543.34/241.73 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (466) 543.34/241.73 Obligation: 543.34/241.73 Q DP problem: 543.34/241.73 The TRS P consists of the following rules: 543.34/241.73 543.34/241.73 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.73 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.73 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.73 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.73 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.73 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.73 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.73 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.73 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.73 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.73 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.73 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.73 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.73 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.73 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.73 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.73 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.73 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.73 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.73 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.73 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.73 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.73 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.73 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.73 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.73 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.73 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))) 543.34/241.73 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))) 543.34/241.73 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.73 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.73 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.73 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.73 TOP(up(g(g(g(g(c)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(c)))))) 543.34/241.73 543.34/241.73 The TRS R consists of the following rules: 543.34/241.73 543.34/241.73 down(a) -> up(f(a)) 543.34/241.73 down(b) -> up(g(b)) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.73 down(f(a)) -> f_flat(down(a)) 543.34/241.73 down(f(b)) -> f_flat(down(b)) 543.34/241.73 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.73 down(f(c)) -> f_flat(down(c)) 543.34/241.73 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.73 down(g(a)) -> g_flat(down(a)) 543.34/241.73 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.73 down(g(b)) -> g_flat(down(b)) 543.34/241.73 down(g(c)) -> g_flat(down(c)) 543.34/241.73 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.73 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.73 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.73 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.73 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.73 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.73 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.73 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.73 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.73 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.73 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.73 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.73 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.73 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.73 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.73 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.73 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.73 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.73 543.34/241.73 The set Q consists of the following terms: 543.34/241.73 543.34/241.73 down(a) 543.34/241.73 down(b) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.73 down(f(a)) 543.34/241.73 down(f(b)) 543.34/241.73 down(f(g(x0))) 543.34/241.73 down(f(c)) 543.34/241.73 down(f(fresh_constant)) 543.34/241.73 down(g(a)) 543.34/241.73 down(g(f(x0))) 543.34/241.73 down(g(b)) 543.34/241.73 down(g(c)) 543.34/241.73 down(g(fresh_constant)) 543.34/241.73 down(f(f(a))) 543.34/241.73 down(f(f(b))) 543.34/241.73 down(f(f(g(x0)))) 543.34/241.73 down(f(f(c))) 543.34/241.73 down(f(f(fresh_constant))) 543.34/241.73 down(g(g(a))) 543.34/241.73 down(g(g(f(x0)))) 543.34/241.73 down(g(g(b))) 543.34/241.73 down(g(g(c))) 543.34/241.73 down(g(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) 543.34/241.73 down(f(f(f(g(x0))))) 543.34/241.73 down(f(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) 543.34/241.73 down(g(g(g(f(x0))))) 543.34/241.73 down(g(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(x0)))))) 543.34/241.73 down(f(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(x0)))))) 543.34/241.73 down(g(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(x0))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(x0))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 f_flat(up(x0)) 543.34/241.73 g_flat(up(x0)) 543.34/241.73 543.34/241.73 We have to consider all minimal (P,Q,R)-chains. 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (467) DependencyGraphProof (EQUIVALENT) 543.34/241.73 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (468) 543.34/241.73 Obligation: 543.34/241.73 Q DP problem: 543.34/241.73 The TRS P consists of the following rules: 543.34/241.73 543.34/241.73 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.73 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.73 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.73 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.73 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.73 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.73 TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))) 543.34/241.73 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.73 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.73 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.73 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.73 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))) 543.34/241.73 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.73 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.73 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.73 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.73 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.73 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.73 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.73 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.73 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.73 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.73 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.73 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.73 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.73 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.73 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.73 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.73 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.73 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.73 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.73 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.73 543.34/241.73 The TRS R consists of the following rules: 543.34/241.73 543.34/241.73 down(a) -> up(f(a)) 543.34/241.73 down(b) -> up(g(b)) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.73 down(f(a)) -> f_flat(down(a)) 543.34/241.73 down(f(b)) -> f_flat(down(b)) 543.34/241.73 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.73 down(f(c)) -> f_flat(down(c)) 543.34/241.73 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.73 down(g(a)) -> g_flat(down(a)) 543.34/241.73 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.73 down(g(b)) -> g_flat(down(b)) 543.34/241.73 down(g(c)) -> g_flat(down(c)) 543.34/241.73 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.73 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.73 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.73 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.73 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.73 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.73 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.73 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.73 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.73 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.73 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.73 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.73 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.73 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.73 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.73 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.73 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.73 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.73 543.34/241.73 The set Q consists of the following terms: 543.34/241.73 543.34/241.73 down(a) 543.34/241.73 down(b) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.73 down(f(a)) 543.34/241.73 down(f(b)) 543.34/241.73 down(f(g(x0))) 543.34/241.73 down(f(c)) 543.34/241.73 down(f(fresh_constant)) 543.34/241.73 down(g(a)) 543.34/241.73 down(g(f(x0))) 543.34/241.73 down(g(b)) 543.34/241.73 down(g(c)) 543.34/241.73 down(g(fresh_constant)) 543.34/241.73 down(f(f(a))) 543.34/241.73 down(f(f(b))) 543.34/241.73 down(f(f(g(x0)))) 543.34/241.73 down(f(f(c))) 543.34/241.73 down(f(f(fresh_constant))) 543.34/241.73 down(g(g(a))) 543.34/241.73 down(g(g(f(x0)))) 543.34/241.73 down(g(g(b))) 543.34/241.73 down(g(g(c))) 543.34/241.73 down(g(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) 543.34/241.73 down(f(f(f(g(x0))))) 543.34/241.73 down(f(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) 543.34/241.73 down(g(g(g(f(x0))))) 543.34/241.73 down(g(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(x0)))))) 543.34/241.73 down(f(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(x0)))))) 543.34/241.73 down(g(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(x0))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(x0))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 f_flat(up(x0)) 543.34/241.73 g_flat(up(x0)) 543.34/241.73 543.34/241.73 We have to consider all minimal (P,Q,R)-chains. 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (469) TransformationProof (EQUIVALENT) 543.34/241.73 By rewriting [LPAR04] the rule TOP(up(f(f(f(a))))) -> TOP(f_flat(f_flat(up(f(f(a)))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.34/241.73 543.34/241.73 (TOP(up(f(f(f(a))))) -> TOP(f_flat(up(f(f(f(a)))))),TOP(up(f(f(f(a))))) -> TOP(f_flat(up(f(f(f(a))))))) 543.34/241.73 543.34/241.73 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (470) 543.34/241.73 Obligation: 543.34/241.73 Q DP problem: 543.34/241.73 The TRS P consists of the following rules: 543.34/241.73 543.34/241.73 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.73 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.73 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.73 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.73 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.73 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.73 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.73 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.73 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.73 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.73 TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))) 543.34/241.73 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.73 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.73 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.73 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.73 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.73 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.73 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.73 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.73 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.73 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.73 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.73 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.73 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.73 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.73 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.73 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.73 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.73 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.73 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.73 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(a))))) -> TOP(f_flat(up(f(f(f(a)))))) 543.34/241.73 543.34/241.73 The TRS R consists of the following rules: 543.34/241.73 543.34/241.73 down(a) -> up(f(a)) 543.34/241.73 down(b) -> up(g(b)) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.73 down(f(a)) -> f_flat(down(a)) 543.34/241.73 down(f(b)) -> f_flat(down(b)) 543.34/241.73 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.73 down(f(c)) -> f_flat(down(c)) 543.34/241.73 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.73 down(g(a)) -> g_flat(down(a)) 543.34/241.73 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.73 down(g(b)) -> g_flat(down(b)) 543.34/241.73 down(g(c)) -> g_flat(down(c)) 543.34/241.73 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.73 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.73 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.73 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.73 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.73 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.73 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.73 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.73 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.73 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.73 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.73 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.73 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.73 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.73 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.73 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.73 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.73 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.73 543.34/241.73 The set Q consists of the following terms: 543.34/241.73 543.34/241.73 down(a) 543.34/241.73 down(b) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.73 down(f(a)) 543.34/241.73 down(f(b)) 543.34/241.73 down(f(g(x0))) 543.34/241.73 down(f(c)) 543.34/241.73 down(f(fresh_constant)) 543.34/241.73 down(g(a)) 543.34/241.73 down(g(f(x0))) 543.34/241.73 down(g(b)) 543.34/241.73 down(g(c)) 543.34/241.73 down(g(fresh_constant)) 543.34/241.73 down(f(f(a))) 543.34/241.73 down(f(f(b))) 543.34/241.73 down(f(f(g(x0)))) 543.34/241.73 down(f(f(c))) 543.34/241.73 down(f(f(fresh_constant))) 543.34/241.73 down(g(g(a))) 543.34/241.73 down(g(g(f(x0)))) 543.34/241.73 down(g(g(b))) 543.34/241.73 down(g(g(c))) 543.34/241.73 down(g(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) 543.34/241.73 down(f(f(f(g(x0))))) 543.34/241.73 down(f(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) 543.34/241.73 down(g(g(g(f(x0))))) 543.34/241.73 down(g(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(x0)))))) 543.34/241.73 down(f(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(x0)))))) 543.34/241.73 down(g(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(x0))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(x0))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 f_flat(up(x0)) 543.34/241.73 g_flat(up(x0)) 543.34/241.73 543.34/241.73 We have to consider all minimal (P,Q,R)-chains. 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (471) TransformationProof (EQUIVALENT) 543.34/241.73 By rewriting [LPAR04] the rule TOP(up(g(g(g(b))))) -> TOP(g_flat(g_flat(up(g(g(b)))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.34/241.73 543.34/241.73 (TOP(up(g(g(g(b))))) -> TOP(g_flat(up(g(g(g(b)))))),TOP(up(g(g(g(b))))) -> TOP(g_flat(up(g(g(g(b))))))) 543.34/241.73 543.34/241.73 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (472) 543.34/241.73 Obligation: 543.34/241.73 Q DP problem: 543.34/241.73 The TRS P consists of the following rules: 543.34/241.73 543.34/241.73 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.73 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.73 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.73 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.73 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.73 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.73 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.73 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.73 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.73 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.73 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.73 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.73 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) 543.34/241.73 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.73 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.73 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.73 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.73 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.73 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.73 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.73 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.73 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.73 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.73 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.73 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.73 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.73 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.73 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.73 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.73 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(a))))) -> TOP(f_flat(up(f(f(f(a)))))) 543.34/241.73 TOP(up(g(g(g(b))))) -> TOP(g_flat(up(g(g(g(b)))))) 543.34/241.73 543.34/241.73 The TRS R consists of the following rules: 543.34/241.73 543.34/241.73 down(a) -> up(f(a)) 543.34/241.73 down(b) -> up(g(b)) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.73 down(f(a)) -> f_flat(down(a)) 543.34/241.73 down(f(b)) -> f_flat(down(b)) 543.34/241.73 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.73 down(f(c)) -> f_flat(down(c)) 543.34/241.73 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.73 down(g(a)) -> g_flat(down(a)) 543.34/241.73 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.73 down(g(b)) -> g_flat(down(b)) 543.34/241.73 down(g(c)) -> g_flat(down(c)) 543.34/241.73 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.73 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.73 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.73 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.73 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.73 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.73 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.73 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.73 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.73 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.73 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.73 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.73 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.73 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.73 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.73 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.73 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.73 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.73 543.34/241.73 The set Q consists of the following terms: 543.34/241.73 543.34/241.73 down(a) 543.34/241.73 down(b) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.73 down(f(a)) 543.34/241.73 down(f(b)) 543.34/241.73 down(f(g(x0))) 543.34/241.73 down(f(c)) 543.34/241.73 down(f(fresh_constant)) 543.34/241.73 down(g(a)) 543.34/241.73 down(g(f(x0))) 543.34/241.73 down(g(b)) 543.34/241.73 down(g(c)) 543.34/241.73 down(g(fresh_constant)) 543.34/241.73 down(f(f(a))) 543.34/241.73 down(f(f(b))) 543.34/241.73 down(f(f(g(x0)))) 543.34/241.73 down(f(f(c))) 543.34/241.73 down(f(f(fresh_constant))) 543.34/241.73 down(g(g(a))) 543.34/241.73 down(g(g(f(x0)))) 543.34/241.73 down(g(g(b))) 543.34/241.73 down(g(g(c))) 543.34/241.73 down(g(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) 543.34/241.73 down(f(f(f(g(x0))))) 543.34/241.73 down(f(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) 543.34/241.73 down(g(g(g(f(x0))))) 543.34/241.73 down(g(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(x0)))))) 543.34/241.73 down(f(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(x0)))))) 543.34/241.73 down(g(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(x0))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(x0))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 f_flat(up(x0)) 543.34/241.73 g_flat(up(x0)) 543.34/241.73 543.34/241.73 We have to consider all minimal (P,Q,R)-chains. 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (473) TransformationProof (EQUIVALENT) 543.34/241.73 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(down(g(fresh_constant)))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.73 543.34/241.73 (TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(fresh_constant)))))),TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(fresh_constant))))))) 543.34/241.73 543.34/241.73 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (474) 543.34/241.73 Obligation: 543.34/241.73 Q DP problem: 543.34/241.73 The TRS P consists of the following rules: 543.34/241.73 543.34/241.73 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.73 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.73 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.73 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.73 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.73 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.73 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.73 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.73 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.73 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.73 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.73 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.73 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.73 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.73 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.73 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.73 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.73 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.73 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.73 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.73 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.73 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.73 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.73 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.73 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.73 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.73 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.73 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.73 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(a))))) -> TOP(f_flat(up(f(f(f(a)))))) 543.34/241.73 TOP(up(g(g(g(b))))) -> TOP(g_flat(up(g(g(g(b)))))) 543.34/241.73 TOP(up(g(g(g(g(fresh_constant)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(fresh_constant)))))) 543.34/241.73 543.34/241.73 The TRS R consists of the following rules: 543.34/241.73 543.34/241.73 down(a) -> up(f(a)) 543.34/241.73 down(b) -> up(g(b)) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.73 down(f(a)) -> f_flat(down(a)) 543.34/241.73 down(f(b)) -> f_flat(down(b)) 543.34/241.73 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.73 down(f(c)) -> f_flat(down(c)) 543.34/241.73 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.73 down(g(a)) -> g_flat(down(a)) 543.34/241.73 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.73 down(g(b)) -> g_flat(down(b)) 543.34/241.73 down(g(c)) -> g_flat(down(c)) 543.34/241.73 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.73 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.73 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.73 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.73 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.73 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.73 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.73 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.73 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.73 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.73 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.73 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.73 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.73 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.73 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.73 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.73 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.73 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.73 543.34/241.73 The set Q consists of the following terms: 543.34/241.73 543.34/241.73 down(a) 543.34/241.73 down(b) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.73 down(f(a)) 543.34/241.73 down(f(b)) 543.34/241.73 down(f(g(x0))) 543.34/241.73 down(f(c)) 543.34/241.73 down(f(fresh_constant)) 543.34/241.73 down(g(a)) 543.34/241.73 down(g(f(x0))) 543.34/241.73 down(g(b)) 543.34/241.73 down(g(c)) 543.34/241.73 down(g(fresh_constant)) 543.34/241.73 down(f(f(a))) 543.34/241.73 down(f(f(b))) 543.34/241.73 down(f(f(g(x0)))) 543.34/241.73 down(f(f(c))) 543.34/241.73 down(f(f(fresh_constant))) 543.34/241.73 down(g(g(a))) 543.34/241.73 down(g(g(f(x0)))) 543.34/241.73 down(g(g(b))) 543.34/241.73 down(g(g(c))) 543.34/241.73 down(g(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) 543.34/241.73 down(f(f(f(g(x0))))) 543.34/241.73 down(f(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) 543.34/241.73 down(g(g(g(f(x0))))) 543.34/241.73 down(g(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(x0)))))) 543.34/241.73 down(f(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(x0)))))) 543.34/241.73 down(g(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(x0))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(x0))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 f_flat(up(x0)) 543.34/241.73 g_flat(up(x0)) 543.34/241.73 543.34/241.73 We have to consider all minimal (P,Q,R)-chains. 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (475) DependencyGraphProof (EQUIVALENT) 543.34/241.73 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (476) 543.34/241.73 Obligation: 543.34/241.73 Q DP problem: 543.34/241.73 The TRS P consists of the following rules: 543.34/241.73 543.34/241.73 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.73 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.73 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.73 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.73 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.73 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.73 TOP(up(f(f(f(a))))) -> TOP(f_flat(up(f(f(f(a)))))) 543.34/241.73 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.73 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.73 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.73 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.73 TOP(up(g(g(g(b))))) -> TOP(g_flat(up(g(g(g(b)))))) 543.34/241.73 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.73 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.73 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.73 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.73 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.73 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.73 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.73 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.73 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.73 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.73 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.73 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.73 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.73 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.73 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.73 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.73 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.73 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.73 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.73 543.34/241.73 The TRS R consists of the following rules: 543.34/241.73 543.34/241.73 down(a) -> up(f(a)) 543.34/241.73 down(b) -> up(g(b)) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.73 down(f(a)) -> f_flat(down(a)) 543.34/241.73 down(f(b)) -> f_flat(down(b)) 543.34/241.73 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.73 down(f(c)) -> f_flat(down(c)) 543.34/241.73 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.73 down(g(a)) -> g_flat(down(a)) 543.34/241.73 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.73 down(g(b)) -> g_flat(down(b)) 543.34/241.73 down(g(c)) -> g_flat(down(c)) 543.34/241.73 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.73 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.73 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.73 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.73 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.73 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.73 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.73 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.73 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.73 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.73 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.73 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.73 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.73 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.73 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.73 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.73 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.73 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.73 543.34/241.73 The set Q consists of the following terms: 543.34/241.73 543.34/241.73 down(a) 543.34/241.73 down(b) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.73 down(f(a)) 543.34/241.73 down(f(b)) 543.34/241.73 down(f(g(x0))) 543.34/241.73 down(f(c)) 543.34/241.73 down(f(fresh_constant)) 543.34/241.73 down(g(a)) 543.34/241.73 down(g(f(x0))) 543.34/241.73 down(g(b)) 543.34/241.73 down(g(c)) 543.34/241.73 down(g(fresh_constant)) 543.34/241.73 down(f(f(a))) 543.34/241.73 down(f(f(b))) 543.34/241.73 down(f(f(g(x0)))) 543.34/241.73 down(f(f(c))) 543.34/241.73 down(f(f(fresh_constant))) 543.34/241.73 down(g(g(a))) 543.34/241.73 down(g(g(f(x0)))) 543.34/241.73 down(g(g(b))) 543.34/241.73 down(g(g(c))) 543.34/241.73 down(g(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) 543.34/241.73 down(f(f(f(g(x0))))) 543.34/241.73 down(f(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) 543.34/241.73 down(g(g(g(f(x0))))) 543.34/241.73 down(g(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(x0)))))) 543.34/241.73 down(f(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(x0)))))) 543.34/241.73 down(g(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(x0))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(x0))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 f_flat(up(x0)) 543.34/241.73 g_flat(up(x0)) 543.34/241.73 543.34/241.73 We have to consider all minimal (P,Q,R)-chains. 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (477) TransformationProof (EQUIVALENT) 543.34/241.73 By rewriting [LPAR04] the rule TOP(up(f(f(f(a))))) -> TOP(f_flat(up(f(f(f(a)))))) at position [0] we obtained the following new rules [LPAR04]: 543.34/241.73 543.34/241.73 (TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))),TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a))))))) 543.34/241.73 543.34/241.73 543.34/241.73 ---------------------------------------- 543.34/241.73 543.34/241.73 (478) 543.34/241.73 Obligation: 543.34/241.73 Q DP problem: 543.34/241.73 The TRS P consists of the following rules: 543.34/241.73 543.34/241.73 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.73 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.73 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.73 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.73 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.73 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.73 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.73 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.73 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.73 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.73 TOP(up(g(g(g(b))))) -> TOP(g_flat(up(g(g(g(b)))))) 543.34/241.73 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.73 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.73 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.73 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.73 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.73 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.73 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.73 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.73 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.73 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.73 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.73 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.73 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.73 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.73 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.73 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.73 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.73 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.73 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.73 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.73 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.73 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.73 543.34/241.73 The TRS R consists of the following rules: 543.34/241.73 543.34/241.73 down(a) -> up(f(a)) 543.34/241.73 down(b) -> up(g(b)) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.73 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.73 down(f(a)) -> f_flat(down(a)) 543.34/241.73 down(f(b)) -> f_flat(down(b)) 543.34/241.73 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.73 down(f(c)) -> f_flat(down(c)) 543.34/241.73 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.73 down(g(a)) -> g_flat(down(a)) 543.34/241.73 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.73 down(g(b)) -> g_flat(down(b)) 543.34/241.73 down(g(c)) -> g_flat(down(c)) 543.34/241.73 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.73 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.73 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.73 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.73 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.73 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.73 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.73 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.73 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.73 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.73 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.73 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.73 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.73 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.73 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.73 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.73 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.73 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.73 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.73 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.73 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.73 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.73 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.73 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.73 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.73 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.73 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.73 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.73 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.73 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.73 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.73 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.73 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.73 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.73 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.73 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.73 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.73 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.73 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.73 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.73 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.73 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.73 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.73 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.73 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.73 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.73 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.73 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.73 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.73 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.73 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.73 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.73 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.73 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.73 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.74 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.74 543.34/241.74 The set Q consists of the following terms: 543.34/241.74 543.34/241.74 down(a) 543.34/241.74 down(b) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.74 down(f(a)) 543.34/241.74 down(f(b)) 543.34/241.74 down(f(g(x0))) 543.34/241.74 down(f(c)) 543.34/241.74 down(f(fresh_constant)) 543.34/241.74 down(g(a)) 543.34/241.74 down(g(f(x0))) 543.34/241.74 down(g(b)) 543.34/241.74 down(g(c)) 543.34/241.74 down(g(fresh_constant)) 543.34/241.74 down(f(f(a))) 543.34/241.74 down(f(f(b))) 543.34/241.74 down(f(f(g(x0)))) 543.34/241.74 down(f(f(c))) 543.34/241.74 down(f(f(fresh_constant))) 543.34/241.74 down(g(g(a))) 543.34/241.74 down(g(g(f(x0)))) 543.34/241.74 down(g(g(b))) 543.34/241.74 down(g(g(c))) 543.34/241.74 down(g(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) 543.34/241.74 down(f(f(f(g(x0))))) 543.34/241.74 down(f(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) 543.34/241.74 down(g(g(g(f(x0))))) 543.34/241.74 down(g(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(x0)))))) 543.34/241.74 down(f(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(x0)))))) 543.34/241.74 down(g(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(x0))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(x0))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 f_flat(up(x0)) 543.34/241.74 g_flat(up(x0)) 543.34/241.74 543.34/241.74 We have to consider all minimal (P,Q,R)-chains. 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (479) TransformationProof (EQUIVALENT) 543.34/241.74 By rewriting [LPAR04] the rule TOP(up(g(g(g(b))))) -> TOP(g_flat(up(g(g(g(b)))))) at position [0] we obtained the following new rules [LPAR04]: 543.34/241.74 543.34/241.74 (TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))),TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b))))))) 543.34/241.74 543.34/241.74 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (480) 543.34/241.74 Obligation: 543.34/241.74 Q DP problem: 543.34/241.74 The TRS P consists of the following rules: 543.34/241.74 543.34/241.74 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.74 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.74 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.74 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.74 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.74 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.74 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.74 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.74 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.74 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.74 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.74 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.74 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) 543.34/241.74 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.74 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.74 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.74 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.74 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.74 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.74 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.74 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.74 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.74 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.74 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.74 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.74 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.74 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.74 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.74 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.74 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.74 543.34/241.74 The TRS R consists of the following rules: 543.34/241.74 543.34/241.74 down(a) -> up(f(a)) 543.34/241.74 down(b) -> up(g(b)) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.74 down(f(a)) -> f_flat(down(a)) 543.34/241.74 down(f(b)) -> f_flat(down(b)) 543.34/241.74 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.74 down(f(c)) -> f_flat(down(c)) 543.34/241.74 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.74 down(g(a)) -> g_flat(down(a)) 543.34/241.74 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.74 down(g(b)) -> g_flat(down(b)) 543.34/241.74 down(g(c)) -> g_flat(down(c)) 543.34/241.74 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.74 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.74 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.74 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.74 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.74 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.74 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.74 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.74 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.74 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.74 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.74 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.74 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.74 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.74 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.74 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.74 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.74 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.74 543.34/241.74 The set Q consists of the following terms: 543.34/241.74 543.34/241.74 down(a) 543.34/241.74 down(b) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.74 down(f(a)) 543.34/241.74 down(f(b)) 543.34/241.74 down(f(g(x0))) 543.34/241.74 down(f(c)) 543.34/241.74 down(f(fresh_constant)) 543.34/241.74 down(g(a)) 543.34/241.74 down(g(f(x0))) 543.34/241.74 down(g(b)) 543.34/241.74 down(g(c)) 543.34/241.74 down(g(fresh_constant)) 543.34/241.74 down(f(f(a))) 543.34/241.74 down(f(f(b))) 543.34/241.74 down(f(f(g(x0)))) 543.34/241.74 down(f(f(c))) 543.34/241.74 down(f(f(fresh_constant))) 543.34/241.74 down(g(g(a))) 543.34/241.74 down(g(g(f(x0)))) 543.34/241.74 down(g(g(b))) 543.34/241.74 down(g(g(c))) 543.34/241.74 down(g(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) 543.34/241.74 down(f(f(f(g(x0))))) 543.34/241.74 down(f(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) 543.34/241.74 down(g(g(g(f(x0))))) 543.34/241.74 down(g(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(x0)))))) 543.34/241.74 down(f(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(x0)))))) 543.34/241.74 down(g(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(x0))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(x0))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 f_flat(up(x0)) 543.34/241.74 g_flat(up(x0)) 543.34/241.74 543.34/241.74 We have to consider all minimal (P,Q,R)-chains. 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (481) TransformationProof (EQUIVALENT) 543.34/241.74 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(a))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.74 543.34/241.74 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.34/241.74 543.34/241.74 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (482) 543.34/241.74 Obligation: 543.34/241.74 Q DP problem: 543.34/241.74 The TRS P consists of the following rules: 543.34/241.74 543.34/241.74 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.74 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.74 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.74 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.74 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.74 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.74 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.74 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.74 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.74 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.74 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.74 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.74 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.74 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.74 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.74 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.74 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.74 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.74 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.74 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.74 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.74 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.74 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.74 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.74 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.74 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.74 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.74 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.74 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.74 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.74 543.34/241.74 The TRS R consists of the following rules: 543.34/241.74 543.34/241.74 down(a) -> up(f(a)) 543.34/241.74 down(b) -> up(g(b)) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.74 down(f(a)) -> f_flat(down(a)) 543.34/241.74 down(f(b)) -> f_flat(down(b)) 543.34/241.74 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.74 down(f(c)) -> f_flat(down(c)) 543.34/241.74 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.74 down(g(a)) -> g_flat(down(a)) 543.34/241.74 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.74 down(g(b)) -> g_flat(down(b)) 543.34/241.74 down(g(c)) -> g_flat(down(c)) 543.34/241.74 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.74 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.74 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.74 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.74 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.74 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.74 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.74 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.74 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.74 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.74 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.74 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.74 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.74 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.74 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.74 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.74 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.74 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.74 543.34/241.74 The set Q consists of the following terms: 543.34/241.74 543.34/241.74 down(a) 543.34/241.74 down(b) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.74 down(f(a)) 543.34/241.74 down(f(b)) 543.34/241.74 down(f(g(x0))) 543.34/241.74 down(f(c)) 543.34/241.74 down(f(fresh_constant)) 543.34/241.74 down(g(a)) 543.34/241.74 down(g(f(x0))) 543.34/241.74 down(g(b)) 543.34/241.74 down(g(c)) 543.34/241.74 down(g(fresh_constant)) 543.34/241.74 down(f(f(a))) 543.34/241.74 down(f(f(b))) 543.34/241.74 down(f(f(g(x0)))) 543.34/241.74 down(f(f(c))) 543.34/241.74 down(f(f(fresh_constant))) 543.34/241.74 down(g(g(a))) 543.34/241.74 down(g(g(f(x0)))) 543.34/241.74 down(g(g(b))) 543.34/241.74 down(g(g(c))) 543.34/241.74 down(g(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) 543.34/241.74 down(f(f(f(g(x0))))) 543.34/241.74 down(f(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) 543.34/241.74 down(g(g(g(f(x0))))) 543.34/241.74 down(g(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(x0)))))) 543.34/241.74 down(f(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(x0)))))) 543.34/241.74 down(g(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(x0))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(x0))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 f_flat(up(x0)) 543.34/241.74 g_flat(up(x0)) 543.34/241.74 543.34/241.74 We have to consider all minimal (P,Q,R)-chains. 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (483) TransformationProof (EQUIVALENT) 543.34/241.74 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.74 543.34/241.74 (TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))),TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.34/241.74 543.34/241.74 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (484) 543.34/241.74 Obligation: 543.34/241.74 Q DP problem: 543.34/241.74 The TRS P consists of the following rules: 543.34/241.74 543.34/241.74 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.74 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.74 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.74 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.74 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.74 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.74 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.74 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.74 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.74 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.74 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.74 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.74 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) 543.34/241.74 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.74 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.74 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.74 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.74 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.74 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.74 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.74 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.74 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.74 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.74 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.74 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.74 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.74 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.74 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.74 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.74 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.74 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.74 543.34/241.74 The TRS R consists of the following rules: 543.34/241.74 543.34/241.74 down(a) -> up(f(a)) 543.34/241.74 down(b) -> up(g(b)) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.74 down(f(a)) -> f_flat(down(a)) 543.34/241.74 down(f(b)) -> f_flat(down(b)) 543.34/241.74 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.74 down(f(c)) -> f_flat(down(c)) 543.34/241.74 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.74 down(g(a)) -> g_flat(down(a)) 543.34/241.74 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.74 down(g(b)) -> g_flat(down(b)) 543.34/241.74 down(g(c)) -> g_flat(down(c)) 543.34/241.74 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.74 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.74 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.74 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.74 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.74 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.74 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.74 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.74 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.74 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.74 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.74 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.74 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.74 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.74 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.74 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.74 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.74 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.74 543.34/241.74 The set Q consists of the following terms: 543.34/241.74 543.34/241.74 down(a) 543.34/241.74 down(b) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.74 down(f(a)) 543.34/241.74 down(f(b)) 543.34/241.74 down(f(g(x0))) 543.34/241.74 down(f(c)) 543.34/241.74 down(f(fresh_constant)) 543.34/241.74 down(g(a)) 543.34/241.74 down(g(f(x0))) 543.34/241.74 down(g(b)) 543.34/241.74 down(g(c)) 543.34/241.74 down(g(fresh_constant)) 543.34/241.74 down(f(f(a))) 543.34/241.74 down(f(f(b))) 543.34/241.74 down(f(f(g(x0)))) 543.34/241.74 down(f(f(c))) 543.34/241.74 down(f(f(fresh_constant))) 543.34/241.74 down(g(g(a))) 543.34/241.74 down(g(g(f(x0)))) 543.34/241.74 down(g(g(b))) 543.34/241.74 down(g(g(c))) 543.34/241.74 down(g(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) 543.34/241.74 down(f(f(f(g(x0))))) 543.34/241.74 down(f(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) 543.34/241.74 down(g(g(g(f(x0))))) 543.34/241.74 down(g(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(x0)))))) 543.34/241.74 down(f(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(x0)))))) 543.34/241.74 down(g(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(x0))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(x0))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 f_flat(up(x0)) 543.34/241.74 g_flat(up(x0)) 543.34/241.74 543.34/241.74 We have to consider all minimal (P,Q,R)-chains. 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (485) TransformationProof (EQUIVALENT) 543.34/241.74 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(c))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.74 543.34/241.74 (TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))),TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.34/241.74 543.34/241.74 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (486) 543.34/241.74 Obligation: 543.34/241.74 Q DP problem: 543.34/241.74 The TRS P consists of the following rules: 543.34/241.74 543.34/241.74 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.74 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.74 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.74 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.74 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.74 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.74 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.74 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.74 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.74 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.74 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.74 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.74 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.74 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.74 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.74 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.74 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.74 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.74 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.74 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.74 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.74 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.74 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.74 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.74 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.74 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.74 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.74 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.74 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.74 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.74 543.34/241.74 The TRS R consists of the following rules: 543.34/241.74 543.34/241.74 down(a) -> up(f(a)) 543.34/241.74 down(b) -> up(g(b)) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.74 down(f(a)) -> f_flat(down(a)) 543.34/241.74 down(f(b)) -> f_flat(down(b)) 543.34/241.74 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.74 down(f(c)) -> f_flat(down(c)) 543.34/241.74 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.74 down(g(a)) -> g_flat(down(a)) 543.34/241.74 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.74 down(g(b)) -> g_flat(down(b)) 543.34/241.74 down(g(c)) -> g_flat(down(c)) 543.34/241.74 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.74 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.74 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.74 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.74 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.74 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.74 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.74 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.74 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.74 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.74 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.74 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.74 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.74 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.74 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.74 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.74 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.74 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.74 543.34/241.74 The set Q consists of the following terms: 543.34/241.74 543.34/241.74 down(a) 543.34/241.74 down(b) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.74 down(f(a)) 543.34/241.74 down(f(b)) 543.34/241.74 down(f(g(x0))) 543.34/241.74 down(f(c)) 543.34/241.74 down(f(fresh_constant)) 543.34/241.74 down(g(a)) 543.34/241.74 down(g(f(x0))) 543.34/241.74 down(g(b)) 543.34/241.74 down(g(c)) 543.34/241.74 down(g(fresh_constant)) 543.34/241.74 down(f(f(a))) 543.34/241.74 down(f(f(b))) 543.34/241.74 down(f(f(g(x0)))) 543.34/241.74 down(f(f(c))) 543.34/241.74 down(f(f(fresh_constant))) 543.34/241.74 down(g(g(a))) 543.34/241.74 down(g(g(f(x0)))) 543.34/241.74 down(g(g(b))) 543.34/241.74 down(g(g(c))) 543.34/241.74 down(g(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) 543.34/241.74 down(f(f(f(g(x0))))) 543.34/241.74 down(f(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) 543.34/241.74 down(g(g(g(f(x0))))) 543.34/241.74 down(g(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(x0)))))) 543.34/241.74 down(f(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(x0)))))) 543.34/241.74 down(g(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(x0))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(x0))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 f_flat(up(x0)) 543.34/241.74 g_flat(up(x0)) 543.34/241.74 543.34/241.74 We have to consider all minimal (P,Q,R)-chains. 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (487) TransformationProof (EQUIVALENT) 543.34/241.74 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.74 543.34/241.74 (TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))),TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.34/241.74 543.34/241.74 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (488) 543.34/241.74 Obligation: 543.34/241.74 Q DP problem: 543.34/241.74 The TRS P consists of the following rules: 543.34/241.74 543.34/241.74 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.74 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.74 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.74 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.74 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.74 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.74 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.74 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.74 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.74 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.74 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.74 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.74 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.74 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.74 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.74 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.74 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.74 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.74 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.74 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.74 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.74 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.74 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.74 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.74 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.74 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.74 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.74 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.74 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.74 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.74 543.34/241.74 The TRS R consists of the following rules: 543.34/241.74 543.34/241.74 down(a) -> up(f(a)) 543.34/241.74 down(b) -> up(g(b)) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.74 down(f(a)) -> f_flat(down(a)) 543.34/241.74 down(f(b)) -> f_flat(down(b)) 543.34/241.74 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.74 down(f(c)) -> f_flat(down(c)) 543.34/241.74 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.74 down(g(a)) -> g_flat(down(a)) 543.34/241.74 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.74 down(g(b)) -> g_flat(down(b)) 543.34/241.74 down(g(c)) -> g_flat(down(c)) 543.34/241.74 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.74 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.74 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.74 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.74 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.74 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.74 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.74 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.74 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.74 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.74 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.74 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.74 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.74 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.74 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.74 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.74 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.74 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.74 543.34/241.74 The set Q consists of the following terms: 543.34/241.74 543.34/241.74 down(a) 543.34/241.74 down(b) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.74 down(f(a)) 543.34/241.74 down(f(b)) 543.34/241.74 down(f(g(x0))) 543.34/241.74 down(f(c)) 543.34/241.74 down(f(fresh_constant)) 543.34/241.74 down(g(a)) 543.34/241.74 down(g(f(x0))) 543.34/241.74 down(g(b)) 543.34/241.74 down(g(c)) 543.34/241.74 down(g(fresh_constant)) 543.34/241.74 down(f(f(a))) 543.34/241.74 down(f(f(b))) 543.34/241.74 down(f(f(g(x0)))) 543.34/241.74 down(f(f(c))) 543.34/241.74 down(f(f(fresh_constant))) 543.34/241.74 down(g(g(a))) 543.34/241.74 down(g(g(f(x0)))) 543.34/241.74 down(g(g(b))) 543.34/241.74 down(g(g(c))) 543.34/241.74 down(g(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) 543.34/241.74 down(f(f(f(g(x0))))) 543.34/241.74 down(f(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) 543.34/241.74 down(g(g(g(f(x0))))) 543.34/241.74 down(g(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(x0)))))) 543.34/241.74 down(f(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(x0)))))) 543.34/241.74 down(g(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(x0))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(x0))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 f_flat(up(x0)) 543.34/241.74 g_flat(up(x0)) 543.34/241.74 543.34/241.74 We have to consider all minimal (P,Q,R)-chains. 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (489) TransformationProof (EQUIVALENT) 543.34/241.74 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(a)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.74 543.34/241.74 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.34/241.74 543.34/241.74 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (490) 543.34/241.74 Obligation: 543.34/241.74 Q DP problem: 543.34/241.74 The TRS P consists of the following rules: 543.34/241.74 543.34/241.74 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.74 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.74 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.74 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.74 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.74 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.74 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.74 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.74 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.74 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.74 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.74 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.74 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.74 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.74 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.74 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.74 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.74 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.74 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.74 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.74 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.74 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.74 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.74 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.74 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.74 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.74 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.74 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.74 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.74 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.74 543.34/241.74 The TRS R consists of the following rules: 543.34/241.74 543.34/241.74 down(a) -> up(f(a)) 543.34/241.74 down(b) -> up(g(b)) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.74 down(f(a)) -> f_flat(down(a)) 543.34/241.74 down(f(b)) -> f_flat(down(b)) 543.34/241.74 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.74 down(f(c)) -> f_flat(down(c)) 543.34/241.74 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.74 down(g(a)) -> g_flat(down(a)) 543.34/241.74 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.74 down(g(b)) -> g_flat(down(b)) 543.34/241.74 down(g(c)) -> g_flat(down(c)) 543.34/241.74 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.74 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.74 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.74 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.74 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.74 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.74 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.74 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.74 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.74 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.74 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.74 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.74 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.74 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.74 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.74 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.74 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.74 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.74 543.34/241.74 The set Q consists of the following terms: 543.34/241.74 543.34/241.74 down(a) 543.34/241.74 down(b) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.74 down(f(a)) 543.34/241.74 down(f(b)) 543.34/241.74 down(f(g(x0))) 543.34/241.74 down(f(c)) 543.34/241.74 down(f(fresh_constant)) 543.34/241.74 down(g(a)) 543.34/241.74 down(g(f(x0))) 543.34/241.74 down(g(b)) 543.34/241.74 down(g(c)) 543.34/241.74 down(g(fresh_constant)) 543.34/241.74 down(f(f(a))) 543.34/241.74 down(f(f(b))) 543.34/241.74 down(f(f(g(x0)))) 543.34/241.74 down(f(f(c))) 543.34/241.74 down(f(f(fresh_constant))) 543.34/241.74 down(g(g(a))) 543.34/241.74 down(g(g(f(x0)))) 543.34/241.74 down(g(g(b))) 543.34/241.74 down(g(g(c))) 543.34/241.74 down(g(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) 543.34/241.74 down(f(f(f(g(x0))))) 543.34/241.74 down(f(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) 543.34/241.74 down(g(g(g(f(x0))))) 543.34/241.74 down(g(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(x0)))))) 543.34/241.74 down(f(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(x0)))))) 543.34/241.74 down(g(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(x0))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(x0))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 f_flat(up(x0)) 543.34/241.74 g_flat(up(x0)) 543.34/241.74 543.34/241.74 We have to consider all minimal (P,Q,R)-chains. 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (491) TransformationProof (EQUIVALENT) 543.34/241.74 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(b)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.74 543.34/241.74 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.34/241.74 543.34/241.74 543.34/241.74 ---------------------------------------- 543.34/241.74 543.34/241.74 (492) 543.34/241.74 Obligation: 543.34/241.74 Q DP problem: 543.34/241.74 The TRS P consists of the following rules: 543.34/241.74 543.34/241.74 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.74 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.74 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.74 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.74 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.74 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.74 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.74 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.74 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.74 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.74 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.74 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.74 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.74 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.74 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.74 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.74 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.74 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.74 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.74 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.74 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.74 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.74 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.74 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.74 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.74 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.74 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.74 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.74 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.74 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.74 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.74 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.74 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.74 543.34/241.74 The TRS R consists of the following rules: 543.34/241.74 543.34/241.74 down(a) -> up(f(a)) 543.34/241.74 down(b) -> up(g(b)) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.74 down(f(a)) -> f_flat(down(a)) 543.34/241.74 down(f(b)) -> f_flat(down(b)) 543.34/241.74 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.74 down(f(c)) -> f_flat(down(c)) 543.34/241.74 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.74 down(g(a)) -> g_flat(down(a)) 543.34/241.74 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.74 down(g(b)) -> g_flat(down(b)) 543.34/241.74 down(g(c)) -> g_flat(down(c)) 543.34/241.74 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.74 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.74 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.74 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.74 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.74 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.74 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.74 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.74 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.74 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.74 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.74 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.74 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.74 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.74 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.74 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.74 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.74 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.74 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.74 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.74 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.74 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.74 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.74 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.74 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.74 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.74 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.74 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.74 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.74 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.74 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.74 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.74 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.74 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.74 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.74 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.74 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.74 543.34/241.74 The set Q consists of the following terms: 543.34/241.74 543.34/241.74 down(a) 543.34/241.74 down(b) 543.34/241.74 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.74 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.74 down(f(a)) 543.34/241.74 down(f(b)) 543.34/241.74 down(f(g(x0))) 543.34/241.74 down(f(c)) 543.34/241.74 down(f(fresh_constant)) 543.34/241.74 down(g(a)) 543.34/241.74 down(g(f(x0))) 543.34/241.74 down(g(b)) 543.34/241.74 down(g(c)) 543.34/241.74 down(g(fresh_constant)) 543.34/241.74 down(f(f(a))) 543.34/241.74 down(f(f(b))) 543.34/241.74 down(f(f(g(x0)))) 543.34/241.74 down(f(f(c))) 543.34/241.74 down(f(f(fresh_constant))) 543.34/241.74 down(g(g(a))) 543.34/241.74 down(g(g(f(x0)))) 543.34/241.74 down(g(g(b))) 543.34/241.74 down(g(g(c))) 543.34/241.74 down(g(g(fresh_constant))) 543.34/241.74 down(f(f(f(a)))) 543.34/241.74 down(f(f(f(b)))) 543.34/241.74 down(f(f(f(g(x0))))) 543.34/241.74 down(f(f(f(c)))) 543.34/241.74 down(f(f(f(fresh_constant)))) 543.34/241.74 down(g(g(g(a)))) 543.34/241.74 down(g(g(g(f(x0))))) 543.34/241.74 down(g(g(g(b)))) 543.34/241.74 down(g(g(g(c)))) 543.34/241.74 down(g(g(g(fresh_constant)))) 543.34/241.74 down(f(f(f(f(a))))) 543.34/241.74 down(f(f(f(f(b))))) 543.34/241.74 down(f(f(f(f(g(x0)))))) 543.34/241.74 down(f(f(f(f(c))))) 543.34/241.74 down(f(f(f(f(fresh_constant))))) 543.34/241.74 down(g(g(g(g(a))))) 543.34/241.74 down(g(g(g(g(f(x0)))))) 543.34/241.74 down(g(g(g(g(b))))) 543.34/241.74 down(g(g(g(g(c))))) 543.34/241.74 down(g(g(g(g(fresh_constant))))) 543.34/241.74 down(f(f(f(f(f(a)))))) 543.34/241.74 down(f(f(f(f(f(b)))))) 543.34/241.74 down(f(f(f(f(f(g(x0))))))) 543.34/241.74 down(f(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(x0))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 f_flat(up(x0)) 543.34/241.75 g_flat(up(x0)) 543.34/241.75 543.34/241.75 We have to consider all minimal (P,Q,R)-chains. 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (493) TransformationProof (EQUIVALENT) 543.34/241.75 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.75 543.34/241.75 (TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))),TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.34/241.75 543.34/241.75 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (494) 543.34/241.75 Obligation: 543.34/241.75 Q DP problem: 543.34/241.75 The TRS P consists of the following rules: 543.34/241.75 543.34/241.75 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.75 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.75 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.75 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.75 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.75 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.75 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.75 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.75 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.75 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.75 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.75 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.75 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) 543.34/241.75 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.75 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.75 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.75 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.75 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.75 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.75 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.75 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.75 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.75 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.75 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.75 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.75 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.75 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.75 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.75 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.75 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.75 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.75 543.34/241.75 The TRS R consists of the following rules: 543.34/241.75 543.34/241.75 down(a) -> up(f(a)) 543.34/241.75 down(b) -> up(g(b)) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.75 down(f(a)) -> f_flat(down(a)) 543.34/241.75 down(f(b)) -> f_flat(down(b)) 543.34/241.75 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.75 down(f(c)) -> f_flat(down(c)) 543.34/241.75 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.75 down(g(a)) -> g_flat(down(a)) 543.34/241.75 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.75 down(g(b)) -> g_flat(down(b)) 543.34/241.75 down(g(c)) -> g_flat(down(c)) 543.34/241.75 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.75 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.75 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.75 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.75 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.75 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.75 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.75 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.75 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.75 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.75 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.75 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.75 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.75 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.75 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.75 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.75 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.75 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.75 543.34/241.75 The set Q consists of the following terms: 543.34/241.75 543.34/241.75 down(a) 543.34/241.75 down(b) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.75 down(f(a)) 543.34/241.75 down(f(b)) 543.34/241.75 down(f(g(x0))) 543.34/241.75 down(f(c)) 543.34/241.75 down(f(fresh_constant)) 543.34/241.75 down(g(a)) 543.34/241.75 down(g(f(x0))) 543.34/241.75 down(g(b)) 543.34/241.75 down(g(c)) 543.34/241.75 down(g(fresh_constant)) 543.34/241.75 down(f(f(a))) 543.34/241.75 down(f(f(b))) 543.34/241.75 down(f(f(g(x0)))) 543.34/241.75 down(f(f(c))) 543.34/241.75 down(f(f(fresh_constant))) 543.34/241.75 down(g(g(a))) 543.34/241.75 down(g(g(f(x0)))) 543.34/241.75 down(g(g(b))) 543.34/241.75 down(g(g(c))) 543.34/241.75 down(g(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) 543.34/241.75 down(f(f(f(g(x0))))) 543.34/241.75 down(f(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) 543.34/241.75 down(g(g(g(f(x0))))) 543.34/241.75 down(g(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(x0)))))) 543.34/241.75 down(f(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(x0)))))) 543.34/241.75 down(g(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(x0))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(x0))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 f_flat(up(x0)) 543.34/241.75 g_flat(up(x0)) 543.34/241.75 543.34/241.75 We have to consider all minimal (P,Q,R)-chains. 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (495) TransformationProof (EQUIVALENT) 543.34/241.75 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(b))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.75 543.34/241.75 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.34/241.75 543.34/241.75 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (496) 543.34/241.75 Obligation: 543.34/241.75 Q DP problem: 543.34/241.75 The TRS P consists of the following rules: 543.34/241.75 543.34/241.75 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.75 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.75 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.75 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.75 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.75 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.75 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.75 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.75 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.75 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.75 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.75 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.75 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) 543.34/241.75 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.75 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.75 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.75 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.75 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.75 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.75 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.75 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.75 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.75 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.75 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.75 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.75 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.75 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.75 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.75 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.75 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.34/241.75 543.34/241.75 The TRS R consists of the following rules: 543.34/241.75 543.34/241.75 down(a) -> up(f(a)) 543.34/241.75 down(b) -> up(g(b)) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.75 down(f(a)) -> f_flat(down(a)) 543.34/241.75 down(f(b)) -> f_flat(down(b)) 543.34/241.75 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.75 down(f(c)) -> f_flat(down(c)) 543.34/241.75 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.75 down(g(a)) -> g_flat(down(a)) 543.34/241.75 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.75 down(g(b)) -> g_flat(down(b)) 543.34/241.75 down(g(c)) -> g_flat(down(c)) 543.34/241.75 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.75 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.75 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.75 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.75 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.75 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.75 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.75 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.75 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.75 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.75 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.75 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.75 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.75 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.75 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.75 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.75 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.75 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.75 543.34/241.75 The set Q consists of the following terms: 543.34/241.75 543.34/241.75 down(a) 543.34/241.75 down(b) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.75 down(f(a)) 543.34/241.75 down(f(b)) 543.34/241.75 down(f(g(x0))) 543.34/241.75 down(f(c)) 543.34/241.75 down(f(fresh_constant)) 543.34/241.75 down(g(a)) 543.34/241.75 down(g(f(x0))) 543.34/241.75 down(g(b)) 543.34/241.75 down(g(c)) 543.34/241.75 down(g(fresh_constant)) 543.34/241.75 down(f(f(a))) 543.34/241.75 down(f(f(b))) 543.34/241.75 down(f(f(g(x0)))) 543.34/241.75 down(f(f(c))) 543.34/241.75 down(f(f(fresh_constant))) 543.34/241.75 down(g(g(a))) 543.34/241.75 down(g(g(f(x0)))) 543.34/241.75 down(g(g(b))) 543.34/241.75 down(g(g(c))) 543.34/241.75 down(g(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) 543.34/241.75 down(f(f(f(g(x0))))) 543.34/241.75 down(f(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) 543.34/241.75 down(g(g(g(f(x0))))) 543.34/241.75 down(g(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(x0)))))) 543.34/241.75 down(f(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(x0)))))) 543.34/241.75 down(g(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(x0))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(x0))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 f_flat(up(x0)) 543.34/241.75 g_flat(up(x0)) 543.34/241.75 543.34/241.75 We have to consider all minimal (P,Q,R)-chains. 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (497) TransformationProof (EQUIVALENT) 543.34/241.75 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(c))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.75 543.34/241.75 (TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))),TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.34/241.75 543.34/241.75 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (498) 543.34/241.75 Obligation: 543.34/241.75 Q DP problem: 543.34/241.75 The TRS P consists of the following rules: 543.34/241.75 543.34/241.75 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.75 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.75 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.75 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.75 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.75 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.75 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.75 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.75 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.75 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.75 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.75 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.75 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.75 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.75 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.75 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.75 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.75 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.75 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.75 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.75 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.75 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.75 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.75 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.75 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.75 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.75 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.75 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.75 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.34/241.75 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.34/241.75 543.34/241.75 The TRS R consists of the following rules: 543.34/241.75 543.34/241.75 down(a) -> up(f(a)) 543.34/241.75 down(b) -> up(g(b)) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.75 down(f(a)) -> f_flat(down(a)) 543.34/241.75 down(f(b)) -> f_flat(down(b)) 543.34/241.75 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.75 down(f(c)) -> f_flat(down(c)) 543.34/241.75 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.75 down(g(a)) -> g_flat(down(a)) 543.34/241.75 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.75 down(g(b)) -> g_flat(down(b)) 543.34/241.75 down(g(c)) -> g_flat(down(c)) 543.34/241.75 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.75 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.75 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.75 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.75 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.75 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.75 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.75 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.75 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.75 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.75 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.75 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.75 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.75 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.75 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.75 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.75 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.75 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.75 543.34/241.75 The set Q consists of the following terms: 543.34/241.75 543.34/241.75 down(a) 543.34/241.75 down(b) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.75 down(f(a)) 543.34/241.75 down(f(b)) 543.34/241.75 down(f(g(x0))) 543.34/241.75 down(f(c)) 543.34/241.75 down(f(fresh_constant)) 543.34/241.75 down(g(a)) 543.34/241.75 down(g(f(x0))) 543.34/241.75 down(g(b)) 543.34/241.75 down(g(c)) 543.34/241.75 down(g(fresh_constant)) 543.34/241.75 down(f(f(a))) 543.34/241.75 down(f(f(b))) 543.34/241.75 down(f(f(g(x0)))) 543.34/241.75 down(f(f(c))) 543.34/241.75 down(f(f(fresh_constant))) 543.34/241.75 down(g(g(a))) 543.34/241.75 down(g(g(f(x0)))) 543.34/241.75 down(g(g(b))) 543.34/241.75 down(g(g(c))) 543.34/241.75 down(g(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) 543.34/241.75 down(f(f(f(g(x0))))) 543.34/241.75 down(f(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) 543.34/241.75 down(g(g(g(f(x0))))) 543.34/241.75 down(g(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(x0)))))) 543.34/241.75 down(f(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(x0)))))) 543.34/241.75 down(g(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(x0))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(x0))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 f_flat(up(x0)) 543.34/241.75 g_flat(up(x0)) 543.34/241.75 543.34/241.75 We have to consider all minimal (P,Q,R)-chains. 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (499) TransformationProof (EQUIVALENT) 543.34/241.75 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.75 543.34/241.75 (TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))),TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.34/241.75 543.34/241.75 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (500) 543.34/241.75 Obligation: 543.34/241.75 Q DP problem: 543.34/241.75 The TRS P consists of the following rules: 543.34/241.75 543.34/241.75 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.75 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.75 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.75 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.75 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.75 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.75 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.75 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.75 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.75 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.75 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.75 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.75 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.75 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.75 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.75 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.75 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.75 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.75 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.75 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.75 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.75 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.75 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.75 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.75 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.75 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.75 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.75 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.34/241.75 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.34/241.75 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.34/241.75 543.34/241.75 The TRS R consists of the following rules: 543.34/241.75 543.34/241.75 down(a) -> up(f(a)) 543.34/241.75 down(b) -> up(g(b)) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.75 down(f(a)) -> f_flat(down(a)) 543.34/241.75 down(f(b)) -> f_flat(down(b)) 543.34/241.75 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.75 down(f(c)) -> f_flat(down(c)) 543.34/241.75 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.75 down(g(a)) -> g_flat(down(a)) 543.34/241.75 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.75 down(g(b)) -> g_flat(down(b)) 543.34/241.75 down(g(c)) -> g_flat(down(c)) 543.34/241.75 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.75 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.75 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.75 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.75 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.75 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.75 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.75 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.75 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.75 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.75 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.75 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.75 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.75 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.75 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.75 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.75 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.75 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.75 543.34/241.75 The set Q consists of the following terms: 543.34/241.75 543.34/241.75 down(a) 543.34/241.75 down(b) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.75 down(f(a)) 543.34/241.75 down(f(b)) 543.34/241.75 down(f(g(x0))) 543.34/241.75 down(f(c)) 543.34/241.75 down(f(fresh_constant)) 543.34/241.75 down(g(a)) 543.34/241.75 down(g(f(x0))) 543.34/241.75 down(g(b)) 543.34/241.75 down(g(c)) 543.34/241.75 down(g(fresh_constant)) 543.34/241.75 down(f(f(a))) 543.34/241.75 down(f(f(b))) 543.34/241.75 down(f(f(g(x0)))) 543.34/241.75 down(f(f(c))) 543.34/241.75 down(f(f(fresh_constant))) 543.34/241.75 down(g(g(a))) 543.34/241.75 down(g(g(f(x0)))) 543.34/241.75 down(g(g(b))) 543.34/241.75 down(g(g(c))) 543.34/241.75 down(g(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) 543.34/241.75 down(f(f(f(g(x0))))) 543.34/241.75 down(f(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) 543.34/241.75 down(g(g(g(f(x0))))) 543.34/241.75 down(g(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(x0)))))) 543.34/241.75 down(f(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(x0)))))) 543.34/241.75 down(g(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(x0))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(x0))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 f_flat(up(x0)) 543.34/241.75 g_flat(up(x0)) 543.34/241.75 543.34/241.75 We have to consider all minimal (P,Q,R)-chains. 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (501) TransformationProof (EQUIVALENT) 543.34/241.75 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(a)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.75 543.34/241.75 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.34/241.75 543.34/241.75 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (502) 543.34/241.75 Obligation: 543.34/241.75 Q DP problem: 543.34/241.75 The TRS P consists of the following rules: 543.34/241.75 543.34/241.75 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.75 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.75 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.75 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.75 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.75 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.75 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.75 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.75 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.75 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.75 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.75 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.75 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.75 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.75 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.75 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.75 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.75 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.75 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.75 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.75 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.75 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.75 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.75 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.75 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.75 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.75 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.75 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.34/241.75 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.34/241.75 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.34/241.75 543.34/241.75 The TRS R consists of the following rules: 543.34/241.75 543.34/241.75 down(a) -> up(f(a)) 543.34/241.75 down(b) -> up(g(b)) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.75 down(f(a)) -> f_flat(down(a)) 543.34/241.75 down(f(b)) -> f_flat(down(b)) 543.34/241.75 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.75 down(f(c)) -> f_flat(down(c)) 543.34/241.75 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.75 down(g(a)) -> g_flat(down(a)) 543.34/241.75 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.75 down(g(b)) -> g_flat(down(b)) 543.34/241.75 down(g(c)) -> g_flat(down(c)) 543.34/241.75 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.75 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.75 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.75 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.75 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.75 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.75 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.75 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.75 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.75 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.75 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.75 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.75 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.75 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.75 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.75 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.75 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.75 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.75 543.34/241.75 The set Q consists of the following terms: 543.34/241.75 543.34/241.75 down(a) 543.34/241.75 down(b) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.75 down(f(a)) 543.34/241.75 down(f(b)) 543.34/241.75 down(f(g(x0))) 543.34/241.75 down(f(c)) 543.34/241.75 down(f(fresh_constant)) 543.34/241.75 down(g(a)) 543.34/241.75 down(g(f(x0))) 543.34/241.75 down(g(b)) 543.34/241.75 down(g(c)) 543.34/241.75 down(g(fresh_constant)) 543.34/241.75 down(f(f(a))) 543.34/241.75 down(f(f(b))) 543.34/241.75 down(f(f(g(x0)))) 543.34/241.75 down(f(f(c))) 543.34/241.75 down(f(f(fresh_constant))) 543.34/241.75 down(g(g(a))) 543.34/241.75 down(g(g(f(x0)))) 543.34/241.75 down(g(g(b))) 543.34/241.75 down(g(g(c))) 543.34/241.75 down(g(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) 543.34/241.75 down(f(f(f(g(x0))))) 543.34/241.75 down(f(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) 543.34/241.75 down(g(g(g(f(x0))))) 543.34/241.75 down(g(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(x0)))))) 543.34/241.75 down(f(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(x0)))))) 543.34/241.75 down(g(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(x0))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(x0))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 f_flat(up(x0)) 543.34/241.75 g_flat(up(x0)) 543.34/241.75 543.34/241.75 We have to consider all minimal (P,Q,R)-chains. 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (503) TransformationProof (EQUIVALENT) 543.34/241.75 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.75 543.34/241.75 (TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))),TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.34/241.75 543.34/241.75 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (504) 543.34/241.75 Obligation: 543.34/241.75 Q DP problem: 543.34/241.75 The TRS P consists of the following rules: 543.34/241.75 543.34/241.75 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.75 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.75 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.75 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.75 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.75 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.75 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.75 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.75 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.75 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.75 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.75 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.75 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.75 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.75 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.75 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.75 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.75 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.75 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.75 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.75 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.75 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.75 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.75 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.75 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.75 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.75 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.75 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.34/241.75 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.34/241.75 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.34/241.75 543.34/241.75 The TRS R consists of the following rules: 543.34/241.75 543.34/241.75 down(a) -> up(f(a)) 543.34/241.75 down(b) -> up(g(b)) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.75 down(f(a)) -> f_flat(down(a)) 543.34/241.75 down(f(b)) -> f_flat(down(b)) 543.34/241.75 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.75 down(f(c)) -> f_flat(down(c)) 543.34/241.75 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.75 down(g(a)) -> g_flat(down(a)) 543.34/241.75 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.75 down(g(b)) -> g_flat(down(b)) 543.34/241.75 down(g(c)) -> g_flat(down(c)) 543.34/241.75 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.75 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.75 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.75 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.75 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.75 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.75 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.75 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.75 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.75 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.75 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.75 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.75 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.75 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.75 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.75 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.75 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.75 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.75 543.34/241.75 The set Q consists of the following terms: 543.34/241.75 543.34/241.75 down(a) 543.34/241.75 down(b) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.75 down(f(a)) 543.34/241.75 down(f(b)) 543.34/241.75 down(f(g(x0))) 543.34/241.75 down(f(c)) 543.34/241.75 down(f(fresh_constant)) 543.34/241.75 down(g(a)) 543.34/241.75 down(g(f(x0))) 543.34/241.75 down(g(b)) 543.34/241.75 down(g(c)) 543.34/241.75 down(g(fresh_constant)) 543.34/241.75 down(f(f(a))) 543.34/241.75 down(f(f(b))) 543.34/241.75 down(f(f(g(x0)))) 543.34/241.75 down(f(f(c))) 543.34/241.75 down(f(f(fresh_constant))) 543.34/241.75 down(g(g(a))) 543.34/241.75 down(g(g(f(x0)))) 543.34/241.75 down(g(g(b))) 543.34/241.75 down(g(g(c))) 543.34/241.75 down(g(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) 543.34/241.75 down(f(f(f(g(x0))))) 543.34/241.75 down(f(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) 543.34/241.75 down(g(g(g(f(x0))))) 543.34/241.75 down(g(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(x0)))))) 543.34/241.75 down(f(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(x0)))))) 543.34/241.75 down(g(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(x0))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(x0))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 f_flat(up(x0)) 543.34/241.75 g_flat(up(x0)) 543.34/241.75 543.34/241.75 We have to consider all minimal (P,Q,R)-chains. 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (505) TransformationProof (EQUIVALENT) 543.34/241.75 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(c)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.75 543.34/241.75 (TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))),TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.34/241.75 543.34/241.75 543.34/241.75 ---------------------------------------- 543.34/241.75 543.34/241.75 (506) 543.34/241.75 Obligation: 543.34/241.75 Q DP problem: 543.34/241.75 The TRS P consists of the following rules: 543.34/241.75 543.34/241.75 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.75 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.75 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.75 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.75 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.75 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.75 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.75 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.75 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.75 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.75 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.75 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.75 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.75 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.75 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.75 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.75 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.75 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.75 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.75 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.75 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.75 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.75 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.75 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.75 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.75 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.75 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.75 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.75 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.75 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.34/241.75 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.34/241.75 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.34/241.75 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.34/241.75 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.34/241.75 543.34/241.75 The TRS R consists of the following rules: 543.34/241.75 543.34/241.75 down(a) -> up(f(a)) 543.34/241.75 down(b) -> up(g(b)) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.75 down(f(a)) -> f_flat(down(a)) 543.34/241.75 down(f(b)) -> f_flat(down(b)) 543.34/241.75 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.75 down(f(c)) -> f_flat(down(c)) 543.34/241.75 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.75 down(g(a)) -> g_flat(down(a)) 543.34/241.75 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.75 down(g(b)) -> g_flat(down(b)) 543.34/241.75 down(g(c)) -> g_flat(down(c)) 543.34/241.75 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.75 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.75 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.75 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.75 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.75 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.75 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.75 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.75 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.75 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.75 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.75 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.75 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.75 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.75 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.75 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.75 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.75 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.75 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.75 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.75 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.75 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.75 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.75 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.75 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.75 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.75 543.34/241.75 The set Q consists of the following terms: 543.34/241.75 543.34/241.75 down(a) 543.34/241.75 down(b) 543.34/241.75 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.75 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.75 down(f(a)) 543.34/241.75 down(f(b)) 543.34/241.75 down(f(g(x0))) 543.34/241.75 down(f(c)) 543.34/241.75 down(f(fresh_constant)) 543.34/241.75 down(g(a)) 543.34/241.75 down(g(f(x0))) 543.34/241.75 down(g(b)) 543.34/241.75 down(g(c)) 543.34/241.75 down(g(fresh_constant)) 543.34/241.75 down(f(f(a))) 543.34/241.75 down(f(f(b))) 543.34/241.75 down(f(f(g(x0)))) 543.34/241.75 down(f(f(c))) 543.34/241.75 down(f(f(fresh_constant))) 543.34/241.75 down(g(g(a))) 543.34/241.75 down(g(g(f(x0)))) 543.34/241.75 down(g(g(b))) 543.34/241.75 down(g(g(c))) 543.34/241.75 down(g(g(fresh_constant))) 543.34/241.75 down(f(f(f(a)))) 543.34/241.75 down(f(f(f(b)))) 543.34/241.75 down(f(f(f(g(x0))))) 543.34/241.75 down(f(f(f(c)))) 543.34/241.75 down(f(f(f(fresh_constant)))) 543.34/241.75 down(g(g(g(a)))) 543.34/241.75 down(g(g(g(f(x0))))) 543.34/241.75 down(g(g(g(b)))) 543.34/241.75 down(g(g(g(c)))) 543.34/241.75 down(g(g(g(fresh_constant)))) 543.34/241.75 down(f(f(f(f(a))))) 543.34/241.75 down(f(f(f(f(b))))) 543.34/241.75 down(f(f(f(f(g(x0)))))) 543.34/241.75 down(f(f(f(f(c))))) 543.34/241.75 down(f(f(f(f(fresh_constant))))) 543.34/241.75 down(g(g(g(g(a))))) 543.34/241.75 down(g(g(g(g(f(x0)))))) 543.34/241.75 down(g(g(g(g(b))))) 543.34/241.75 down(g(g(g(g(c))))) 543.34/241.75 down(g(g(g(g(fresh_constant))))) 543.34/241.75 down(f(f(f(f(f(a)))))) 543.34/241.75 down(f(f(f(f(f(b)))))) 543.34/241.75 down(f(f(f(f(f(g(x0))))))) 543.34/241.75 down(f(f(f(f(f(c)))))) 543.34/241.75 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.75 down(g(g(g(g(g(a)))))) 543.34/241.75 down(g(g(g(g(g(f(x0))))))) 543.34/241.75 down(g(g(g(g(g(b)))))) 543.34/241.75 down(g(g(g(g(g(c)))))) 543.34/241.75 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.75 down(f(f(f(f(f(f(a))))))) 543.34/241.75 down(f(f(f(f(f(f(b))))))) 543.34/241.75 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.75 down(f(f(f(f(f(f(c))))))) 543.34/241.75 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.76 down(g(g(g(g(g(g(a))))))) 543.34/241.76 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.76 down(g(g(g(g(g(g(b))))))) 543.34/241.76 down(g(g(g(g(g(g(c))))))) 543.34/241.76 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.76 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.76 f_flat(up(x0)) 543.34/241.76 g_flat(up(x0)) 543.34/241.76 543.34/241.76 We have to consider all minimal (P,Q,R)-chains. 543.34/241.76 ---------------------------------------- 543.34/241.76 543.34/241.76 (507) TransformationProof (EQUIVALENT) 543.34/241.76 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.76 543.34/241.76 (TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))),TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.34/241.76 543.34/241.76 543.34/241.76 ---------------------------------------- 543.34/241.76 543.34/241.76 (508) 543.34/241.76 Obligation: 543.34/241.76 Q DP problem: 543.34/241.76 The TRS P consists of the following rules: 543.34/241.76 543.34/241.76 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.76 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.76 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.76 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.76 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.76 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.76 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.76 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.76 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.76 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.76 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.76 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.76 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.76 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.76 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.76 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.76 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.76 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.76 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.76 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.76 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.76 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.76 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.76 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.76 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.76 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.76 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.76 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.76 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.76 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.34/241.76 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.34/241.76 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.34/241.76 543.34/241.76 The TRS R consists of the following rules: 543.34/241.76 543.34/241.76 down(a) -> up(f(a)) 543.34/241.76 down(b) -> up(g(b)) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.76 down(f(a)) -> f_flat(down(a)) 543.34/241.76 down(f(b)) -> f_flat(down(b)) 543.34/241.76 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.76 down(f(c)) -> f_flat(down(c)) 543.34/241.76 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.76 down(g(a)) -> g_flat(down(a)) 543.34/241.76 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.76 down(g(b)) -> g_flat(down(b)) 543.34/241.76 down(g(c)) -> g_flat(down(c)) 543.34/241.76 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.76 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.76 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.76 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.76 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.76 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.76 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.76 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.76 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.76 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.76 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.76 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.76 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.76 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.76 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.76 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.76 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.76 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.76 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.76 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.76 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.76 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.76 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.76 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.76 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.76 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.76 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.76 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.76 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.76 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.76 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.76 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.76 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.76 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.76 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.76 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.76 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.76 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.76 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.76 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.76 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.76 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.76 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.76 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.76 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.76 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.76 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.76 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.76 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.76 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.76 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.76 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.76 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.76 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.76 543.34/241.76 The set Q consists of the following terms: 543.34/241.76 543.34/241.76 down(a) 543.34/241.76 down(b) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.76 down(f(a)) 543.34/241.76 down(f(b)) 543.34/241.76 down(f(g(x0))) 543.34/241.76 down(f(c)) 543.34/241.76 down(f(fresh_constant)) 543.34/241.76 down(g(a)) 543.34/241.76 down(g(f(x0))) 543.34/241.76 down(g(b)) 543.34/241.76 down(g(c)) 543.34/241.76 down(g(fresh_constant)) 543.34/241.76 down(f(f(a))) 543.34/241.76 down(f(f(b))) 543.34/241.76 down(f(f(g(x0)))) 543.34/241.76 down(f(f(c))) 543.34/241.76 down(f(f(fresh_constant))) 543.34/241.76 down(g(g(a))) 543.34/241.76 down(g(g(f(x0)))) 543.34/241.76 down(g(g(b))) 543.34/241.76 down(g(g(c))) 543.34/241.76 down(g(g(fresh_constant))) 543.34/241.76 down(f(f(f(a)))) 543.34/241.76 down(f(f(f(b)))) 543.34/241.76 down(f(f(f(g(x0))))) 543.34/241.76 down(f(f(f(c)))) 543.34/241.76 down(f(f(f(fresh_constant)))) 543.34/241.76 down(g(g(g(a)))) 543.34/241.76 down(g(g(g(f(x0))))) 543.34/241.76 down(g(g(g(b)))) 543.34/241.76 down(g(g(g(c)))) 543.34/241.76 down(g(g(g(fresh_constant)))) 543.34/241.76 down(f(f(f(f(a))))) 543.34/241.76 down(f(f(f(f(b))))) 543.34/241.76 down(f(f(f(f(g(x0)))))) 543.34/241.76 down(f(f(f(f(c))))) 543.34/241.76 down(f(f(f(f(fresh_constant))))) 543.34/241.76 down(g(g(g(g(a))))) 543.34/241.76 down(g(g(g(g(f(x0)))))) 543.34/241.76 down(g(g(g(g(b))))) 543.34/241.76 down(g(g(g(g(c))))) 543.34/241.76 down(g(g(g(g(fresh_constant))))) 543.34/241.76 down(f(f(f(f(f(a)))))) 543.34/241.76 down(f(f(f(f(f(b)))))) 543.34/241.76 down(f(f(f(f(f(g(x0))))))) 543.34/241.76 down(f(f(f(f(f(c)))))) 543.34/241.76 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.76 down(g(g(g(g(g(a)))))) 543.34/241.76 down(g(g(g(g(g(f(x0))))))) 543.34/241.76 down(g(g(g(g(g(b)))))) 543.34/241.76 down(g(g(g(g(g(c)))))) 543.34/241.76 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.76 down(f(f(f(f(f(f(a))))))) 543.34/241.76 down(f(f(f(f(f(f(b))))))) 543.34/241.76 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.76 down(f(f(f(f(f(f(c))))))) 543.34/241.76 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.76 down(g(g(g(g(g(g(a))))))) 543.34/241.76 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.76 down(g(g(g(g(g(g(b))))))) 543.34/241.76 down(g(g(g(g(g(g(c))))))) 543.34/241.76 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.76 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.76 f_flat(up(x0)) 543.34/241.76 g_flat(up(x0)) 543.34/241.76 543.34/241.76 We have to consider all minimal (P,Q,R)-chains. 543.34/241.76 ---------------------------------------- 543.34/241.76 543.34/241.76 (509) TransformationProof (EQUIVALENT) 543.34/241.76 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.76 543.34/241.76 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.34/241.76 543.34/241.76 543.34/241.76 ---------------------------------------- 543.34/241.76 543.34/241.76 (510) 543.34/241.76 Obligation: 543.34/241.76 Q DP problem: 543.34/241.76 The TRS P consists of the following rules: 543.34/241.76 543.34/241.76 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.76 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.76 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.76 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.76 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.76 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.76 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.76 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.76 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.76 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.76 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.76 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.76 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.76 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.76 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.76 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.76 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.76 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.76 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.76 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.76 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.76 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.76 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.76 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.76 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.76 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.76 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.76 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.76 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.76 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.34/241.76 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.34/241.76 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.34/241.76 543.34/241.76 The TRS R consists of the following rules: 543.34/241.76 543.34/241.76 down(a) -> up(f(a)) 543.34/241.76 down(b) -> up(g(b)) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.76 down(f(a)) -> f_flat(down(a)) 543.34/241.76 down(f(b)) -> f_flat(down(b)) 543.34/241.76 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.76 down(f(c)) -> f_flat(down(c)) 543.34/241.76 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.76 down(g(a)) -> g_flat(down(a)) 543.34/241.76 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.76 down(g(b)) -> g_flat(down(b)) 543.34/241.76 down(g(c)) -> g_flat(down(c)) 543.34/241.76 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.76 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.76 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.76 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.76 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.76 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.76 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.76 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.76 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.76 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.76 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.76 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.76 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.76 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.76 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.76 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.76 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.76 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.76 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.76 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.76 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.76 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.76 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.76 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.76 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.76 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.76 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.76 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.76 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.76 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.76 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.76 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.76 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.76 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.76 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.76 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.76 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.76 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.76 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.76 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.76 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.76 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.76 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.76 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.76 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.76 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.76 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.76 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.76 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.76 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.76 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.76 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.76 g_flat(up(x_1)) -> up(g(x_1)) 543.34/241.76 f_flat(up(x_1)) -> up(f(x_1)) 543.34/241.76 543.34/241.76 The set Q consists of the following terms: 543.34/241.76 543.34/241.76 down(a) 543.34/241.76 down(b) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.34/241.76 down(f(a)) 543.34/241.76 down(f(b)) 543.34/241.76 down(f(g(x0))) 543.34/241.76 down(f(c)) 543.34/241.76 down(f(fresh_constant)) 543.34/241.76 down(g(a)) 543.34/241.76 down(g(f(x0))) 543.34/241.76 down(g(b)) 543.34/241.76 down(g(c)) 543.34/241.76 down(g(fresh_constant)) 543.34/241.76 down(f(f(a))) 543.34/241.76 down(f(f(b))) 543.34/241.76 down(f(f(g(x0)))) 543.34/241.76 down(f(f(c))) 543.34/241.76 down(f(f(fresh_constant))) 543.34/241.76 down(g(g(a))) 543.34/241.76 down(g(g(f(x0)))) 543.34/241.76 down(g(g(b))) 543.34/241.76 down(g(g(c))) 543.34/241.76 down(g(g(fresh_constant))) 543.34/241.76 down(f(f(f(a)))) 543.34/241.76 down(f(f(f(b)))) 543.34/241.76 down(f(f(f(g(x0))))) 543.34/241.76 down(f(f(f(c)))) 543.34/241.76 down(f(f(f(fresh_constant)))) 543.34/241.76 down(g(g(g(a)))) 543.34/241.76 down(g(g(g(f(x0))))) 543.34/241.76 down(g(g(g(b)))) 543.34/241.76 down(g(g(g(c)))) 543.34/241.76 down(g(g(g(fresh_constant)))) 543.34/241.76 down(f(f(f(f(a))))) 543.34/241.76 down(f(f(f(f(b))))) 543.34/241.76 down(f(f(f(f(g(x0)))))) 543.34/241.76 down(f(f(f(f(c))))) 543.34/241.76 down(f(f(f(f(fresh_constant))))) 543.34/241.76 down(g(g(g(g(a))))) 543.34/241.76 down(g(g(g(g(f(x0)))))) 543.34/241.76 down(g(g(g(g(b))))) 543.34/241.76 down(g(g(g(g(c))))) 543.34/241.76 down(g(g(g(g(fresh_constant))))) 543.34/241.76 down(f(f(f(f(f(a)))))) 543.34/241.76 down(f(f(f(f(f(b)))))) 543.34/241.76 down(f(f(f(f(f(g(x0))))))) 543.34/241.76 down(f(f(f(f(f(c)))))) 543.34/241.76 down(f(f(f(f(f(fresh_constant)))))) 543.34/241.76 down(g(g(g(g(g(a)))))) 543.34/241.76 down(g(g(g(g(g(f(x0))))))) 543.34/241.76 down(g(g(g(g(g(b)))))) 543.34/241.76 down(g(g(g(g(g(c)))))) 543.34/241.76 down(g(g(g(g(g(fresh_constant)))))) 543.34/241.76 down(f(f(f(f(f(f(a))))))) 543.34/241.76 down(f(f(f(f(f(f(b))))))) 543.34/241.76 down(f(f(f(f(f(f(g(x0)))))))) 543.34/241.76 down(f(f(f(f(f(f(c))))))) 543.34/241.76 down(f(f(f(f(f(f(fresh_constant))))))) 543.34/241.76 down(g(g(g(g(g(g(a))))))) 543.34/241.76 down(g(g(g(g(g(g(f(x0)))))))) 543.34/241.76 down(g(g(g(g(g(g(b))))))) 543.34/241.76 down(g(g(g(g(g(g(c))))))) 543.34/241.76 down(g(g(g(g(g(g(fresh_constant))))))) 543.34/241.76 down(f(f(f(f(f(f(f(a)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(b)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(g(x0))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(c)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(a)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(f(x0))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(b)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(c)))))))) 543.34/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(a))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(b))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(c))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(a))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(b))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(c))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.76 f_flat(up(x0)) 543.34/241.76 g_flat(up(x0)) 543.34/241.76 543.34/241.76 We have to consider all minimal (P,Q,R)-chains. 543.34/241.76 ---------------------------------------- 543.34/241.76 543.34/241.76 (511) TransformationProof (EQUIVALENT) 543.34/241.76 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.34/241.76 543.34/241.76 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.34/241.76 543.34/241.76 543.34/241.76 ---------------------------------------- 543.34/241.76 543.34/241.76 (512) 543.34/241.76 Obligation: 543.34/241.76 Q DP problem: 543.34/241.76 The TRS P consists of the following rules: 543.34/241.76 543.34/241.76 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.34/241.76 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.34/241.76 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.34/241.76 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.34/241.76 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.34/241.76 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.34/241.76 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.34/241.76 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.34/241.76 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.34/241.76 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.34/241.76 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.34/241.76 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.34/241.76 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.34/241.76 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.34/241.76 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.34/241.76 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.34/241.76 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.34/241.76 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.34/241.76 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.34/241.76 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.34/241.76 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.34/241.76 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.34/241.76 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.34/241.76 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.34/241.76 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.34/241.76 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.34/241.76 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.34/241.76 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.34/241.76 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.34/241.76 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.34/241.76 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.34/241.76 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.34/241.76 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.34/241.76 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.34/241.76 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.34/241.76 543.34/241.76 The TRS R consists of the following rules: 543.34/241.76 543.34/241.76 down(a) -> up(f(a)) 543.34/241.76 down(b) -> up(g(b)) 543.34/241.76 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.34/241.76 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.34/241.76 down(f(a)) -> f_flat(down(a)) 543.34/241.76 down(f(b)) -> f_flat(down(b)) 543.34/241.76 down(f(g(y4))) -> f_flat(down(g(y4))) 543.34/241.76 down(f(c)) -> f_flat(down(c)) 543.34/241.76 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.34/241.76 down(g(a)) -> g_flat(down(a)) 543.34/241.76 down(g(f(y6))) -> g_flat(down(f(y6))) 543.34/241.76 down(g(b)) -> g_flat(down(b)) 543.34/241.76 down(g(c)) -> g_flat(down(c)) 543.34/241.76 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.34/241.76 down(f(f(a))) -> f_flat(down(f(a))) 543.34/241.76 down(f(f(b))) -> f_flat(down(f(b))) 543.34/241.76 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.34/241.76 down(f(f(c))) -> f_flat(down(f(c))) 543.34/241.76 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.34/241.76 down(g(g(a))) -> g_flat(down(g(a))) 543.34/241.76 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.34/241.76 down(g(g(b))) -> g_flat(down(g(b))) 543.34/241.76 down(g(g(c))) -> g_flat(down(g(c))) 543.34/241.76 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.34/241.76 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.34/241.76 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.34/241.76 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.34/241.76 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.34/241.76 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.34/241.76 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.34/241.76 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.34/241.76 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.34/241.76 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.34/241.76 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.34/241.76 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.34/241.76 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.34/241.76 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.34/241.76 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.34/241.76 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.34/241.76 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.34/241.76 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.34/241.76 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.34/241.76 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.34/241.76 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.34/241.76 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.34/241.76 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.34/241.76 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.34/241.76 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.34/241.76 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.34/241.76 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.34/241.76 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.34/241.76 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.34/241.76 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.34/241.76 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.34/241.76 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.34/241.76 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.34/241.76 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.34/241.76 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.34/241.76 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.34/241.76 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.34/241.76 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.34/241.76 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.34/241.76 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.34/241.76 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.34/241.76 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.76 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.76 543.59/241.76 The set Q consists of the following terms: 543.59/241.76 543.59/241.76 down(a) 543.59/241.76 down(b) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.76 down(f(a)) 543.59/241.76 down(f(b)) 543.59/241.76 down(f(g(x0))) 543.59/241.76 down(f(c)) 543.59/241.76 down(f(fresh_constant)) 543.59/241.76 down(g(a)) 543.59/241.76 down(g(f(x0))) 543.59/241.76 down(g(b)) 543.59/241.76 down(g(c)) 543.59/241.76 down(g(fresh_constant)) 543.59/241.76 down(f(f(a))) 543.59/241.76 down(f(f(b))) 543.59/241.76 down(f(f(g(x0)))) 543.59/241.76 down(f(f(c))) 543.59/241.76 down(f(f(fresh_constant))) 543.59/241.76 down(g(g(a))) 543.59/241.76 down(g(g(f(x0)))) 543.59/241.76 down(g(g(b))) 543.59/241.76 down(g(g(c))) 543.59/241.76 down(g(g(fresh_constant))) 543.59/241.76 down(f(f(f(a)))) 543.59/241.76 down(f(f(f(b)))) 543.59/241.76 down(f(f(f(g(x0))))) 543.59/241.76 down(f(f(f(c)))) 543.59/241.76 down(f(f(f(fresh_constant)))) 543.59/241.76 down(g(g(g(a)))) 543.59/241.76 down(g(g(g(f(x0))))) 543.59/241.76 down(g(g(g(b)))) 543.59/241.76 down(g(g(g(c)))) 543.59/241.76 down(g(g(g(fresh_constant)))) 543.59/241.76 down(f(f(f(f(a))))) 543.59/241.76 down(f(f(f(f(b))))) 543.59/241.76 down(f(f(f(f(g(x0)))))) 543.59/241.76 down(f(f(f(f(c))))) 543.59/241.76 down(f(f(f(f(fresh_constant))))) 543.59/241.76 down(g(g(g(g(a))))) 543.59/241.76 down(g(g(g(g(f(x0)))))) 543.59/241.76 down(g(g(g(g(b))))) 543.59/241.76 down(g(g(g(g(c))))) 543.59/241.76 down(g(g(g(g(fresh_constant))))) 543.59/241.76 down(f(f(f(f(f(a)))))) 543.59/241.76 down(f(f(f(f(f(b)))))) 543.59/241.76 down(f(f(f(f(f(g(x0))))))) 543.59/241.76 down(f(f(f(f(f(c)))))) 543.59/241.76 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.76 down(g(g(g(g(g(a)))))) 543.59/241.76 down(g(g(g(g(g(f(x0))))))) 543.59/241.76 down(g(g(g(g(g(b)))))) 543.59/241.76 down(g(g(g(g(g(c)))))) 543.59/241.76 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.76 down(f(f(f(f(f(f(a))))))) 543.59/241.76 down(f(f(f(f(f(f(b))))))) 543.59/241.76 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.76 down(f(f(f(f(f(f(c))))))) 543.59/241.76 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.76 down(g(g(g(g(g(g(a))))))) 543.59/241.76 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.76 down(g(g(g(g(g(g(b))))))) 543.59/241.76 down(g(g(g(g(g(g(c))))))) 543.59/241.76 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.76 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 f_flat(up(x0)) 543.59/241.76 g_flat(up(x0)) 543.59/241.76 543.59/241.76 We have to consider all minimal (P,Q,R)-chains. 543.59/241.76 ---------------------------------------- 543.59/241.76 543.59/241.76 (513) TransformationProof (EQUIVALENT) 543.59/241.76 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.76 543.59/241.76 (TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))),TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.59/241.76 543.59/241.76 543.59/241.76 ---------------------------------------- 543.59/241.76 543.59/241.76 (514) 543.59/241.76 Obligation: 543.59/241.76 Q DP problem: 543.59/241.76 The TRS P consists of the following rules: 543.59/241.76 543.59/241.76 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.76 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.76 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.76 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.76 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.76 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.76 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.76 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.76 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.76 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.76 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.76 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.76 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.76 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.76 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.76 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.76 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.76 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.76 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.76 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.76 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.76 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.76 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.76 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.76 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.76 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.76 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.76 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.76 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.76 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.76 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.76 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.76 543.59/241.76 The TRS R consists of the following rules: 543.59/241.76 543.59/241.76 down(a) -> up(f(a)) 543.59/241.76 down(b) -> up(g(b)) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.76 down(f(a)) -> f_flat(down(a)) 543.59/241.76 down(f(b)) -> f_flat(down(b)) 543.59/241.76 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.76 down(f(c)) -> f_flat(down(c)) 543.59/241.76 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.76 down(g(a)) -> g_flat(down(a)) 543.59/241.76 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.76 down(g(b)) -> g_flat(down(b)) 543.59/241.76 down(g(c)) -> g_flat(down(c)) 543.59/241.76 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.76 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.76 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.76 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.76 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.76 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.76 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.76 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.76 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.76 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.76 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.76 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.76 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.76 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.76 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.76 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.76 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.76 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.76 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.76 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.76 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.76 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.76 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.76 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.76 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.76 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.76 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.76 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.76 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.76 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.76 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.76 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.76 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.76 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.76 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.76 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.76 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.76 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.76 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.76 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.76 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.76 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.76 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.76 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.76 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.76 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.76 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.76 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.76 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.76 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.76 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.76 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.76 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.76 543.59/241.76 The set Q consists of the following terms: 543.59/241.76 543.59/241.76 down(a) 543.59/241.76 down(b) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.76 down(f(a)) 543.59/241.76 down(f(b)) 543.59/241.76 down(f(g(x0))) 543.59/241.76 down(f(c)) 543.59/241.76 down(f(fresh_constant)) 543.59/241.76 down(g(a)) 543.59/241.76 down(g(f(x0))) 543.59/241.76 down(g(b)) 543.59/241.76 down(g(c)) 543.59/241.76 down(g(fresh_constant)) 543.59/241.76 down(f(f(a))) 543.59/241.76 down(f(f(b))) 543.59/241.76 down(f(f(g(x0)))) 543.59/241.76 down(f(f(c))) 543.59/241.76 down(f(f(fresh_constant))) 543.59/241.76 down(g(g(a))) 543.59/241.76 down(g(g(f(x0)))) 543.59/241.76 down(g(g(b))) 543.59/241.76 down(g(g(c))) 543.59/241.76 down(g(g(fresh_constant))) 543.59/241.76 down(f(f(f(a)))) 543.59/241.76 down(f(f(f(b)))) 543.59/241.76 down(f(f(f(g(x0))))) 543.59/241.76 down(f(f(f(c)))) 543.59/241.76 down(f(f(f(fresh_constant)))) 543.59/241.76 down(g(g(g(a)))) 543.59/241.76 down(g(g(g(f(x0))))) 543.59/241.76 down(g(g(g(b)))) 543.59/241.76 down(g(g(g(c)))) 543.59/241.76 down(g(g(g(fresh_constant)))) 543.59/241.76 down(f(f(f(f(a))))) 543.59/241.76 down(f(f(f(f(b))))) 543.59/241.76 down(f(f(f(f(g(x0)))))) 543.59/241.76 down(f(f(f(f(c))))) 543.59/241.76 down(f(f(f(f(fresh_constant))))) 543.59/241.76 down(g(g(g(g(a))))) 543.59/241.76 down(g(g(g(g(f(x0)))))) 543.59/241.76 down(g(g(g(g(b))))) 543.59/241.76 down(g(g(g(g(c))))) 543.59/241.76 down(g(g(g(g(fresh_constant))))) 543.59/241.76 down(f(f(f(f(f(a)))))) 543.59/241.76 down(f(f(f(f(f(b)))))) 543.59/241.76 down(f(f(f(f(f(g(x0))))))) 543.59/241.76 down(f(f(f(f(f(c)))))) 543.59/241.76 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.76 down(g(g(g(g(g(a)))))) 543.59/241.76 down(g(g(g(g(g(f(x0))))))) 543.59/241.76 down(g(g(g(g(g(b)))))) 543.59/241.76 down(g(g(g(g(g(c)))))) 543.59/241.76 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.76 down(f(f(f(f(f(f(a))))))) 543.59/241.76 down(f(f(f(f(f(f(b))))))) 543.59/241.76 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.76 down(f(f(f(f(f(f(c))))))) 543.59/241.76 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.76 down(g(g(g(g(g(g(a))))))) 543.59/241.76 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.76 down(g(g(g(g(g(g(b))))))) 543.59/241.76 down(g(g(g(g(g(g(c))))))) 543.59/241.76 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.76 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 f_flat(up(x0)) 543.59/241.76 g_flat(up(x0)) 543.59/241.76 543.59/241.76 We have to consider all minimal (P,Q,R)-chains. 543.59/241.76 ---------------------------------------- 543.59/241.76 543.59/241.76 (515) TransformationProof (EQUIVALENT) 543.59/241.76 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(b)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.76 543.59/241.76 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.59/241.76 543.59/241.76 543.59/241.76 ---------------------------------------- 543.59/241.76 543.59/241.76 (516) 543.59/241.76 Obligation: 543.59/241.76 Q DP problem: 543.59/241.76 The TRS P consists of the following rules: 543.59/241.76 543.59/241.76 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.76 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.76 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.76 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.76 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.76 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.76 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.76 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.76 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.76 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.76 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.76 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.76 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.76 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.76 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.76 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.76 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.76 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.76 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.76 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.76 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.76 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.76 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.76 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.76 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.76 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.76 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.76 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.76 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.76 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.76 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.76 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.76 543.59/241.76 The TRS R consists of the following rules: 543.59/241.76 543.59/241.76 down(a) -> up(f(a)) 543.59/241.76 down(b) -> up(g(b)) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.76 down(f(a)) -> f_flat(down(a)) 543.59/241.76 down(f(b)) -> f_flat(down(b)) 543.59/241.76 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.76 down(f(c)) -> f_flat(down(c)) 543.59/241.76 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.76 down(g(a)) -> g_flat(down(a)) 543.59/241.76 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.76 down(g(b)) -> g_flat(down(b)) 543.59/241.76 down(g(c)) -> g_flat(down(c)) 543.59/241.76 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.76 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.76 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.76 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.76 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.76 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.76 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.76 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.76 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.76 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.76 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.76 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.76 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.76 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.76 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.76 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.76 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.76 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.76 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.76 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.76 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.76 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.76 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.76 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.76 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.76 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.76 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.76 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.76 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.76 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.76 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.76 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.76 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.76 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.76 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.76 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.76 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.76 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.76 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.76 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.76 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.76 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.76 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.76 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.76 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.76 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.76 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.76 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.76 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.76 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.76 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.76 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.76 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.76 543.59/241.76 The set Q consists of the following terms: 543.59/241.76 543.59/241.76 down(a) 543.59/241.76 down(b) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.76 down(f(a)) 543.59/241.76 down(f(b)) 543.59/241.76 down(f(g(x0))) 543.59/241.76 down(f(c)) 543.59/241.76 down(f(fresh_constant)) 543.59/241.76 down(g(a)) 543.59/241.76 down(g(f(x0))) 543.59/241.76 down(g(b)) 543.59/241.76 down(g(c)) 543.59/241.76 down(g(fresh_constant)) 543.59/241.76 down(f(f(a))) 543.59/241.76 down(f(f(b))) 543.59/241.76 down(f(f(g(x0)))) 543.59/241.76 down(f(f(c))) 543.59/241.76 down(f(f(fresh_constant))) 543.59/241.76 down(g(g(a))) 543.59/241.76 down(g(g(f(x0)))) 543.59/241.76 down(g(g(b))) 543.59/241.76 down(g(g(c))) 543.59/241.76 down(g(g(fresh_constant))) 543.59/241.76 down(f(f(f(a)))) 543.59/241.76 down(f(f(f(b)))) 543.59/241.76 down(f(f(f(g(x0))))) 543.59/241.76 down(f(f(f(c)))) 543.59/241.76 down(f(f(f(fresh_constant)))) 543.59/241.76 down(g(g(g(a)))) 543.59/241.76 down(g(g(g(f(x0))))) 543.59/241.76 down(g(g(g(b)))) 543.59/241.76 down(g(g(g(c)))) 543.59/241.76 down(g(g(g(fresh_constant)))) 543.59/241.76 down(f(f(f(f(a))))) 543.59/241.76 down(f(f(f(f(b))))) 543.59/241.76 down(f(f(f(f(g(x0)))))) 543.59/241.76 down(f(f(f(f(c))))) 543.59/241.76 down(f(f(f(f(fresh_constant))))) 543.59/241.76 down(g(g(g(g(a))))) 543.59/241.76 down(g(g(g(g(f(x0)))))) 543.59/241.76 down(g(g(g(g(b))))) 543.59/241.76 down(g(g(g(g(c))))) 543.59/241.76 down(g(g(g(g(fresh_constant))))) 543.59/241.76 down(f(f(f(f(f(a)))))) 543.59/241.76 down(f(f(f(f(f(b)))))) 543.59/241.76 down(f(f(f(f(f(g(x0))))))) 543.59/241.76 down(f(f(f(f(f(c)))))) 543.59/241.76 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.76 down(g(g(g(g(g(a)))))) 543.59/241.76 down(g(g(g(g(g(f(x0))))))) 543.59/241.76 down(g(g(g(g(g(b)))))) 543.59/241.76 down(g(g(g(g(g(c)))))) 543.59/241.76 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.76 down(f(f(f(f(f(f(a))))))) 543.59/241.76 down(f(f(f(f(f(f(b))))))) 543.59/241.76 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.76 down(f(f(f(f(f(f(c))))))) 543.59/241.76 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.76 down(g(g(g(g(g(g(a))))))) 543.59/241.76 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.76 down(g(g(g(g(g(g(b))))))) 543.59/241.76 down(g(g(g(g(g(g(c))))))) 543.59/241.76 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.76 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 f_flat(up(x0)) 543.59/241.76 g_flat(up(x0)) 543.59/241.76 543.59/241.76 We have to consider all minimal (P,Q,R)-chains. 543.59/241.76 ---------------------------------------- 543.59/241.76 543.59/241.76 (517) TransformationProof (EQUIVALENT) 543.59/241.76 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(c)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.76 543.59/241.76 (TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))),TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.59/241.76 543.59/241.76 543.59/241.76 ---------------------------------------- 543.59/241.76 543.59/241.76 (518) 543.59/241.76 Obligation: 543.59/241.76 Q DP problem: 543.59/241.76 The TRS P consists of the following rules: 543.59/241.76 543.59/241.76 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.76 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.76 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.76 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.76 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.76 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.76 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.76 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.76 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.76 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.76 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.76 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.76 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.76 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.76 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.76 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.76 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.76 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.76 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.76 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.76 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.76 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.76 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.76 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.76 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.76 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.76 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.76 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.76 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.76 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.76 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.76 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.76 543.59/241.76 The TRS R consists of the following rules: 543.59/241.76 543.59/241.76 down(a) -> up(f(a)) 543.59/241.76 down(b) -> up(g(b)) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.76 down(f(a)) -> f_flat(down(a)) 543.59/241.76 down(f(b)) -> f_flat(down(b)) 543.59/241.76 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.76 down(f(c)) -> f_flat(down(c)) 543.59/241.76 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.76 down(g(a)) -> g_flat(down(a)) 543.59/241.76 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.76 down(g(b)) -> g_flat(down(b)) 543.59/241.76 down(g(c)) -> g_flat(down(c)) 543.59/241.76 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.76 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.76 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.76 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.76 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.76 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.76 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.76 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.76 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.76 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.76 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.76 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.76 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.76 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.76 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.76 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.76 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.76 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.76 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.76 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.76 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.76 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.76 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.76 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.76 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.76 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.76 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.76 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.76 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.76 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.76 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.76 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.76 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.76 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.76 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.76 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.76 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.76 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.76 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.76 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.76 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.76 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.76 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.76 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.76 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.76 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.76 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.76 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.76 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.76 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.76 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.76 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.76 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.76 543.59/241.76 The set Q consists of the following terms: 543.59/241.76 543.59/241.76 down(a) 543.59/241.76 down(b) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.76 down(f(a)) 543.59/241.76 down(f(b)) 543.59/241.76 down(f(g(x0))) 543.59/241.76 down(f(c)) 543.59/241.76 down(f(fresh_constant)) 543.59/241.76 down(g(a)) 543.59/241.76 down(g(f(x0))) 543.59/241.76 down(g(b)) 543.59/241.76 down(g(c)) 543.59/241.76 down(g(fresh_constant)) 543.59/241.76 down(f(f(a))) 543.59/241.76 down(f(f(b))) 543.59/241.76 down(f(f(g(x0)))) 543.59/241.76 down(f(f(c))) 543.59/241.76 down(f(f(fresh_constant))) 543.59/241.76 down(g(g(a))) 543.59/241.76 down(g(g(f(x0)))) 543.59/241.76 down(g(g(b))) 543.59/241.76 down(g(g(c))) 543.59/241.76 down(g(g(fresh_constant))) 543.59/241.76 down(f(f(f(a)))) 543.59/241.76 down(f(f(f(b)))) 543.59/241.76 down(f(f(f(g(x0))))) 543.59/241.76 down(f(f(f(c)))) 543.59/241.76 down(f(f(f(fresh_constant)))) 543.59/241.76 down(g(g(g(a)))) 543.59/241.76 down(g(g(g(f(x0))))) 543.59/241.76 down(g(g(g(b)))) 543.59/241.76 down(g(g(g(c)))) 543.59/241.76 down(g(g(g(fresh_constant)))) 543.59/241.76 down(f(f(f(f(a))))) 543.59/241.76 down(f(f(f(f(b))))) 543.59/241.76 down(f(f(f(f(g(x0)))))) 543.59/241.76 down(f(f(f(f(c))))) 543.59/241.76 down(f(f(f(f(fresh_constant))))) 543.59/241.76 down(g(g(g(g(a))))) 543.59/241.76 down(g(g(g(g(f(x0)))))) 543.59/241.76 down(g(g(g(g(b))))) 543.59/241.76 down(g(g(g(g(c))))) 543.59/241.76 down(g(g(g(g(fresh_constant))))) 543.59/241.76 down(f(f(f(f(f(a)))))) 543.59/241.76 down(f(f(f(f(f(b)))))) 543.59/241.76 down(f(f(f(f(f(g(x0))))))) 543.59/241.76 down(f(f(f(f(f(c)))))) 543.59/241.76 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.76 down(g(g(g(g(g(a)))))) 543.59/241.76 down(g(g(g(g(g(f(x0))))))) 543.59/241.76 down(g(g(g(g(g(b)))))) 543.59/241.76 down(g(g(g(g(g(c)))))) 543.59/241.76 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.76 down(f(f(f(f(f(f(a))))))) 543.59/241.76 down(f(f(f(f(f(f(b))))))) 543.59/241.76 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.76 down(f(f(f(f(f(f(c))))))) 543.59/241.76 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.76 down(g(g(g(g(g(g(a))))))) 543.59/241.76 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.76 down(g(g(g(g(g(g(b))))))) 543.59/241.76 down(g(g(g(g(g(g(c))))))) 543.59/241.76 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.76 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 f_flat(up(x0)) 543.59/241.76 g_flat(up(x0)) 543.59/241.76 543.59/241.76 We have to consider all minimal (P,Q,R)-chains. 543.59/241.76 ---------------------------------------- 543.59/241.76 543.59/241.76 (519) TransformationProof (EQUIVALENT) 543.59/241.76 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.76 543.59/241.76 (TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))),TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.59/241.76 543.59/241.76 543.59/241.76 ---------------------------------------- 543.59/241.76 543.59/241.76 (520) 543.59/241.76 Obligation: 543.59/241.76 Q DP problem: 543.59/241.76 The TRS P consists of the following rules: 543.59/241.76 543.59/241.76 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.76 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.76 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.76 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.76 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.76 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.76 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.76 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.76 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.76 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.76 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.76 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.76 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.76 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.76 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.76 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.76 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.76 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.76 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.76 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.76 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.76 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.76 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.76 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.76 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.76 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.76 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.76 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.76 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.76 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.76 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.76 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.76 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.76 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.76 543.59/241.76 The TRS R consists of the following rules: 543.59/241.76 543.59/241.76 down(a) -> up(f(a)) 543.59/241.76 down(b) -> up(g(b)) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.76 down(f(a)) -> f_flat(down(a)) 543.59/241.76 down(f(b)) -> f_flat(down(b)) 543.59/241.76 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.76 down(f(c)) -> f_flat(down(c)) 543.59/241.76 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.76 down(g(a)) -> g_flat(down(a)) 543.59/241.76 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.76 down(g(b)) -> g_flat(down(b)) 543.59/241.76 down(g(c)) -> g_flat(down(c)) 543.59/241.76 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.76 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.76 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.76 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.76 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.76 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.76 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.76 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.76 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.76 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.76 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.76 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.76 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.76 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.76 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.76 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.76 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.76 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.76 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.76 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.76 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.76 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.76 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.76 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.76 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.76 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.76 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.76 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.76 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.76 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.76 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.76 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.76 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.76 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.76 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.76 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.76 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.76 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.76 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.76 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.76 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.76 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.76 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.76 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.76 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.76 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.76 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.76 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.76 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.76 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.76 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.76 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.76 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.76 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.76 543.59/241.76 The set Q consists of the following terms: 543.59/241.76 543.59/241.76 down(a) 543.59/241.76 down(b) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.76 down(f(a)) 543.59/241.76 down(f(b)) 543.59/241.76 down(f(g(x0))) 543.59/241.76 down(f(c)) 543.59/241.76 down(f(fresh_constant)) 543.59/241.76 down(g(a)) 543.59/241.76 down(g(f(x0))) 543.59/241.76 down(g(b)) 543.59/241.76 down(g(c)) 543.59/241.76 down(g(fresh_constant)) 543.59/241.76 down(f(f(a))) 543.59/241.76 down(f(f(b))) 543.59/241.76 down(f(f(g(x0)))) 543.59/241.76 down(f(f(c))) 543.59/241.76 down(f(f(fresh_constant))) 543.59/241.76 down(g(g(a))) 543.59/241.76 down(g(g(f(x0)))) 543.59/241.76 down(g(g(b))) 543.59/241.76 down(g(g(c))) 543.59/241.76 down(g(g(fresh_constant))) 543.59/241.76 down(f(f(f(a)))) 543.59/241.76 down(f(f(f(b)))) 543.59/241.76 down(f(f(f(g(x0))))) 543.59/241.76 down(f(f(f(c)))) 543.59/241.76 down(f(f(f(fresh_constant)))) 543.59/241.76 down(g(g(g(a)))) 543.59/241.76 down(g(g(g(f(x0))))) 543.59/241.76 down(g(g(g(b)))) 543.59/241.76 down(g(g(g(c)))) 543.59/241.76 down(g(g(g(fresh_constant)))) 543.59/241.76 down(f(f(f(f(a))))) 543.59/241.76 down(f(f(f(f(b))))) 543.59/241.76 down(f(f(f(f(g(x0)))))) 543.59/241.76 down(f(f(f(f(c))))) 543.59/241.76 down(f(f(f(f(fresh_constant))))) 543.59/241.76 down(g(g(g(g(a))))) 543.59/241.76 down(g(g(g(g(f(x0)))))) 543.59/241.76 down(g(g(g(g(b))))) 543.59/241.76 down(g(g(g(g(c))))) 543.59/241.76 down(g(g(g(g(fresh_constant))))) 543.59/241.76 down(f(f(f(f(f(a)))))) 543.59/241.76 down(f(f(f(f(f(b)))))) 543.59/241.76 down(f(f(f(f(f(g(x0))))))) 543.59/241.76 down(f(f(f(f(f(c)))))) 543.59/241.76 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.76 down(g(g(g(g(g(a)))))) 543.59/241.76 down(g(g(g(g(g(f(x0))))))) 543.59/241.76 down(g(g(g(g(g(b)))))) 543.59/241.76 down(g(g(g(g(g(c)))))) 543.59/241.76 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.76 down(f(f(f(f(f(f(a))))))) 543.59/241.76 down(f(f(f(f(f(f(b))))))) 543.59/241.76 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.76 down(f(f(f(f(f(f(c))))))) 543.59/241.76 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.76 down(g(g(g(g(g(g(a))))))) 543.59/241.76 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.76 down(g(g(g(g(g(g(b))))))) 543.59/241.76 down(g(g(g(g(g(g(c))))))) 543.59/241.76 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.76 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.76 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.76 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.76 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 f_flat(up(x0)) 543.59/241.77 g_flat(up(x0)) 543.59/241.77 543.59/241.77 We have to consider all minimal (P,Q,R)-chains. 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (521) TransformationProof (EQUIVALENT) 543.59/241.77 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.77 543.59/241.77 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.59/241.77 543.59/241.77 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (522) 543.59/241.77 Obligation: 543.59/241.77 Q DP problem: 543.59/241.77 The TRS P consists of the following rules: 543.59/241.77 543.59/241.77 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.77 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.77 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.77 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.77 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.77 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.77 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.77 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.77 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.77 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.77 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.77 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.77 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.77 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.77 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.77 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.77 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.77 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.77 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.77 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.77 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.77 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.77 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.77 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.77 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.77 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.77 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.77 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.77 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.77 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.77 543.59/241.77 The TRS R consists of the following rules: 543.59/241.77 543.59/241.77 down(a) -> up(f(a)) 543.59/241.77 down(b) -> up(g(b)) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.77 down(f(a)) -> f_flat(down(a)) 543.59/241.77 down(f(b)) -> f_flat(down(b)) 543.59/241.77 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.77 down(f(c)) -> f_flat(down(c)) 543.59/241.77 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.77 down(g(a)) -> g_flat(down(a)) 543.59/241.77 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.77 down(g(b)) -> g_flat(down(b)) 543.59/241.77 down(g(c)) -> g_flat(down(c)) 543.59/241.77 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.77 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.77 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.77 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.77 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.77 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.77 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.77 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.77 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.77 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.77 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.77 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.77 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.77 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.77 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.77 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.77 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.77 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.77 543.59/241.77 The set Q consists of the following terms: 543.59/241.77 543.59/241.77 down(a) 543.59/241.77 down(b) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.77 down(f(a)) 543.59/241.77 down(f(b)) 543.59/241.77 down(f(g(x0))) 543.59/241.77 down(f(c)) 543.59/241.77 down(f(fresh_constant)) 543.59/241.77 down(g(a)) 543.59/241.77 down(g(f(x0))) 543.59/241.77 down(g(b)) 543.59/241.77 down(g(c)) 543.59/241.77 down(g(fresh_constant)) 543.59/241.77 down(f(f(a))) 543.59/241.77 down(f(f(b))) 543.59/241.77 down(f(f(g(x0)))) 543.59/241.77 down(f(f(c))) 543.59/241.77 down(f(f(fresh_constant))) 543.59/241.77 down(g(g(a))) 543.59/241.77 down(g(g(f(x0)))) 543.59/241.77 down(g(g(b))) 543.59/241.77 down(g(g(c))) 543.59/241.77 down(g(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) 543.59/241.77 down(f(f(f(g(x0))))) 543.59/241.77 down(f(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) 543.59/241.77 down(g(g(g(f(x0))))) 543.59/241.77 down(g(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(x0)))))) 543.59/241.77 down(f(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(x0)))))) 543.59/241.77 down(g(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(x0))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(x0))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 f_flat(up(x0)) 543.59/241.77 g_flat(up(x0)) 543.59/241.77 543.59/241.77 We have to consider all minimal (P,Q,R)-chains. 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (523) TransformationProof (EQUIVALENT) 543.59/241.77 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.77 543.59/241.77 (TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))),TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.59/241.77 543.59/241.77 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (524) 543.59/241.77 Obligation: 543.59/241.77 Q DP problem: 543.59/241.77 The TRS P consists of the following rules: 543.59/241.77 543.59/241.77 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.77 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.77 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.77 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.77 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.77 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.77 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.77 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.77 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.77 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.77 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.77 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.77 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.77 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.77 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.77 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.77 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.77 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.77 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.77 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.77 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.77 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.77 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.77 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.77 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.77 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.77 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.77 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.77 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.77 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.77 543.59/241.77 The TRS R consists of the following rules: 543.59/241.77 543.59/241.77 down(a) -> up(f(a)) 543.59/241.77 down(b) -> up(g(b)) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.77 down(f(a)) -> f_flat(down(a)) 543.59/241.77 down(f(b)) -> f_flat(down(b)) 543.59/241.77 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.77 down(f(c)) -> f_flat(down(c)) 543.59/241.77 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.77 down(g(a)) -> g_flat(down(a)) 543.59/241.77 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.77 down(g(b)) -> g_flat(down(b)) 543.59/241.77 down(g(c)) -> g_flat(down(c)) 543.59/241.77 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.77 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.77 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.77 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.77 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.77 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.77 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.77 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.77 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.77 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.77 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.77 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.77 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.77 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.77 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.77 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.77 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.77 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.77 543.59/241.77 The set Q consists of the following terms: 543.59/241.77 543.59/241.77 down(a) 543.59/241.77 down(b) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.77 down(f(a)) 543.59/241.77 down(f(b)) 543.59/241.77 down(f(g(x0))) 543.59/241.77 down(f(c)) 543.59/241.77 down(f(fresh_constant)) 543.59/241.77 down(g(a)) 543.59/241.77 down(g(f(x0))) 543.59/241.77 down(g(b)) 543.59/241.77 down(g(c)) 543.59/241.77 down(g(fresh_constant)) 543.59/241.77 down(f(f(a))) 543.59/241.77 down(f(f(b))) 543.59/241.77 down(f(f(g(x0)))) 543.59/241.77 down(f(f(c))) 543.59/241.77 down(f(f(fresh_constant))) 543.59/241.77 down(g(g(a))) 543.59/241.77 down(g(g(f(x0)))) 543.59/241.77 down(g(g(b))) 543.59/241.77 down(g(g(c))) 543.59/241.77 down(g(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) 543.59/241.77 down(f(f(f(g(x0))))) 543.59/241.77 down(f(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) 543.59/241.77 down(g(g(g(f(x0))))) 543.59/241.77 down(g(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(x0)))))) 543.59/241.77 down(f(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(x0)))))) 543.59/241.77 down(g(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(x0))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(x0))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 f_flat(up(x0)) 543.59/241.77 g_flat(up(x0)) 543.59/241.77 543.59/241.77 We have to consider all minimal (P,Q,R)-chains. 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (525) TransformationProof (EQUIVALENT) 543.59/241.77 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.77 543.59/241.77 (TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))),TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.59/241.77 543.59/241.77 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (526) 543.59/241.77 Obligation: 543.59/241.77 Q DP problem: 543.59/241.77 The TRS P consists of the following rules: 543.59/241.77 543.59/241.77 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.77 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.77 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.77 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.77 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.77 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.77 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.77 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.77 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.77 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.77 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.77 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.77 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.77 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.77 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.77 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.77 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.77 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.77 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.77 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.77 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.77 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.77 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.77 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.77 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.77 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.77 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.77 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.77 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.77 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.77 543.59/241.77 The TRS R consists of the following rules: 543.59/241.77 543.59/241.77 down(a) -> up(f(a)) 543.59/241.77 down(b) -> up(g(b)) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.77 down(f(a)) -> f_flat(down(a)) 543.59/241.77 down(f(b)) -> f_flat(down(b)) 543.59/241.77 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.77 down(f(c)) -> f_flat(down(c)) 543.59/241.77 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.77 down(g(a)) -> g_flat(down(a)) 543.59/241.77 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.77 down(g(b)) -> g_flat(down(b)) 543.59/241.77 down(g(c)) -> g_flat(down(c)) 543.59/241.77 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.77 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.77 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.77 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.77 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.77 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.77 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.77 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.77 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.77 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.77 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.77 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.77 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.77 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.77 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.77 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.77 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.77 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.77 543.59/241.77 The set Q consists of the following terms: 543.59/241.77 543.59/241.77 down(a) 543.59/241.77 down(b) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.77 down(f(a)) 543.59/241.77 down(f(b)) 543.59/241.77 down(f(g(x0))) 543.59/241.77 down(f(c)) 543.59/241.77 down(f(fresh_constant)) 543.59/241.77 down(g(a)) 543.59/241.77 down(g(f(x0))) 543.59/241.77 down(g(b)) 543.59/241.77 down(g(c)) 543.59/241.77 down(g(fresh_constant)) 543.59/241.77 down(f(f(a))) 543.59/241.77 down(f(f(b))) 543.59/241.77 down(f(f(g(x0)))) 543.59/241.77 down(f(f(c))) 543.59/241.77 down(f(f(fresh_constant))) 543.59/241.77 down(g(g(a))) 543.59/241.77 down(g(g(f(x0)))) 543.59/241.77 down(g(g(b))) 543.59/241.77 down(g(g(c))) 543.59/241.77 down(g(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) 543.59/241.77 down(f(f(f(g(x0))))) 543.59/241.77 down(f(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) 543.59/241.77 down(g(g(g(f(x0))))) 543.59/241.77 down(g(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(x0)))))) 543.59/241.77 down(f(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(x0)))))) 543.59/241.77 down(g(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(x0))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(x0))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 f_flat(up(x0)) 543.59/241.77 g_flat(up(x0)) 543.59/241.77 543.59/241.77 We have to consider all minimal (P,Q,R)-chains. 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (527) TransformationProof (EQUIVALENT) 543.59/241.77 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.77 543.59/241.77 (TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))),TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.59/241.77 543.59/241.77 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (528) 543.59/241.77 Obligation: 543.59/241.77 Q DP problem: 543.59/241.77 The TRS P consists of the following rules: 543.59/241.77 543.59/241.77 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.77 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.77 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.77 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.77 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.77 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.77 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.77 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.77 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.77 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.77 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.77 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.77 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.77 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.77 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.77 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.77 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.77 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.77 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.77 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.77 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.77 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.77 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.77 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.77 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.77 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.77 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.77 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.77 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.77 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.77 543.59/241.77 The TRS R consists of the following rules: 543.59/241.77 543.59/241.77 down(a) -> up(f(a)) 543.59/241.77 down(b) -> up(g(b)) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.77 down(f(a)) -> f_flat(down(a)) 543.59/241.77 down(f(b)) -> f_flat(down(b)) 543.59/241.77 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.77 down(f(c)) -> f_flat(down(c)) 543.59/241.77 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.77 down(g(a)) -> g_flat(down(a)) 543.59/241.77 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.77 down(g(b)) -> g_flat(down(b)) 543.59/241.77 down(g(c)) -> g_flat(down(c)) 543.59/241.77 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.77 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.77 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.77 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.77 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.77 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.77 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.77 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.77 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.77 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.77 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.77 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.77 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.77 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.77 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.77 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.77 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.77 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.77 543.59/241.77 The set Q consists of the following terms: 543.59/241.77 543.59/241.77 down(a) 543.59/241.77 down(b) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.77 down(f(a)) 543.59/241.77 down(f(b)) 543.59/241.77 down(f(g(x0))) 543.59/241.77 down(f(c)) 543.59/241.77 down(f(fresh_constant)) 543.59/241.77 down(g(a)) 543.59/241.77 down(g(f(x0))) 543.59/241.77 down(g(b)) 543.59/241.77 down(g(c)) 543.59/241.77 down(g(fresh_constant)) 543.59/241.77 down(f(f(a))) 543.59/241.77 down(f(f(b))) 543.59/241.77 down(f(f(g(x0)))) 543.59/241.77 down(f(f(c))) 543.59/241.77 down(f(f(fresh_constant))) 543.59/241.77 down(g(g(a))) 543.59/241.77 down(g(g(f(x0)))) 543.59/241.77 down(g(g(b))) 543.59/241.77 down(g(g(c))) 543.59/241.77 down(g(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) 543.59/241.77 down(f(f(f(g(x0))))) 543.59/241.77 down(f(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) 543.59/241.77 down(g(g(g(f(x0))))) 543.59/241.77 down(g(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(x0)))))) 543.59/241.77 down(f(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(x0)))))) 543.59/241.77 down(g(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(x0))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(x0))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 f_flat(up(x0)) 543.59/241.77 g_flat(up(x0)) 543.59/241.77 543.59/241.77 We have to consider all minimal (P,Q,R)-chains. 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (529) TransformationProof (EQUIVALENT) 543.59/241.77 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.77 543.59/241.77 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.59/241.77 543.59/241.77 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (530) 543.59/241.77 Obligation: 543.59/241.77 Q DP problem: 543.59/241.77 The TRS P consists of the following rules: 543.59/241.77 543.59/241.77 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.77 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.77 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.77 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.77 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.77 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.77 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.77 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.77 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.77 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.77 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.77 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.77 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.77 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.77 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.77 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.77 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.77 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.77 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.77 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.77 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.77 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.77 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.77 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.77 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.77 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.77 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.77 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.77 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.77 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.77 543.59/241.77 The TRS R consists of the following rules: 543.59/241.77 543.59/241.77 down(a) -> up(f(a)) 543.59/241.77 down(b) -> up(g(b)) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.77 down(f(a)) -> f_flat(down(a)) 543.59/241.77 down(f(b)) -> f_flat(down(b)) 543.59/241.77 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.77 down(f(c)) -> f_flat(down(c)) 543.59/241.77 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.77 down(g(a)) -> g_flat(down(a)) 543.59/241.77 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.77 down(g(b)) -> g_flat(down(b)) 543.59/241.77 down(g(c)) -> g_flat(down(c)) 543.59/241.77 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.77 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.77 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.77 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.77 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.77 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.77 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.77 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.77 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.77 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.77 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.77 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.77 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.77 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.77 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.77 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.77 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.77 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.77 543.59/241.77 The set Q consists of the following terms: 543.59/241.77 543.59/241.77 down(a) 543.59/241.77 down(b) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.77 down(f(a)) 543.59/241.77 down(f(b)) 543.59/241.77 down(f(g(x0))) 543.59/241.77 down(f(c)) 543.59/241.77 down(f(fresh_constant)) 543.59/241.77 down(g(a)) 543.59/241.77 down(g(f(x0))) 543.59/241.77 down(g(b)) 543.59/241.77 down(g(c)) 543.59/241.77 down(g(fresh_constant)) 543.59/241.77 down(f(f(a))) 543.59/241.77 down(f(f(b))) 543.59/241.77 down(f(f(g(x0)))) 543.59/241.77 down(f(f(c))) 543.59/241.77 down(f(f(fresh_constant))) 543.59/241.77 down(g(g(a))) 543.59/241.77 down(g(g(f(x0)))) 543.59/241.77 down(g(g(b))) 543.59/241.77 down(g(g(c))) 543.59/241.77 down(g(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) 543.59/241.77 down(f(f(f(g(x0))))) 543.59/241.77 down(f(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) 543.59/241.77 down(g(g(g(f(x0))))) 543.59/241.77 down(g(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(x0)))))) 543.59/241.77 down(f(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(x0)))))) 543.59/241.77 down(g(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(x0))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(x0))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 f_flat(up(x0)) 543.59/241.77 g_flat(up(x0)) 543.59/241.77 543.59/241.77 We have to consider all minimal (P,Q,R)-chains. 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (531) TransformationProof (EQUIVALENT) 543.59/241.77 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.77 543.59/241.77 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.59/241.77 543.59/241.77 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (532) 543.59/241.77 Obligation: 543.59/241.77 Q DP problem: 543.59/241.77 The TRS P consists of the following rules: 543.59/241.77 543.59/241.77 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.77 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.77 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.77 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.77 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.77 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.77 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.77 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.77 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.77 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.77 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.77 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.77 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.77 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.77 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.77 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.77 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.77 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.77 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.77 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.77 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.77 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.77 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.77 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.77 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.77 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.77 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.77 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.77 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.77 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.77 543.59/241.77 The TRS R consists of the following rules: 543.59/241.77 543.59/241.77 down(a) -> up(f(a)) 543.59/241.77 down(b) -> up(g(b)) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.77 down(f(a)) -> f_flat(down(a)) 543.59/241.77 down(f(b)) -> f_flat(down(b)) 543.59/241.77 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.77 down(f(c)) -> f_flat(down(c)) 543.59/241.77 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.77 down(g(a)) -> g_flat(down(a)) 543.59/241.77 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.77 down(g(b)) -> g_flat(down(b)) 543.59/241.77 down(g(c)) -> g_flat(down(c)) 543.59/241.77 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.77 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.77 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.77 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.77 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.77 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.77 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.77 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.77 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.77 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.77 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.77 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.77 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.77 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.77 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.77 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.77 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.77 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.77 543.59/241.77 The set Q consists of the following terms: 543.59/241.77 543.59/241.77 down(a) 543.59/241.77 down(b) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.77 down(f(a)) 543.59/241.77 down(f(b)) 543.59/241.77 down(f(g(x0))) 543.59/241.77 down(f(c)) 543.59/241.77 down(f(fresh_constant)) 543.59/241.77 down(g(a)) 543.59/241.77 down(g(f(x0))) 543.59/241.77 down(g(b)) 543.59/241.77 down(g(c)) 543.59/241.77 down(g(fresh_constant)) 543.59/241.77 down(f(f(a))) 543.59/241.77 down(f(f(b))) 543.59/241.77 down(f(f(g(x0)))) 543.59/241.77 down(f(f(c))) 543.59/241.77 down(f(f(fresh_constant))) 543.59/241.77 down(g(g(a))) 543.59/241.77 down(g(g(f(x0)))) 543.59/241.77 down(g(g(b))) 543.59/241.77 down(g(g(c))) 543.59/241.77 down(g(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) 543.59/241.77 down(f(f(f(g(x0))))) 543.59/241.77 down(f(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) 543.59/241.77 down(g(g(g(f(x0))))) 543.59/241.77 down(g(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(x0)))))) 543.59/241.77 down(f(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(x0)))))) 543.59/241.77 down(g(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(x0))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(x0))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 f_flat(up(x0)) 543.59/241.77 g_flat(up(x0)) 543.59/241.77 543.59/241.77 We have to consider all minimal (P,Q,R)-chains. 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (533) TransformationProof (EQUIVALENT) 543.59/241.77 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.77 543.59/241.77 (TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))),TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.59/241.77 543.59/241.77 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (534) 543.59/241.77 Obligation: 543.59/241.77 Q DP problem: 543.59/241.77 The TRS P consists of the following rules: 543.59/241.77 543.59/241.77 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.77 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.77 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.77 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.77 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.77 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.77 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.77 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.77 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.77 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.77 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.77 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.77 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.77 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.77 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.77 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.77 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.77 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.77 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.77 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.77 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.77 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.77 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.77 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.77 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.77 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.77 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.77 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.77 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.77 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.77 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.77 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.77 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.77 543.59/241.77 The TRS R consists of the following rules: 543.59/241.77 543.59/241.77 down(a) -> up(f(a)) 543.59/241.77 down(b) -> up(g(b)) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.77 down(f(a)) -> f_flat(down(a)) 543.59/241.77 down(f(b)) -> f_flat(down(b)) 543.59/241.77 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.77 down(f(c)) -> f_flat(down(c)) 543.59/241.77 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.77 down(g(a)) -> g_flat(down(a)) 543.59/241.77 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.77 down(g(b)) -> g_flat(down(b)) 543.59/241.77 down(g(c)) -> g_flat(down(c)) 543.59/241.77 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.77 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.77 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.77 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.77 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.77 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.77 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.77 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.77 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.77 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.77 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.77 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.77 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.77 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.77 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.77 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.77 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.77 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.77 543.59/241.77 The set Q consists of the following terms: 543.59/241.77 543.59/241.77 down(a) 543.59/241.77 down(b) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.77 down(f(a)) 543.59/241.77 down(f(b)) 543.59/241.77 down(f(g(x0))) 543.59/241.77 down(f(c)) 543.59/241.77 down(f(fresh_constant)) 543.59/241.77 down(g(a)) 543.59/241.77 down(g(f(x0))) 543.59/241.77 down(g(b)) 543.59/241.77 down(g(c)) 543.59/241.77 down(g(fresh_constant)) 543.59/241.77 down(f(f(a))) 543.59/241.77 down(f(f(b))) 543.59/241.77 down(f(f(g(x0)))) 543.59/241.77 down(f(f(c))) 543.59/241.77 down(f(f(fresh_constant))) 543.59/241.77 down(g(g(a))) 543.59/241.77 down(g(g(f(x0)))) 543.59/241.77 down(g(g(b))) 543.59/241.77 down(g(g(c))) 543.59/241.77 down(g(g(fresh_constant))) 543.59/241.77 down(f(f(f(a)))) 543.59/241.77 down(f(f(f(b)))) 543.59/241.77 down(f(f(f(g(x0))))) 543.59/241.77 down(f(f(f(c)))) 543.59/241.77 down(f(f(f(fresh_constant)))) 543.59/241.77 down(g(g(g(a)))) 543.59/241.77 down(g(g(g(f(x0))))) 543.59/241.77 down(g(g(g(b)))) 543.59/241.77 down(g(g(g(c)))) 543.59/241.77 down(g(g(g(fresh_constant)))) 543.59/241.77 down(f(f(f(f(a))))) 543.59/241.77 down(f(f(f(f(b))))) 543.59/241.77 down(f(f(f(f(g(x0)))))) 543.59/241.77 down(f(f(f(f(c))))) 543.59/241.77 down(f(f(f(f(fresh_constant))))) 543.59/241.77 down(g(g(g(g(a))))) 543.59/241.77 down(g(g(g(g(f(x0)))))) 543.59/241.77 down(g(g(g(g(b))))) 543.59/241.77 down(g(g(g(g(c))))) 543.59/241.77 down(g(g(g(g(fresh_constant))))) 543.59/241.77 down(f(f(f(f(f(a)))))) 543.59/241.77 down(f(f(f(f(f(b)))))) 543.59/241.77 down(f(f(f(f(f(g(x0))))))) 543.59/241.77 down(f(f(f(f(f(c)))))) 543.59/241.77 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.77 down(g(g(g(g(g(a)))))) 543.59/241.77 down(g(g(g(g(g(f(x0))))))) 543.59/241.77 down(g(g(g(g(g(b)))))) 543.59/241.77 down(g(g(g(g(g(c)))))) 543.59/241.77 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.77 down(f(f(f(f(f(f(a))))))) 543.59/241.77 down(f(f(f(f(f(f(b))))))) 543.59/241.77 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.77 down(f(f(f(f(f(f(c))))))) 543.59/241.77 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.77 down(g(g(g(g(g(g(a))))))) 543.59/241.77 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.77 down(g(g(g(g(g(g(b))))))) 543.59/241.77 down(g(g(g(g(g(g(c))))))) 543.59/241.77 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.77 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.77 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.77 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.77 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.77 f_flat(up(x0)) 543.59/241.77 g_flat(up(x0)) 543.59/241.77 543.59/241.77 We have to consider all minimal (P,Q,R)-chains. 543.59/241.77 ---------------------------------------- 543.59/241.77 543.59/241.77 (535) TransformationProof (EQUIVALENT) 543.59/241.77 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.78 543.59/241.78 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.59/241.78 543.59/241.78 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (536) 543.59/241.78 Obligation: 543.59/241.78 Q DP problem: 543.59/241.78 The TRS P consists of the following rules: 543.59/241.78 543.59/241.78 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.78 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.78 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.78 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.78 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.78 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.78 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.78 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.78 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.78 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.78 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.78 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.78 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.78 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.78 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.78 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.78 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.78 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.78 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.78 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.78 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.78 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.78 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.78 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.78 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.78 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.78 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.78 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.78 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.78 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.78 543.59/241.78 The TRS R consists of the following rules: 543.59/241.78 543.59/241.78 down(a) -> up(f(a)) 543.59/241.78 down(b) -> up(g(b)) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.78 down(f(a)) -> f_flat(down(a)) 543.59/241.78 down(f(b)) -> f_flat(down(b)) 543.59/241.78 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.78 down(f(c)) -> f_flat(down(c)) 543.59/241.78 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.78 down(g(a)) -> g_flat(down(a)) 543.59/241.78 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.78 down(g(b)) -> g_flat(down(b)) 543.59/241.78 down(g(c)) -> g_flat(down(c)) 543.59/241.78 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.78 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.78 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.78 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.78 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.78 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.78 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.78 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.78 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.78 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.78 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.78 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.78 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.78 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.78 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.78 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.78 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.78 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.78 543.59/241.78 The set Q consists of the following terms: 543.59/241.78 543.59/241.78 down(a) 543.59/241.78 down(b) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.78 down(f(a)) 543.59/241.78 down(f(b)) 543.59/241.78 down(f(g(x0))) 543.59/241.78 down(f(c)) 543.59/241.78 down(f(fresh_constant)) 543.59/241.78 down(g(a)) 543.59/241.78 down(g(f(x0))) 543.59/241.78 down(g(b)) 543.59/241.78 down(g(c)) 543.59/241.78 down(g(fresh_constant)) 543.59/241.78 down(f(f(a))) 543.59/241.78 down(f(f(b))) 543.59/241.78 down(f(f(g(x0)))) 543.59/241.78 down(f(f(c))) 543.59/241.78 down(f(f(fresh_constant))) 543.59/241.78 down(g(g(a))) 543.59/241.78 down(g(g(f(x0)))) 543.59/241.78 down(g(g(b))) 543.59/241.78 down(g(g(c))) 543.59/241.78 down(g(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) 543.59/241.78 down(f(f(f(g(x0))))) 543.59/241.78 down(f(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) 543.59/241.78 down(g(g(g(f(x0))))) 543.59/241.78 down(g(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(x0)))))) 543.59/241.78 down(f(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(x0)))))) 543.59/241.78 down(g(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(x0))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(x0))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 f_flat(up(x0)) 543.59/241.78 g_flat(up(x0)) 543.59/241.78 543.59/241.78 We have to consider all minimal (P,Q,R)-chains. 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (537) TransformationProof (EQUIVALENT) 543.59/241.78 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.78 543.59/241.78 (TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))),TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.59/241.78 543.59/241.78 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (538) 543.59/241.78 Obligation: 543.59/241.78 Q DP problem: 543.59/241.78 The TRS P consists of the following rules: 543.59/241.78 543.59/241.78 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.78 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.78 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.78 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.78 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.78 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.78 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.78 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.78 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.78 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.78 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.78 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.78 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.78 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.78 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.78 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.78 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.78 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.78 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.78 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.78 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.78 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.78 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.78 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.78 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.78 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.78 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.78 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.78 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.78 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.59/241.78 543.59/241.78 The TRS R consists of the following rules: 543.59/241.78 543.59/241.78 down(a) -> up(f(a)) 543.59/241.78 down(b) -> up(g(b)) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.78 down(f(a)) -> f_flat(down(a)) 543.59/241.78 down(f(b)) -> f_flat(down(b)) 543.59/241.78 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.78 down(f(c)) -> f_flat(down(c)) 543.59/241.78 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.78 down(g(a)) -> g_flat(down(a)) 543.59/241.78 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.78 down(g(b)) -> g_flat(down(b)) 543.59/241.78 down(g(c)) -> g_flat(down(c)) 543.59/241.78 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.78 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.78 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.78 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.78 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.78 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.78 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.78 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.78 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.78 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.78 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.78 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.78 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.78 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.78 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.78 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.78 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.78 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.78 543.59/241.78 The set Q consists of the following terms: 543.59/241.78 543.59/241.78 down(a) 543.59/241.78 down(b) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.78 down(f(a)) 543.59/241.78 down(f(b)) 543.59/241.78 down(f(g(x0))) 543.59/241.78 down(f(c)) 543.59/241.78 down(f(fresh_constant)) 543.59/241.78 down(g(a)) 543.59/241.78 down(g(f(x0))) 543.59/241.78 down(g(b)) 543.59/241.78 down(g(c)) 543.59/241.78 down(g(fresh_constant)) 543.59/241.78 down(f(f(a))) 543.59/241.78 down(f(f(b))) 543.59/241.78 down(f(f(g(x0)))) 543.59/241.78 down(f(f(c))) 543.59/241.78 down(f(f(fresh_constant))) 543.59/241.78 down(g(g(a))) 543.59/241.78 down(g(g(f(x0)))) 543.59/241.78 down(g(g(b))) 543.59/241.78 down(g(g(c))) 543.59/241.78 down(g(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) 543.59/241.78 down(f(f(f(g(x0))))) 543.59/241.78 down(f(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) 543.59/241.78 down(g(g(g(f(x0))))) 543.59/241.78 down(g(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(x0)))))) 543.59/241.78 down(f(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(x0)))))) 543.59/241.78 down(g(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(x0))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(x0))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 f_flat(up(x0)) 543.59/241.78 g_flat(up(x0)) 543.59/241.78 543.59/241.78 We have to consider all minimal (P,Q,R)-chains. 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (539) TransformationProof (EQUIVALENT) 543.59/241.78 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.78 543.59/241.78 (TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))),TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.59/241.78 543.59/241.78 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (540) 543.59/241.78 Obligation: 543.59/241.78 Q DP problem: 543.59/241.78 The TRS P consists of the following rules: 543.59/241.78 543.59/241.78 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.78 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.78 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.78 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.78 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.78 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.78 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.78 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.78 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.78 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.78 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.78 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.78 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.78 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.78 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.78 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.78 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.78 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.78 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.78 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.78 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.78 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.78 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.78 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.78 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.78 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.78 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.78 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.78 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.78 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.59/241.78 543.59/241.78 The TRS R consists of the following rules: 543.59/241.78 543.59/241.78 down(a) -> up(f(a)) 543.59/241.78 down(b) -> up(g(b)) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.78 down(f(a)) -> f_flat(down(a)) 543.59/241.78 down(f(b)) -> f_flat(down(b)) 543.59/241.78 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.78 down(f(c)) -> f_flat(down(c)) 543.59/241.78 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.78 down(g(a)) -> g_flat(down(a)) 543.59/241.78 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.78 down(g(b)) -> g_flat(down(b)) 543.59/241.78 down(g(c)) -> g_flat(down(c)) 543.59/241.78 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.78 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.78 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.78 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.78 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.78 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.78 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.78 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.78 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.78 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.78 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.78 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.78 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.78 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.78 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.78 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.78 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.78 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.78 543.59/241.78 The set Q consists of the following terms: 543.59/241.78 543.59/241.78 down(a) 543.59/241.78 down(b) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.78 down(f(a)) 543.59/241.78 down(f(b)) 543.59/241.78 down(f(g(x0))) 543.59/241.78 down(f(c)) 543.59/241.78 down(f(fresh_constant)) 543.59/241.78 down(g(a)) 543.59/241.78 down(g(f(x0))) 543.59/241.78 down(g(b)) 543.59/241.78 down(g(c)) 543.59/241.78 down(g(fresh_constant)) 543.59/241.78 down(f(f(a))) 543.59/241.78 down(f(f(b))) 543.59/241.78 down(f(f(g(x0)))) 543.59/241.78 down(f(f(c))) 543.59/241.78 down(f(f(fresh_constant))) 543.59/241.78 down(g(g(a))) 543.59/241.78 down(g(g(f(x0)))) 543.59/241.78 down(g(g(b))) 543.59/241.78 down(g(g(c))) 543.59/241.78 down(g(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) 543.59/241.78 down(f(f(f(g(x0))))) 543.59/241.78 down(f(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) 543.59/241.78 down(g(g(g(f(x0))))) 543.59/241.78 down(g(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(x0)))))) 543.59/241.78 down(f(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(x0)))))) 543.59/241.78 down(g(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(x0))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(x0))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 f_flat(up(x0)) 543.59/241.78 g_flat(up(x0)) 543.59/241.78 543.59/241.78 We have to consider all minimal (P,Q,R)-chains. 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (541) TransformationProof (EQUIVALENT) 543.59/241.78 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.78 543.59/241.78 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.59/241.78 543.59/241.78 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (542) 543.59/241.78 Obligation: 543.59/241.78 Q DP problem: 543.59/241.78 The TRS P consists of the following rules: 543.59/241.78 543.59/241.78 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.78 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.78 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.78 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.78 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.78 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.78 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.78 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.78 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.78 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.78 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.78 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.78 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.78 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.78 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.78 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.78 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.78 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.78 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.78 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.78 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.78 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.78 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.78 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.78 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.78 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.78 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.78 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.78 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.78 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.59/241.78 543.59/241.78 The TRS R consists of the following rules: 543.59/241.78 543.59/241.78 down(a) -> up(f(a)) 543.59/241.78 down(b) -> up(g(b)) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.78 down(f(a)) -> f_flat(down(a)) 543.59/241.78 down(f(b)) -> f_flat(down(b)) 543.59/241.78 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.78 down(f(c)) -> f_flat(down(c)) 543.59/241.78 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.78 down(g(a)) -> g_flat(down(a)) 543.59/241.78 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.78 down(g(b)) -> g_flat(down(b)) 543.59/241.78 down(g(c)) -> g_flat(down(c)) 543.59/241.78 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.78 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.78 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.78 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.78 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.78 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.78 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.78 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.78 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.78 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.78 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.78 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.78 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.78 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.78 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.78 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.78 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.78 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.78 543.59/241.78 The set Q consists of the following terms: 543.59/241.78 543.59/241.78 down(a) 543.59/241.78 down(b) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.78 down(f(a)) 543.59/241.78 down(f(b)) 543.59/241.78 down(f(g(x0))) 543.59/241.78 down(f(c)) 543.59/241.78 down(f(fresh_constant)) 543.59/241.78 down(g(a)) 543.59/241.78 down(g(f(x0))) 543.59/241.78 down(g(b)) 543.59/241.78 down(g(c)) 543.59/241.78 down(g(fresh_constant)) 543.59/241.78 down(f(f(a))) 543.59/241.78 down(f(f(b))) 543.59/241.78 down(f(f(g(x0)))) 543.59/241.78 down(f(f(c))) 543.59/241.78 down(f(f(fresh_constant))) 543.59/241.78 down(g(g(a))) 543.59/241.78 down(g(g(f(x0)))) 543.59/241.78 down(g(g(b))) 543.59/241.78 down(g(g(c))) 543.59/241.78 down(g(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) 543.59/241.78 down(f(f(f(g(x0))))) 543.59/241.78 down(f(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) 543.59/241.78 down(g(g(g(f(x0))))) 543.59/241.78 down(g(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(x0)))))) 543.59/241.78 down(f(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(x0)))))) 543.59/241.78 down(g(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(x0))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(x0))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 f_flat(up(x0)) 543.59/241.78 g_flat(up(x0)) 543.59/241.78 543.59/241.78 We have to consider all minimal (P,Q,R)-chains. 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (543) TransformationProof (EQUIVALENT) 543.59/241.78 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.78 543.59/241.78 (TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))),TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.59/241.78 543.59/241.78 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (544) 543.59/241.78 Obligation: 543.59/241.78 Q DP problem: 543.59/241.78 The TRS P consists of the following rules: 543.59/241.78 543.59/241.78 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.78 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.78 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.78 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.78 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.78 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.78 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.78 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.78 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.78 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.78 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.78 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.78 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.78 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.78 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.78 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.78 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.78 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.78 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.78 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.78 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.78 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.78 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.78 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.78 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.78 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.78 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.78 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.78 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.78 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.59/241.78 543.59/241.78 The TRS R consists of the following rules: 543.59/241.78 543.59/241.78 down(a) -> up(f(a)) 543.59/241.78 down(b) -> up(g(b)) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.78 down(f(a)) -> f_flat(down(a)) 543.59/241.78 down(f(b)) -> f_flat(down(b)) 543.59/241.78 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.78 down(f(c)) -> f_flat(down(c)) 543.59/241.78 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.78 down(g(a)) -> g_flat(down(a)) 543.59/241.78 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.78 down(g(b)) -> g_flat(down(b)) 543.59/241.78 down(g(c)) -> g_flat(down(c)) 543.59/241.78 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.78 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.78 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.78 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.78 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.78 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.78 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.78 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.78 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.78 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.78 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.78 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.78 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.78 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.78 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.78 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.78 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.78 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.78 543.59/241.78 The set Q consists of the following terms: 543.59/241.78 543.59/241.78 down(a) 543.59/241.78 down(b) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.78 down(f(a)) 543.59/241.78 down(f(b)) 543.59/241.78 down(f(g(x0))) 543.59/241.78 down(f(c)) 543.59/241.78 down(f(fresh_constant)) 543.59/241.78 down(g(a)) 543.59/241.78 down(g(f(x0))) 543.59/241.78 down(g(b)) 543.59/241.78 down(g(c)) 543.59/241.78 down(g(fresh_constant)) 543.59/241.78 down(f(f(a))) 543.59/241.78 down(f(f(b))) 543.59/241.78 down(f(f(g(x0)))) 543.59/241.78 down(f(f(c))) 543.59/241.78 down(f(f(fresh_constant))) 543.59/241.78 down(g(g(a))) 543.59/241.78 down(g(g(f(x0)))) 543.59/241.78 down(g(g(b))) 543.59/241.78 down(g(g(c))) 543.59/241.78 down(g(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) 543.59/241.78 down(f(f(f(g(x0))))) 543.59/241.78 down(f(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) 543.59/241.78 down(g(g(g(f(x0))))) 543.59/241.78 down(g(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(x0)))))) 543.59/241.78 down(f(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(x0)))))) 543.59/241.78 down(g(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(x0))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(x0))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 f_flat(up(x0)) 543.59/241.78 g_flat(up(x0)) 543.59/241.78 543.59/241.78 We have to consider all minimal (P,Q,R)-chains. 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (545) TransformationProof (EQUIVALENT) 543.59/241.78 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.78 543.59/241.78 (TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))),TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.59/241.78 543.59/241.78 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (546) 543.59/241.78 Obligation: 543.59/241.78 Q DP problem: 543.59/241.78 The TRS P consists of the following rules: 543.59/241.78 543.59/241.78 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.78 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.78 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.78 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.78 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.78 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.78 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.78 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.78 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.78 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.78 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.78 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.78 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.78 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.78 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.78 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.78 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.78 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.78 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.78 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.78 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.78 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.78 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.78 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.78 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.78 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.78 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.78 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.78 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.78 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.59/241.78 543.59/241.78 The TRS R consists of the following rules: 543.59/241.78 543.59/241.78 down(a) -> up(f(a)) 543.59/241.78 down(b) -> up(g(b)) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.78 down(f(a)) -> f_flat(down(a)) 543.59/241.78 down(f(b)) -> f_flat(down(b)) 543.59/241.78 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.78 down(f(c)) -> f_flat(down(c)) 543.59/241.78 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.78 down(g(a)) -> g_flat(down(a)) 543.59/241.78 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.78 down(g(b)) -> g_flat(down(b)) 543.59/241.78 down(g(c)) -> g_flat(down(c)) 543.59/241.78 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.78 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.78 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.78 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.78 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.78 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.78 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.78 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.78 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.78 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.78 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.78 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.78 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.78 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.78 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.78 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.78 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.78 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.78 543.59/241.78 The set Q consists of the following terms: 543.59/241.78 543.59/241.78 down(a) 543.59/241.78 down(b) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.78 down(f(a)) 543.59/241.78 down(f(b)) 543.59/241.78 down(f(g(x0))) 543.59/241.78 down(f(c)) 543.59/241.78 down(f(fresh_constant)) 543.59/241.78 down(g(a)) 543.59/241.78 down(g(f(x0))) 543.59/241.78 down(g(b)) 543.59/241.78 down(g(c)) 543.59/241.78 down(g(fresh_constant)) 543.59/241.78 down(f(f(a))) 543.59/241.78 down(f(f(b))) 543.59/241.78 down(f(f(g(x0)))) 543.59/241.78 down(f(f(c))) 543.59/241.78 down(f(f(fresh_constant))) 543.59/241.78 down(g(g(a))) 543.59/241.78 down(g(g(f(x0)))) 543.59/241.78 down(g(g(b))) 543.59/241.78 down(g(g(c))) 543.59/241.78 down(g(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) 543.59/241.78 down(f(f(f(g(x0))))) 543.59/241.78 down(f(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) 543.59/241.78 down(g(g(g(f(x0))))) 543.59/241.78 down(g(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(x0)))))) 543.59/241.78 down(f(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(x0)))))) 543.59/241.78 down(g(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(x0))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(x0))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 f_flat(up(x0)) 543.59/241.78 g_flat(up(x0)) 543.59/241.78 543.59/241.78 We have to consider all minimal (P,Q,R)-chains. 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (547) TransformationProof (EQUIVALENT) 543.59/241.78 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.78 543.59/241.78 (TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))),TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.59/241.78 543.59/241.78 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (548) 543.59/241.78 Obligation: 543.59/241.78 Q DP problem: 543.59/241.78 The TRS P consists of the following rules: 543.59/241.78 543.59/241.78 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.78 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.78 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.78 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.78 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.78 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.78 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.78 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.78 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.78 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.78 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.78 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.78 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.78 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.78 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.78 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.78 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.78 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.78 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.78 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.78 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.78 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.78 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.78 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.78 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.78 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.78 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.78 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.78 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.78 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.78 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 543.59/241.78 The TRS R consists of the following rules: 543.59/241.78 543.59/241.78 down(a) -> up(f(a)) 543.59/241.78 down(b) -> up(g(b)) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.78 down(f(a)) -> f_flat(down(a)) 543.59/241.78 down(f(b)) -> f_flat(down(b)) 543.59/241.78 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.78 down(f(c)) -> f_flat(down(c)) 543.59/241.78 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.78 down(g(a)) -> g_flat(down(a)) 543.59/241.78 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.78 down(g(b)) -> g_flat(down(b)) 543.59/241.78 down(g(c)) -> g_flat(down(c)) 543.59/241.78 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.78 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.78 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.78 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.78 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.78 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.78 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.78 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.78 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.78 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.78 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.78 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.78 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.78 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.78 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.78 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.78 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.78 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.78 543.59/241.78 The set Q consists of the following terms: 543.59/241.78 543.59/241.78 down(a) 543.59/241.78 down(b) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.78 down(f(a)) 543.59/241.78 down(f(b)) 543.59/241.78 down(f(g(x0))) 543.59/241.78 down(f(c)) 543.59/241.78 down(f(fresh_constant)) 543.59/241.78 down(g(a)) 543.59/241.78 down(g(f(x0))) 543.59/241.78 down(g(b)) 543.59/241.78 down(g(c)) 543.59/241.78 down(g(fresh_constant)) 543.59/241.78 down(f(f(a))) 543.59/241.78 down(f(f(b))) 543.59/241.78 down(f(f(g(x0)))) 543.59/241.78 down(f(f(c))) 543.59/241.78 down(f(f(fresh_constant))) 543.59/241.78 down(g(g(a))) 543.59/241.78 down(g(g(f(x0)))) 543.59/241.78 down(g(g(b))) 543.59/241.78 down(g(g(c))) 543.59/241.78 down(g(g(fresh_constant))) 543.59/241.78 down(f(f(f(a)))) 543.59/241.78 down(f(f(f(b)))) 543.59/241.78 down(f(f(f(g(x0))))) 543.59/241.78 down(f(f(f(c)))) 543.59/241.78 down(f(f(f(fresh_constant)))) 543.59/241.78 down(g(g(g(a)))) 543.59/241.78 down(g(g(g(f(x0))))) 543.59/241.78 down(g(g(g(b)))) 543.59/241.78 down(g(g(g(c)))) 543.59/241.78 down(g(g(g(fresh_constant)))) 543.59/241.78 down(f(f(f(f(a))))) 543.59/241.78 down(f(f(f(f(b))))) 543.59/241.78 down(f(f(f(f(g(x0)))))) 543.59/241.78 down(f(f(f(f(c))))) 543.59/241.78 down(f(f(f(f(fresh_constant))))) 543.59/241.78 down(g(g(g(g(a))))) 543.59/241.78 down(g(g(g(g(f(x0)))))) 543.59/241.78 down(g(g(g(g(b))))) 543.59/241.78 down(g(g(g(g(c))))) 543.59/241.78 down(g(g(g(g(fresh_constant))))) 543.59/241.78 down(f(f(f(f(f(a)))))) 543.59/241.78 down(f(f(f(f(f(b)))))) 543.59/241.78 down(f(f(f(f(f(g(x0))))))) 543.59/241.78 down(f(f(f(f(f(c)))))) 543.59/241.78 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.78 down(g(g(g(g(g(a)))))) 543.59/241.78 down(g(g(g(g(g(f(x0))))))) 543.59/241.78 down(g(g(g(g(g(b)))))) 543.59/241.78 down(g(g(g(g(g(c)))))) 543.59/241.78 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.78 down(f(f(f(f(f(f(a))))))) 543.59/241.78 down(f(f(f(f(f(f(b))))))) 543.59/241.78 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.78 down(f(f(f(f(f(f(c))))))) 543.59/241.78 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.78 down(g(g(g(g(g(g(a))))))) 543.59/241.78 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.78 down(g(g(g(g(g(g(b))))))) 543.59/241.78 down(g(g(g(g(g(g(c))))))) 543.59/241.78 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.78 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.78 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.78 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.78 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.78 f_flat(up(x0)) 543.59/241.78 g_flat(up(x0)) 543.59/241.78 543.59/241.78 We have to consider all minimal (P,Q,R)-chains. 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (549) TransformationProof (EQUIVALENT) 543.59/241.78 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(a))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.78 543.59/241.78 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a)))))))))))) 543.59/241.78 543.59/241.78 543.59/241.78 ---------------------------------------- 543.59/241.78 543.59/241.78 (550) 543.59/241.78 Obligation: 543.59/241.78 Q DP problem: 543.59/241.78 The TRS P consists of the following rules: 543.59/241.78 543.59/241.78 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.78 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.78 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.78 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.78 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.78 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.78 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.78 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.78 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.78 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.78 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.78 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) 543.59/241.78 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.78 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.79 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.79 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.79 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.79 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.79 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.79 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.79 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.79 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.79 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.79 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.79 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.79 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.79 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.79 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.79 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.79 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.79 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.79 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.79 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.79 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.59/241.79 543.59/241.79 The TRS R consists of the following rules: 543.59/241.79 543.59/241.79 down(a) -> up(f(a)) 543.59/241.79 down(b) -> up(g(b)) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.79 down(f(a)) -> f_flat(down(a)) 543.59/241.79 down(f(b)) -> f_flat(down(b)) 543.59/241.79 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.79 down(f(c)) -> f_flat(down(c)) 543.59/241.79 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.79 down(g(a)) -> g_flat(down(a)) 543.59/241.79 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.79 down(g(b)) -> g_flat(down(b)) 543.59/241.79 down(g(c)) -> g_flat(down(c)) 543.59/241.79 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.79 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.79 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.79 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.79 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.79 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.79 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.79 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.79 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.79 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.79 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.79 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.79 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.79 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.79 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.79 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.79 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.79 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.79 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.79 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.79 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.79 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.79 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.79 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.79 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.79 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.79 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.79 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.79 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.79 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.79 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.79 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.79 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.79 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.79 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.79 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.79 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.79 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.79 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.79 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.79 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.79 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.79 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.79 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.79 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.79 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.79 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.79 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.79 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.79 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.79 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.79 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.79 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.79 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.79 543.59/241.79 The set Q consists of the following terms: 543.59/241.79 543.59/241.79 down(a) 543.59/241.79 down(b) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.79 down(f(a)) 543.59/241.79 down(f(b)) 543.59/241.79 down(f(g(x0))) 543.59/241.79 down(f(c)) 543.59/241.79 down(f(fresh_constant)) 543.59/241.79 down(g(a)) 543.59/241.79 down(g(f(x0))) 543.59/241.79 down(g(b)) 543.59/241.79 down(g(c)) 543.59/241.79 down(g(fresh_constant)) 543.59/241.79 down(f(f(a))) 543.59/241.79 down(f(f(b))) 543.59/241.79 down(f(f(g(x0)))) 543.59/241.79 down(f(f(c))) 543.59/241.79 down(f(f(fresh_constant))) 543.59/241.79 down(g(g(a))) 543.59/241.79 down(g(g(f(x0)))) 543.59/241.79 down(g(g(b))) 543.59/241.79 down(g(g(c))) 543.59/241.79 down(g(g(fresh_constant))) 543.59/241.79 down(f(f(f(a)))) 543.59/241.79 down(f(f(f(b)))) 543.59/241.79 down(f(f(f(g(x0))))) 543.59/241.79 down(f(f(f(c)))) 543.59/241.79 down(f(f(f(fresh_constant)))) 543.59/241.79 down(g(g(g(a)))) 543.59/241.79 down(g(g(g(f(x0))))) 543.59/241.79 down(g(g(g(b)))) 543.59/241.79 down(g(g(g(c)))) 543.59/241.79 down(g(g(g(fresh_constant)))) 543.59/241.79 down(f(f(f(f(a))))) 543.59/241.79 down(f(f(f(f(b))))) 543.59/241.79 down(f(f(f(f(g(x0)))))) 543.59/241.79 down(f(f(f(f(c))))) 543.59/241.79 down(f(f(f(f(fresh_constant))))) 543.59/241.79 down(g(g(g(g(a))))) 543.59/241.79 down(g(g(g(g(f(x0)))))) 543.59/241.79 down(g(g(g(g(b))))) 543.59/241.79 down(g(g(g(g(c))))) 543.59/241.79 down(g(g(g(g(fresh_constant))))) 543.59/241.79 down(f(f(f(f(f(a)))))) 543.59/241.79 down(f(f(f(f(f(b)))))) 543.59/241.79 down(f(f(f(f(f(g(x0))))))) 543.59/241.79 down(f(f(f(f(f(c)))))) 543.59/241.79 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.79 down(g(g(g(g(g(a)))))) 543.59/241.79 down(g(g(g(g(g(f(x0))))))) 543.59/241.79 down(g(g(g(g(g(b)))))) 543.59/241.79 down(g(g(g(g(g(c)))))) 543.59/241.79 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.79 down(f(f(f(f(f(f(a))))))) 543.59/241.79 down(f(f(f(f(f(f(b))))))) 543.59/241.79 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.79 down(f(f(f(f(f(f(c))))))) 543.59/241.79 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.79 down(g(g(g(g(g(g(a))))))) 543.59/241.79 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.79 down(g(g(g(g(g(g(b))))))) 543.59/241.79 down(g(g(g(g(g(g(c))))))) 543.59/241.79 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.79 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.79 f_flat(up(x0)) 543.59/241.79 g_flat(up(x0)) 543.59/241.79 543.59/241.79 We have to consider all minimal (P,Q,R)-chains. 543.59/241.79 ---------------------------------------- 543.59/241.79 543.59/241.79 (551) TransformationProof (EQUIVALENT) 543.59/241.79 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(b))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.79 543.59/241.79 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b)))))))))))) 543.59/241.79 543.59/241.79 543.59/241.79 ---------------------------------------- 543.59/241.79 543.59/241.79 (552) 543.59/241.79 Obligation: 543.59/241.79 Q DP problem: 543.59/241.79 The TRS P consists of the following rules: 543.59/241.79 543.59/241.79 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.79 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.79 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.79 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.79 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.79 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.79 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.79 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.79 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.79 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.79 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.79 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.79 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.79 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.79 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.79 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.79 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.79 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.79 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.79 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.79 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.79 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.79 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.79 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.79 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.79 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.79 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.79 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.79 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.79 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.79 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.79 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.59/241.79 543.59/241.79 The TRS R consists of the following rules: 543.59/241.79 543.59/241.79 down(a) -> up(f(a)) 543.59/241.79 down(b) -> up(g(b)) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.79 down(f(a)) -> f_flat(down(a)) 543.59/241.79 down(f(b)) -> f_flat(down(b)) 543.59/241.79 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.79 down(f(c)) -> f_flat(down(c)) 543.59/241.79 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.79 down(g(a)) -> g_flat(down(a)) 543.59/241.79 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.79 down(g(b)) -> g_flat(down(b)) 543.59/241.79 down(g(c)) -> g_flat(down(c)) 543.59/241.79 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.79 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.79 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.79 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.79 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.79 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.79 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.79 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.79 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.79 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.79 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.79 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.79 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.79 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.79 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.79 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.79 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.79 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.79 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.79 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.79 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.79 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.79 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.79 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.79 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.79 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.79 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.79 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.79 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.79 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.79 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.79 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.79 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.79 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.79 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.79 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.79 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.79 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.79 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.79 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.79 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.79 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.79 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.79 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.79 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.79 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.79 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.79 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.79 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.79 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.79 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.79 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.79 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.79 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.79 543.59/241.79 The set Q consists of the following terms: 543.59/241.79 543.59/241.79 down(a) 543.59/241.79 down(b) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.79 down(f(a)) 543.59/241.79 down(f(b)) 543.59/241.79 down(f(g(x0))) 543.59/241.79 down(f(c)) 543.59/241.79 down(f(fresh_constant)) 543.59/241.79 down(g(a)) 543.59/241.79 down(g(f(x0))) 543.59/241.79 down(g(b)) 543.59/241.79 down(g(c)) 543.59/241.79 down(g(fresh_constant)) 543.59/241.79 down(f(f(a))) 543.59/241.79 down(f(f(b))) 543.59/241.79 down(f(f(g(x0)))) 543.59/241.79 down(f(f(c))) 543.59/241.79 down(f(f(fresh_constant))) 543.59/241.79 down(g(g(a))) 543.59/241.79 down(g(g(f(x0)))) 543.59/241.79 down(g(g(b))) 543.59/241.79 down(g(g(c))) 543.59/241.79 down(g(g(fresh_constant))) 543.59/241.79 down(f(f(f(a)))) 543.59/241.79 down(f(f(f(b)))) 543.59/241.79 down(f(f(f(g(x0))))) 543.59/241.79 down(f(f(f(c)))) 543.59/241.79 down(f(f(f(fresh_constant)))) 543.59/241.79 down(g(g(g(a)))) 543.59/241.79 down(g(g(g(f(x0))))) 543.59/241.79 down(g(g(g(b)))) 543.59/241.79 down(g(g(g(c)))) 543.59/241.79 down(g(g(g(fresh_constant)))) 543.59/241.79 down(f(f(f(f(a))))) 543.59/241.79 down(f(f(f(f(b))))) 543.59/241.79 down(f(f(f(f(g(x0)))))) 543.59/241.79 down(f(f(f(f(c))))) 543.59/241.79 down(f(f(f(f(fresh_constant))))) 543.59/241.79 down(g(g(g(g(a))))) 543.59/241.79 down(g(g(g(g(f(x0)))))) 543.59/241.79 down(g(g(g(g(b))))) 543.59/241.79 down(g(g(g(g(c))))) 543.59/241.79 down(g(g(g(g(fresh_constant))))) 543.59/241.79 down(f(f(f(f(f(a)))))) 543.59/241.79 down(f(f(f(f(f(b)))))) 543.59/241.79 down(f(f(f(f(f(g(x0))))))) 543.59/241.79 down(f(f(f(f(f(c)))))) 543.59/241.79 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.79 down(g(g(g(g(g(a)))))) 543.59/241.79 down(g(g(g(g(g(f(x0))))))) 543.59/241.79 down(g(g(g(g(g(b)))))) 543.59/241.79 down(g(g(g(g(g(c)))))) 543.59/241.79 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.79 down(f(f(f(f(f(f(a))))))) 543.59/241.79 down(f(f(f(f(f(f(b))))))) 543.59/241.79 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.79 down(f(f(f(f(f(f(c))))))) 543.59/241.79 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.79 down(g(g(g(g(g(g(a))))))) 543.59/241.79 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.79 down(g(g(g(g(g(g(b))))))) 543.59/241.79 down(g(g(g(g(g(g(c))))))) 543.59/241.79 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.79 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(c))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(a))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(b))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(c))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.79 f_flat(up(x0)) 543.59/241.79 g_flat(up(x0)) 543.59/241.79 543.59/241.79 We have to consider all minimal (P,Q,R)-chains. 543.59/241.79 ---------------------------------------- 543.59/241.79 543.59/241.79 (553) TransformationProof (EQUIVALENT) 543.59/241.79 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(g(x0)))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.59/241.79 543.59/241.79 (TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0))))))))))))) 543.59/241.79 543.59/241.79 543.59/241.79 ---------------------------------------- 543.59/241.79 543.59/241.79 (554) 543.59/241.79 Obligation: 543.59/241.79 Q DP problem: 543.59/241.79 The TRS P consists of the following rules: 543.59/241.79 543.59/241.79 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.59/241.79 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.59/241.79 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.59/241.79 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.59/241.79 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.59/241.79 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.59/241.79 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.59/241.79 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.59/241.79 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.59/241.79 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.59/241.79 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.59/241.79 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.59/241.79 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.59/241.79 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.59/241.79 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.59/241.79 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.59/241.79 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.59/241.79 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.59/241.79 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.59/241.79 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.59/241.79 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.59/241.79 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.59/241.79 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.59/241.79 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.59/241.79 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.59/241.79 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.59/241.79 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.59/241.79 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.59/241.79 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.59/241.79 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.59/241.79 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.59/241.79 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.59/241.79 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.59/241.79 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.59/241.79 543.59/241.79 The TRS R consists of the following rules: 543.59/241.79 543.59/241.79 down(a) -> up(f(a)) 543.59/241.79 down(b) -> up(g(b)) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.59/241.79 down(f(a)) -> f_flat(down(a)) 543.59/241.79 down(f(b)) -> f_flat(down(b)) 543.59/241.79 down(f(g(y4))) -> f_flat(down(g(y4))) 543.59/241.79 down(f(c)) -> f_flat(down(c)) 543.59/241.79 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.59/241.79 down(g(a)) -> g_flat(down(a)) 543.59/241.79 down(g(f(y6))) -> g_flat(down(f(y6))) 543.59/241.79 down(g(b)) -> g_flat(down(b)) 543.59/241.79 down(g(c)) -> g_flat(down(c)) 543.59/241.79 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.59/241.79 down(f(f(a))) -> f_flat(down(f(a))) 543.59/241.79 down(f(f(b))) -> f_flat(down(f(b))) 543.59/241.79 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.59/241.79 down(f(f(c))) -> f_flat(down(f(c))) 543.59/241.79 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.59/241.79 down(g(g(a))) -> g_flat(down(g(a))) 543.59/241.79 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.59/241.79 down(g(g(b))) -> g_flat(down(g(b))) 543.59/241.79 down(g(g(c))) -> g_flat(down(g(c))) 543.59/241.79 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.59/241.79 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.59/241.79 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.59/241.79 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.59/241.79 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.59/241.79 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.59/241.79 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.59/241.79 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.59/241.79 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.59/241.79 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.59/241.79 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.59/241.79 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.59/241.79 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.59/241.79 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.59/241.79 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.59/241.79 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.59/241.79 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.59/241.79 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.59/241.79 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.59/241.79 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.59/241.79 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.59/241.79 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.59/241.79 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.59/241.79 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.59/241.79 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.59/241.79 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.59/241.79 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.59/241.79 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.59/241.79 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.59/241.79 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.59/241.79 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.59/241.79 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.59/241.79 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.59/241.79 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.59/241.79 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.59/241.79 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.59/241.79 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.59/241.79 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.59/241.79 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.59/241.79 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.59/241.79 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.59/241.79 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.59/241.79 g_flat(up(x_1)) -> up(g(x_1)) 543.59/241.79 f_flat(up(x_1)) -> up(f(x_1)) 543.59/241.79 543.59/241.79 The set Q consists of the following terms: 543.59/241.79 543.59/241.79 down(a) 543.59/241.79 down(b) 543.59/241.79 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.59/241.79 down(f(a)) 543.59/241.79 down(f(b)) 543.59/241.79 down(f(g(x0))) 543.59/241.79 down(f(c)) 543.59/241.79 down(f(fresh_constant)) 543.59/241.79 down(g(a)) 543.59/241.79 down(g(f(x0))) 543.59/241.79 down(g(b)) 543.59/241.79 down(g(c)) 543.59/241.79 down(g(fresh_constant)) 543.59/241.79 down(f(f(a))) 543.59/241.79 down(f(f(b))) 543.59/241.79 down(f(f(g(x0)))) 543.59/241.79 down(f(f(c))) 543.59/241.79 down(f(f(fresh_constant))) 543.59/241.79 down(g(g(a))) 543.59/241.79 down(g(g(f(x0)))) 543.59/241.79 down(g(g(b))) 543.59/241.79 down(g(g(c))) 543.59/241.79 down(g(g(fresh_constant))) 543.59/241.79 down(f(f(f(a)))) 543.59/241.79 down(f(f(f(b)))) 543.59/241.79 down(f(f(f(g(x0))))) 543.59/241.79 down(f(f(f(c)))) 543.59/241.79 down(f(f(f(fresh_constant)))) 543.59/241.79 down(g(g(g(a)))) 543.59/241.79 down(g(g(g(f(x0))))) 543.59/241.79 down(g(g(g(b)))) 543.59/241.79 down(g(g(g(c)))) 543.59/241.79 down(g(g(g(fresh_constant)))) 543.59/241.79 down(f(f(f(f(a))))) 543.59/241.79 down(f(f(f(f(b))))) 543.59/241.79 down(f(f(f(f(g(x0)))))) 543.59/241.79 down(f(f(f(f(c))))) 543.59/241.79 down(f(f(f(f(fresh_constant))))) 543.59/241.79 down(g(g(g(g(a))))) 543.59/241.79 down(g(g(g(g(f(x0)))))) 543.59/241.79 down(g(g(g(g(b))))) 543.59/241.79 down(g(g(g(g(c))))) 543.59/241.79 down(g(g(g(g(fresh_constant))))) 543.59/241.79 down(f(f(f(f(f(a)))))) 543.59/241.79 down(f(f(f(f(f(b)))))) 543.59/241.79 down(f(f(f(f(f(g(x0))))))) 543.59/241.79 down(f(f(f(f(f(c)))))) 543.59/241.79 down(f(f(f(f(f(fresh_constant)))))) 543.59/241.79 down(g(g(g(g(g(a)))))) 543.59/241.79 down(g(g(g(g(g(f(x0))))))) 543.59/241.79 down(g(g(g(g(g(b)))))) 543.59/241.79 down(g(g(g(g(g(c)))))) 543.59/241.79 down(g(g(g(g(g(fresh_constant)))))) 543.59/241.79 down(f(f(f(f(f(f(a))))))) 543.59/241.79 down(f(f(f(f(f(f(b))))))) 543.59/241.79 down(f(f(f(f(f(f(g(x0)))))))) 543.59/241.79 down(f(f(f(f(f(f(c))))))) 543.59/241.79 down(f(f(f(f(f(f(fresh_constant))))))) 543.59/241.79 down(g(g(g(g(g(g(a))))))) 543.59/241.79 down(g(g(g(g(g(g(f(x0)))))))) 543.59/241.79 down(g(g(g(g(g(g(b))))))) 543.59/241.79 down(g(g(g(g(g(g(c))))))) 543.59/241.79 down(g(g(g(g(g(g(fresh_constant))))))) 543.59/241.79 down(f(f(f(f(f(f(f(a)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(b)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(g(x0))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(c)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(a)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(f(x0))))))))) 543.59/241.79 down(g(g(g(g(g(g(g(b)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(c)))))))) 543.59/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(a))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(b))))))))) 543.59/241.79 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 f_flat(up(x0)) 543.64/241.79 g_flat(up(x0)) 543.64/241.79 543.64/241.79 We have to consider all minimal (P,Q,R)-chains. 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (555) TransformationProof (EQUIVALENT) 543.64/241.79 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.79 543.64/241.79 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.64/241.79 543.64/241.79 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (556) 543.64/241.79 Obligation: 543.64/241.79 Q DP problem: 543.64/241.79 The TRS P consists of the following rules: 543.64/241.79 543.64/241.79 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.79 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.79 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.79 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.79 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.79 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.79 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.79 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.79 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.79 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.79 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.79 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.79 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.64/241.79 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.64/241.79 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.64/241.79 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.79 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.79 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.79 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.79 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.79 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.79 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.79 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.79 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.79 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.79 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.79 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.79 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.79 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.79 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.79 543.64/241.79 The TRS R consists of the following rules: 543.64/241.79 543.64/241.79 down(a) -> up(f(a)) 543.64/241.79 down(b) -> up(g(b)) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.79 down(f(a)) -> f_flat(down(a)) 543.64/241.79 down(f(b)) -> f_flat(down(b)) 543.64/241.79 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.79 down(f(c)) -> f_flat(down(c)) 543.64/241.79 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.79 down(g(a)) -> g_flat(down(a)) 543.64/241.79 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.79 down(g(b)) -> g_flat(down(b)) 543.64/241.79 down(g(c)) -> g_flat(down(c)) 543.64/241.79 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.79 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.79 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.79 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.79 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.79 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.79 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.79 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.79 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.79 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.79 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.79 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.79 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.79 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.79 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.79 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.79 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.79 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.79 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.79 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.79 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.79 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.79 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.79 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.79 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.79 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.79 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.79 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.79 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.79 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.79 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.79 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.79 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.79 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.79 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.79 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.79 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.79 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.79 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.79 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.79 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.79 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.79 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.79 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.79 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.79 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.79 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.79 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.79 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.79 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.79 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.79 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.79 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.79 543.64/241.79 The set Q consists of the following terms: 543.64/241.79 543.64/241.79 down(a) 543.64/241.79 down(b) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.79 down(f(a)) 543.64/241.79 down(f(b)) 543.64/241.79 down(f(g(x0))) 543.64/241.79 down(f(c)) 543.64/241.79 down(f(fresh_constant)) 543.64/241.79 down(g(a)) 543.64/241.79 down(g(f(x0))) 543.64/241.79 down(g(b)) 543.64/241.79 down(g(c)) 543.64/241.79 down(g(fresh_constant)) 543.64/241.79 down(f(f(a))) 543.64/241.79 down(f(f(b))) 543.64/241.79 down(f(f(g(x0)))) 543.64/241.79 down(f(f(c))) 543.64/241.79 down(f(f(fresh_constant))) 543.64/241.79 down(g(g(a))) 543.64/241.79 down(g(g(f(x0)))) 543.64/241.79 down(g(g(b))) 543.64/241.79 down(g(g(c))) 543.64/241.79 down(g(g(fresh_constant))) 543.64/241.79 down(f(f(f(a)))) 543.64/241.79 down(f(f(f(b)))) 543.64/241.79 down(f(f(f(g(x0))))) 543.64/241.79 down(f(f(f(c)))) 543.64/241.79 down(f(f(f(fresh_constant)))) 543.64/241.79 down(g(g(g(a)))) 543.64/241.79 down(g(g(g(f(x0))))) 543.64/241.79 down(g(g(g(b)))) 543.64/241.79 down(g(g(g(c)))) 543.64/241.79 down(g(g(g(fresh_constant)))) 543.64/241.79 down(f(f(f(f(a))))) 543.64/241.79 down(f(f(f(f(b))))) 543.64/241.79 down(f(f(f(f(g(x0)))))) 543.64/241.79 down(f(f(f(f(c))))) 543.64/241.79 down(f(f(f(f(fresh_constant))))) 543.64/241.79 down(g(g(g(g(a))))) 543.64/241.79 down(g(g(g(g(f(x0)))))) 543.64/241.79 down(g(g(g(g(b))))) 543.64/241.79 down(g(g(g(g(c))))) 543.64/241.79 down(g(g(g(g(fresh_constant))))) 543.64/241.79 down(f(f(f(f(f(a)))))) 543.64/241.79 down(f(f(f(f(f(b)))))) 543.64/241.79 down(f(f(f(f(f(g(x0))))))) 543.64/241.79 down(f(f(f(f(f(c)))))) 543.64/241.79 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.79 down(g(g(g(g(g(a)))))) 543.64/241.79 down(g(g(g(g(g(f(x0))))))) 543.64/241.79 down(g(g(g(g(g(b)))))) 543.64/241.79 down(g(g(g(g(g(c)))))) 543.64/241.79 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.79 down(f(f(f(f(f(f(a))))))) 543.64/241.79 down(f(f(f(f(f(f(b))))))) 543.64/241.79 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.79 down(f(f(f(f(f(f(c))))))) 543.64/241.79 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.79 down(g(g(g(g(g(g(a))))))) 543.64/241.79 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.79 down(g(g(g(g(g(g(b))))))) 543.64/241.79 down(g(g(g(g(g(g(c))))))) 543.64/241.79 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.79 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 f_flat(up(x0)) 543.64/241.79 g_flat(up(x0)) 543.64/241.79 543.64/241.79 We have to consider all minimal (P,Q,R)-chains. 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (557) TransformationProof (EQUIVALENT) 543.64/241.79 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.79 543.64/241.79 (TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))),TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.64/241.79 543.64/241.79 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (558) 543.64/241.79 Obligation: 543.64/241.79 Q DP problem: 543.64/241.79 The TRS P consists of the following rules: 543.64/241.79 543.64/241.79 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.79 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.79 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.79 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.79 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.79 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.79 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.79 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.79 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.79 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.79 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.79 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.79 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.64/241.79 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.64/241.79 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.64/241.79 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.79 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.79 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.79 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.79 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.79 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.79 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.79 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.79 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.79 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.79 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.79 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.79 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.79 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.79 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.79 543.64/241.79 The TRS R consists of the following rules: 543.64/241.79 543.64/241.79 down(a) -> up(f(a)) 543.64/241.79 down(b) -> up(g(b)) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.79 down(f(a)) -> f_flat(down(a)) 543.64/241.79 down(f(b)) -> f_flat(down(b)) 543.64/241.79 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.79 down(f(c)) -> f_flat(down(c)) 543.64/241.79 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.79 down(g(a)) -> g_flat(down(a)) 543.64/241.79 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.79 down(g(b)) -> g_flat(down(b)) 543.64/241.79 down(g(c)) -> g_flat(down(c)) 543.64/241.79 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.79 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.79 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.79 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.79 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.79 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.79 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.79 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.79 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.79 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.79 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.79 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.79 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.79 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.79 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.79 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.79 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.79 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.79 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.79 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.79 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.79 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.79 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.79 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.79 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.79 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.79 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.79 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.79 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.79 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.79 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.79 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.79 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.79 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.79 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.79 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.79 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.79 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.79 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.79 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.79 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.79 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.79 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.79 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.79 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.79 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.79 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.79 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.79 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.79 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.79 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.79 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.79 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.79 543.64/241.79 The set Q consists of the following terms: 543.64/241.79 543.64/241.79 down(a) 543.64/241.79 down(b) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.79 down(f(a)) 543.64/241.79 down(f(b)) 543.64/241.79 down(f(g(x0))) 543.64/241.79 down(f(c)) 543.64/241.79 down(f(fresh_constant)) 543.64/241.79 down(g(a)) 543.64/241.79 down(g(f(x0))) 543.64/241.79 down(g(b)) 543.64/241.79 down(g(c)) 543.64/241.79 down(g(fresh_constant)) 543.64/241.79 down(f(f(a))) 543.64/241.79 down(f(f(b))) 543.64/241.79 down(f(f(g(x0)))) 543.64/241.79 down(f(f(c))) 543.64/241.79 down(f(f(fresh_constant))) 543.64/241.79 down(g(g(a))) 543.64/241.79 down(g(g(f(x0)))) 543.64/241.79 down(g(g(b))) 543.64/241.79 down(g(g(c))) 543.64/241.79 down(g(g(fresh_constant))) 543.64/241.79 down(f(f(f(a)))) 543.64/241.79 down(f(f(f(b)))) 543.64/241.79 down(f(f(f(g(x0))))) 543.64/241.79 down(f(f(f(c)))) 543.64/241.79 down(f(f(f(fresh_constant)))) 543.64/241.79 down(g(g(g(a)))) 543.64/241.79 down(g(g(g(f(x0))))) 543.64/241.79 down(g(g(g(b)))) 543.64/241.79 down(g(g(g(c)))) 543.64/241.79 down(g(g(g(fresh_constant)))) 543.64/241.79 down(f(f(f(f(a))))) 543.64/241.79 down(f(f(f(f(b))))) 543.64/241.79 down(f(f(f(f(g(x0)))))) 543.64/241.79 down(f(f(f(f(c))))) 543.64/241.79 down(f(f(f(f(fresh_constant))))) 543.64/241.79 down(g(g(g(g(a))))) 543.64/241.79 down(g(g(g(g(f(x0)))))) 543.64/241.79 down(g(g(g(g(b))))) 543.64/241.79 down(g(g(g(g(c))))) 543.64/241.79 down(g(g(g(g(fresh_constant))))) 543.64/241.79 down(f(f(f(f(f(a)))))) 543.64/241.79 down(f(f(f(f(f(b)))))) 543.64/241.79 down(f(f(f(f(f(g(x0))))))) 543.64/241.79 down(f(f(f(f(f(c)))))) 543.64/241.79 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.79 down(g(g(g(g(g(a)))))) 543.64/241.79 down(g(g(g(g(g(f(x0))))))) 543.64/241.79 down(g(g(g(g(g(b)))))) 543.64/241.79 down(g(g(g(g(g(c)))))) 543.64/241.79 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.79 down(f(f(f(f(f(f(a))))))) 543.64/241.79 down(f(f(f(f(f(f(b))))))) 543.64/241.79 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.79 down(f(f(f(f(f(f(c))))))) 543.64/241.79 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.79 down(g(g(g(g(g(g(a))))))) 543.64/241.79 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.79 down(g(g(g(g(g(g(b))))))) 543.64/241.79 down(g(g(g(g(g(g(c))))))) 543.64/241.79 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.79 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 f_flat(up(x0)) 543.64/241.79 g_flat(up(x0)) 543.64/241.79 543.64/241.79 We have to consider all minimal (P,Q,R)-chains. 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (559) TransformationProof (EQUIVALENT) 543.64/241.79 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.79 543.64/241.79 (TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))),TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.64/241.79 543.64/241.79 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (560) 543.64/241.79 Obligation: 543.64/241.79 Q DP problem: 543.64/241.79 The TRS P consists of the following rules: 543.64/241.79 543.64/241.79 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.79 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.79 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.79 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.79 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.79 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.79 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.79 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.79 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.79 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.79 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.79 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.79 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.64/241.79 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.64/241.79 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.64/241.79 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.79 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.79 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.79 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.79 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.79 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.79 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.79 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.79 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.79 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.79 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.79 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.79 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.79 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.79 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 543.64/241.79 The TRS R consists of the following rules: 543.64/241.79 543.64/241.79 down(a) -> up(f(a)) 543.64/241.79 down(b) -> up(g(b)) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.79 down(f(a)) -> f_flat(down(a)) 543.64/241.79 down(f(b)) -> f_flat(down(b)) 543.64/241.79 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.79 down(f(c)) -> f_flat(down(c)) 543.64/241.79 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.79 down(g(a)) -> g_flat(down(a)) 543.64/241.79 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.79 down(g(b)) -> g_flat(down(b)) 543.64/241.79 down(g(c)) -> g_flat(down(c)) 543.64/241.79 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.79 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.79 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.79 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.79 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.79 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.79 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.79 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.79 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.79 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.79 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.79 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.79 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.79 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.79 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.79 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.79 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.79 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.79 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.79 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.79 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.79 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.79 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.79 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.79 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.79 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.79 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.79 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.79 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.79 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.79 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.79 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.79 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.79 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.79 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.79 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.79 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.79 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.79 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.79 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.79 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.79 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.79 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.79 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.79 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.79 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.79 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.79 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.79 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.79 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.79 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.79 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.79 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.79 543.64/241.79 The set Q consists of the following terms: 543.64/241.79 543.64/241.79 down(a) 543.64/241.79 down(b) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.79 down(f(a)) 543.64/241.79 down(f(b)) 543.64/241.79 down(f(g(x0))) 543.64/241.79 down(f(c)) 543.64/241.79 down(f(fresh_constant)) 543.64/241.79 down(g(a)) 543.64/241.79 down(g(f(x0))) 543.64/241.79 down(g(b)) 543.64/241.79 down(g(c)) 543.64/241.79 down(g(fresh_constant)) 543.64/241.79 down(f(f(a))) 543.64/241.79 down(f(f(b))) 543.64/241.79 down(f(f(g(x0)))) 543.64/241.79 down(f(f(c))) 543.64/241.79 down(f(f(fresh_constant))) 543.64/241.79 down(g(g(a))) 543.64/241.79 down(g(g(f(x0)))) 543.64/241.79 down(g(g(b))) 543.64/241.79 down(g(g(c))) 543.64/241.79 down(g(g(fresh_constant))) 543.64/241.79 down(f(f(f(a)))) 543.64/241.79 down(f(f(f(b)))) 543.64/241.79 down(f(f(f(g(x0))))) 543.64/241.79 down(f(f(f(c)))) 543.64/241.79 down(f(f(f(fresh_constant)))) 543.64/241.79 down(g(g(g(a)))) 543.64/241.79 down(g(g(g(f(x0))))) 543.64/241.79 down(g(g(g(b)))) 543.64/241.79 down(g(g(g(c)))) 543.64/241.79 down(g(g(g(fresh_constant)))) 543.64/241.79 down(f(f(f(f(a))))) 543.64/241.79 down(f(f(f(f(b))))) 543.64/241.79 down(f(f(f(f(g(x0)))))) 543.64/241.79 down(f(f(f(f(c))))) 543.64/241.79 down(f(f(f(f(fresh_constant))))) 543.64/241.79 down(g(g(g(g(a))))) 543.64/241.79 down(g(g(g(g(f(x0)))))) 543.64/241.79 down(g(g(g(g(b))))) 543.64/241.79 down(g(g(g(g(c))))) 543.64/241.79 down(g(g(g(g(fresh_constant))))) 543.64/241.79 down(f(f(f(f(f(a)))))) 543.64/241.79 down(f(f(f(f(f(b)))))) 543.64/241.79 down(f(f(f(f(f(g(x0))))))) 543.64/241.79 down(f(f(f(f(f(c)))))) 543.64/241.79 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.79 down(g(g(g(g(g(a)))))) 543.64/241.79 down(g(g(g(g(g(f(x0))))))) 543.64/241.79 down(g(g(g(g(g(b)))))) 543.64/241.79 down(g(g(g(g(g(c)))))) 543.64/241.79 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.79 down(f(f(f(f(f(f(a))))))) 543.64/241.79 down(f(f(f(f(f(f(b))))))) 543.64/241.79 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.79 down(f(f(f(f(f(f(c))))))) 543.64/241.79 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.79 down(g(g(g(g(g(g(a))))))) 543.64/241.79 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.79 down(g(g(g(g(g(g(b))))))) 543.64/241.79 down(g(g(g(g(g(g(c))))))) 543.64/241.79 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.79 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 f_flat(up(x0)) 543.64/241.79 g_flat(up(x0)) 543.64/241.79 543.64/241.79 We have to consider all minimal (P,Q,R)-chains. 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (561) TransformationProof (EQUIVALENT) 543.64/241.79 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(a))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.79 543.64/241.79 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a)))))))))))) 543.64/241.79 543.64/241.79 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (562) 543.64/241.79 Obligation: 543.64/241.79 Q DP problem: 543.64/241.79 The TRS P consists of the following rules: 543.64/241.79 543.64/241.79 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.79 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.79 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.79 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.79 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.79 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.79 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.79 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.79 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.79 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.79 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.79 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.79 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.64/241.79 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.64/241.79 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.64/241.79 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.79 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.79 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.79 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.79 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.79 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.79 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.79 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.79 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.79 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.79 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.79 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.79 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.79 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.79 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.79 543.64/241.79 The TRS R consists of the following rules: 543.64/241.79 543.64/241.79 down(a) -> up(f(a)) 543.64/241.79 down(b) -> up(g(b)) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.79 down(f(a)) -> f_flat(down(a)) 543.64/241.79 down(f(b)) -> f_flat(down(b)) 543.64/241.79 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.79 down(f(c)) -> f_flat(down(c)) 543.64/241.79 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.79 down(g(a)) -> g_flat(down(a)) 543.64/241.79 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.79 down(g(b)) -> g_flat(down(b)) 543.64/241.79 down(g(c)) -> g_flat(down(c)) 543.64/241.79 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.79 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.79 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.79 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.79 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.79 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.79 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.79 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.79 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.79 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.79 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.79 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.79 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.79 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.79 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.79 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.79 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.79 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.79 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.79 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.79 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.79 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.79 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.79 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.79 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.79 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.79 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.79 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.79 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.79 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.79 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.79 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.79 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.79 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.79 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.79 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.79 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.79 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.79 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.79 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.79 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.79 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.79 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.79 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.79 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.79 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.79 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.79 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.79 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.79 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.79 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.79 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.79 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.79 543.64/241.79 The set Q consists of the following terms: 543.64/241.79 543.64/241.79 down(a) 543.64/241.79 down(b) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.79 down(f(a)) 543.64/241.79 down(f(b)) 543.64/241.79 down(f(g(x0))) 543.64/241.79 down(f(c)) 543.64/241.79 down(f(fresh_constant)) 543.64/241.79 down(g(a)) 543.64/241.79 down(g(f(x0))) 543.64/241.79 down(g(b)) 543.64/241.79 down(g(c)) 543.64/241.79 down(g(fresh_constant)) 543.64/241.79 down(f(f(a))) 543.64/241.79 down(f(f(b))) 543.64/241.79 down(f(f(g(x0)))) 543.64/241.79 down(f(f(c))) 543.64/241.79 down(f(f(fresh_constant))) 543.64/241.79 down(g(g(a))) 543.64/241.79 down(g(g(f(x0)))) 543.64/241.79 down(g(g(b))) 543.64/241.79 down(g(g(c))) 543.64/241.79 down(g(g(fresh_constant))) 543.64/241.79 down(f(f(f(a)))) 543.64/241.79 down(f(f(f(b)))) 543.64/241.79 down(f(f(f(g(x0))))) 543.64/241.79 down(f(f(f(c)))) 543.64/241.79 down(f(f(f(fresh_constant)))) 543.64/241.79 down(g(g(g(a)))) 543.64/241.79 down(g(g(g(f(x0))))) 543.64/241.79 down(g(g(g(b)))) 543.64/241.79 down(g(g(g(c)))) 543.64/241.79 down(g(g(g(fresh_constant)))) 543.64/241.79 down(f(f(f(f(a))))) 543.64/241.79 down(f(f(f(f(b))))) 543.64/241.79 down(f(f(f(f(g(x0)))))) 543.64/241.79 down(f(f(f(f(c))))) 543.64/241.79 down(f(f(f(f(fresh_constant))))) 543.64/241.79 down(g(g(g(g(a))))) 543.64/241.79 down(g(g(g(g(f(x0)))))) 543.64/241.79 down(g(g(g(g(b))))) 543.64/241.79 down(g(g(g(g(c))))) 543.64/241.79 down(g(g(g(g(fresh_constant))))) 543.64/241.79 down(f(f(f(f(f(a)))))) 543.64/241.79 down(f(f(f(f(f(b)))))) 543.64/241.79 down(f(f(f(f(f(g(x0))))))) 543.64/241.79 down(f(f(f(f(f(c)))))) 543.64/241.79 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.79 down(g(g(g(g(g(a)))))) 543.64/241.79 down(g(g(g(g(g(f(x0))))))) 543.64/241.79 down(g(g(g(g(g(b)))))) 543.64/241.79 down(g(g(g(g(g(c)))))) 543.64/241.79 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.79 down(f(f(f(f(f(f(a))))))) 543.64/241.79 down(f(f(f(f(f(f(b))))))) 543.64/241.79 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.79 down(f(f(f(f(f(f(c))))))) 543.64/241.79 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.79 down(g(g(g(g(g(g(a))))))) 543.64/241.79 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.79 down(g(g(g(g(g(g(b))))))) 543.64/241.79 down(g(g(g(g(g(g(c))))))) 543.64/241.79 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.79 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.79 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.79 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.79 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.79 f_flat(up(x0)) 543.64/241.79 g_flat(up(x0)) 543.64/241.79 543.64/241.79 We have to consider all minimal (P,Q,R)-chains. 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (563) TransformationProof (EQUIVALENT) 543.64/241.79 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(f(x0)))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.79 543.64/241.79 (TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0))))))))))))) 543.64/241.79 543.64/241.79 543.64/241.79 ---------------------------------------- 543.64/241.79 543.64/241.79 (564) 543.64/241.79 Obligation: 543.64/241.79 Q DP problem: 543.64/241.79 The TRS P consists of the following rules: 543.64/241.79 543.64/241.79 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.79 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.79 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.79 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.79 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.79 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.79 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.79 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.79 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.79 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.79 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.79 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.79 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.64/241.79 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.64/241.79 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.64/241.79 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.79 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.79 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.79 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.79 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.79 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.79 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.79 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.79 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.79 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.79 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.79 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.79 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.79 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.79 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.79 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.79 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.79 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.80 543.64/241.80 The TRS R consists of the following rules: 543.64/241.80 543.64/241.80 down(a) -> up(f(a)) 543.64/241.80 down(b) -> up(g(b)) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.80 down(f(a)) -> f_flat(down(a)) 543.64/241.80 down(f(b)) -> f_flat(down(b)) 543.64/241.80 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.80 down(f(c)) -> f_flat(down(c)) 543.64/241.80 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.80 down(g(a)) -> g_flat(down(a)) 543.64/241.80 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.80 down(g(b)) -> g_flat(down(b)) 543.64/241.80 down(g(c)) -> g_flat(down(c)) 543.64/241.80 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.80 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.80 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.80 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.80 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.80 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.80 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.80 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.80 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.80 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.80 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.80 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.80 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.80 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.80 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.80 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.80 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.80 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.80 543.64/241.80 The set Q consists of the following terms: 543.64/241.80 543.64/241.80 down(a) 543.64/241.80 down(b) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.80 down(f(a)) 543.64/241.80 down(f(b)) 543.64/241.80 down(f(g(x0))) 543.64/241.80 down(f(c)) 543.64/241.80 down(f(fresh_constant)) 543.64/241.80 down(g(a)) 543.64/241.80 down(g(f(x0))) 543.64/241.80 down(g(b)) 543.64/241.80 down(g(c)) 543.64/241.80 down(g(fresh_constant)) 543.64/241.80 down(f(f(a))) 543.64/241.80 down(f(f(b))) 543.64/241.80 down(f(f(g(x0)))) 543.64/241.80 down(f(f(c))) 543.64/241.80 down(f(f(fresh_constant))) 543.64/241.80 down(g(g(a))) 543.64/241.80 down(g(g(f(x0)))) 543.64/241.80 down(g(g(b))) 543.64/241.80 down(g(g(c))) 543.64/241.80 down(g(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) 543.64/241.80 down(f(f(f(g(x0))))) 543.64/241.80 down(f(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) 543.64/241.80 down(g(g(g(f(x0))))) 543.64/241.80 down(g(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(x0)))))) 543.64/241.80 down(f(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(x0)))))) 543.64/241.80 down(g(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(x0))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(x0))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 f_flat(up(x0)) 543.64/241.80 g_flat(up(x0)) 543.64/241.80 543.64/241.80 We have to consider all minimal (P,Q,R)-chains. 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (565) TransformationProof (EQUIVALENT) 543.64/241.80 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(c))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.80 543.64/241.80 (TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c)))))))))))) 543.64/241.80 543.64/241.80 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (566) 543.64/241.80 Obligation: 543.64/241.80 Q DP problem: 543.64/241.80 The TRS P consists of the following rules: 543.64/241.80 543.64/241.80 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.80 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.80 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.80 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.80 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.80 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.80 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.80 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.80 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.80 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.80 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.80 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.80 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.64/241.80 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.64/241.80 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.64/241.80 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.80 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.80 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.80 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.80 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.80 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.80 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.80 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.80 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.80 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.80 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.80 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.80 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.80 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.80 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.80 543.64/241.80 The TRS R consists of the following rules: 543.64/241.80 543.64/241.80 down(a) -> up(f(a)) 543.64/241.80 down(b) -> up(g(b)) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.80 down(f(a)) -> f_flat(down(a)) 543.64/241.80 down(f(b)) -> f_flat(down(b)) 543.64/241.80 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.80 down(f(c)) -> f_flat(down(c)) 543.64/241.80 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.80 down(g(a)) -> g_flat(down(a)) 543.64/241.80 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.80 down(g(b)) -> g_flat(down(b)) 543.64/241.80 down(g(c)) -> g_flat(down(c)) 543.64/241.80 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.80 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.80 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.80 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.80 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.80 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.80 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.80 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.80 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.80 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.80 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.80 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.80 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.80 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.80 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.80 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.80 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.80 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.80 543.64/241.80 The set Q consists of the following terms: 543.64/241.80 543.64/241.80 down(a) 543.64/241.80 down(b) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.80 down(f(a)) 543.64/241.80 down(f(b)) 543.64/241.80 down(f(g(x0))) 543.64/241.80 down(f(c)) 543.64/241.80 down(f(fresh_constant)) 543.64/241.80 down(g(a)) 543.64/241.80 down(g(f(x0))) 543.64/241.80 down(g(b)) 543.64/241.80 down(g(c)) 543.64/241.80 down(g(fresh_constant)) 543.64/241.80 down(f(f(a))) 543.64/241.80 down(f(f(b))) 543.64/241.80 down(f(f(g(x0)))) 543.64/241.80 down(f(f(c))) 543.64/241.80 down(f(f(fresh_constant))) 543.64/241.80 down(g(g(a))) 543.64/241.80 down(g(g(f(x0)))) 543.64/241.80 down(g(g(b))) 543.64/241.80 down(g(g(c))) 543.64/241.80 down(g(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) 543.64/241.80 down(f(f(f(g(x0))))) 543.64/241.80 down(f(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) 543.64/241.80 down(g(g(g(f(x0))))) 543.64/241.80 down(g(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(x0)))))) 543.64/241.80 down(f(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(x0)))))) 543.64/241.80 down(g(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(x0))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(x0))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 f_flat(up(x0)) 543.64/241.80 g_flat(up(x0)) 543.64/241.80 543.64/241.80 We have to consider all minimal (P,Q,R)-chains. 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (567) TransformationProof (EQUIVALENT) 543.64/241.80 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(down(f(f(f(f(f(f(fresh_constant))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.80 543.64/241.80 (TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant)))))))))))) 543.64/241.80 543.64/241.80 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (568) 543.64/241.80 Obligation: 543.64/241.80 Q DP problem: 543.64/241.80 The TRS P consists of the following rules: 543.64/241.80 543.64/241.80 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.80 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.80 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.80 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.80 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.80 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.80 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.80 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.80 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.80 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.80 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.80 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.80 TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) 543.64/241.80 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.64/241.80 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.64/241.80 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.80 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.80 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.80 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.80 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.80 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.80 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.80 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.80 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.80 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.80 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.80 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.80 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.80 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.80 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.80 543.64/241.80 The TRS R consists of the following rules: 543.64/241.80 543.64/241.80 down(a) -> up(f(a)) 543.64/241.80 down(b) -> up(g(b)) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.80 down(f(a)) -> f_flat(down(a)) 543.64/241.80 down(f(b)) -> f_flat(down(b)) 543.64/241.80 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.80 down(f(c)) -> f_flat(down(c)) 543.64/241.80 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.80 down(g(a)) -> g_flat(down(a)) 543.64/241.80 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.80 down(g(b)) -> g_flat(down(b)) 543.64/241.80 down(g(c)) -> g_flat(down(c)) 543.64/241.80 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.80 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.80 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.80 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.80 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.80 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.80 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.80 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.80 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.80 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.80 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.80 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.80 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.80 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.80 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.80 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.80 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.80 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.80 543.64/241.80 The set Q consists of the following terms: 543.64/241.80 543.64/241.80 down(a) 543.64/241.80 down(b) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.80 down(f(a)) 543.64/241.80 down(f(b)) 543.64/241.80 down(f(g(x0))) 543.64/241.80 down(f(c)) 543.64/241.80 down(f(fresh_constant)) 543.64/241.80 down(g(a)) 543.64/241.80 down(g(f(x0))) 543.64/241.80 down(g(b)) 543.64/241.80 down(g(c)) 543.64/241.80 down(g(fresh_constant)) 543.64/241.80 down(f(f(a))) 543.64/241.80 down(f(f(b))) 543.64/241.80 down(f(f(g(x0)))) 543.64/241.80 down(f(f(c))) 543.64/241.80 down(f(f(fresh_constant))) 543.64/241.80 down(g(g(a))) 543.64/241.80 down(g(g(f(x0)))) 543.64/241.80 down(g(g(b))) 543.64/241.80 down(g(g(c))) 543.64/241.80 down(g(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) 543.64/241.80 down(f(f(f(g(x0))))) 543.64/241.80 down(f(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) 543.64/241.80 down(g(g(g(f(x0))))) 543.64/241.80 down(g(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(x0)))))) 543.64/241.80 down(f(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(x0)))))) 543.64/241.80 down(g(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(x0))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(x0))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 f_flat(up(x0)) 543.64/241.80 g_flat(up(x0)) 543.64/241.80 543.64/241.80 We have to consider all minimal (P,Q,R)-chains. 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (569) TransformationProof (EQUIVALENT) 543.64/241.80 By rewriting [LPAR04] the rule TOP(up(f(f(b)))) -> TOP(f_flat(up(f(g(b))))) at position [0] we obtained the following new rules [LPAR04]: 543.64/241.80 543.64/241.80 (TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))),TOP(up(f(f(b)))) -> TOP(up(f(f(g(b)))))) 543.64/241.80 543.64/241.80 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (570) 543.64/241.80 Obligation: 543.64/241.80 Q DP problem: 543.64/241.80 The TRS P consists of the following rules: 543.64/241.80 543.64/241.80 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.80 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.80 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.80 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.80 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.80 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.80 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.80 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.80 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.80 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.80 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.80 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.80 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) 543.64/241.80 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.64/241.80 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.80 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.80 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.80 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.80 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.80 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.80 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.80 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.80 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.80 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.80 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.80 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.80 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.80 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.80 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.80 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.80 543.64/241.80 The TRS R consists of the following rules: 543.64/241.80 543.64/241.80 down(a) -> up(f(a)) 543.64/241.80 down(b) -> up(g(b)) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.80 down(f(a)) -> f_flat(down(a)) 543.64/241.80 down(f(b)) -> f_flat(down(b)) 543.64/241.80 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.80 down(f(c)) -> f_flat(down(c)) 543.64/241.80 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.80 down(g(a)) -> g_flat(down(a)) 543.64/241.80 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.80 down(g(b)) -> g_flat(down(b)) 543.64/241.80 down(g(c)) -> g_flat(down(c)) 543.64/241.80 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.80 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.80 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.80 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.80 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.80 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.80 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.80 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.80 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.80 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.80 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.80 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.80 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.80 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.80 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.80 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.80 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.80 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.80 543.64/241.80 The set Q consists of the following terms: 543.64/241.80 543.64/241.80 down(a) 543.64/241.80 down(b) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.80 down(f(a)) 543.64/241.80 down(f(b)) 543.64/241.80 down(f(g(x0))) 543.64/241.80 down(f(c)) 543.64/241.80 down(f(fresh_constant)) 543.64/241.80 down(g(a)) 543.64/241.80 down(g(f(x0))) 543.64/241.80 down(g(b)) 543.64/241.80 down(g(c)) 543.64/241.80 down(g(fresh_constant)) 543.64/241.80 down(f(f(a))) 543.64/241.80 down(f(f(b))) 543.64/241.80 down(f(f(g(x0)))) 543.64/241.80 down(f(f(c))) 543.64/241.80 down(f(f(fresh_constant))) 543.64/241.80 down(g(g(a))) 543.64/241.80 down(g(g(f(x0)))) 543.64/241.80 down(g(g(b))) 543.64/241.80 down(g(g(c))) 543.64/241.80 down(g(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) 543.64/241.80 down(f(f(f(g(x0))))) 543.64/241.80 down(f(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) 543.64/241.80 down(g(g(g(f(x0))))) 543.64/241.80 down(g(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(x0)))))) 543.64/241.80 down(f(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(x0)))))) 543.64/241.80 down(g(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(x0))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(x0))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 f_flat(up(x0)) 543.64/241.80 g_flat(up(x0)) 543.64/241.80 543.64/241.80 We have to consider all minimal (P,Q,R)-chains. 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (571) TransformationProof (EQUIVALENT) 543.64/241.80 By rewriting [LPAR04] the rule TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(f_flat(up(g(b)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.80 543.64/241.80 (TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))),TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b))))))) 543.64/241.80 543.64/241.80 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (572) 543.64/241.80 Obligation: 543.64/241.80 Q DP problem: 543.64/241.80 The TRS P consists of the following rules: 543.64/241.80 543.64/241.80 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.80 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.80 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.80 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.80 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.80 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.80 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.80 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.80 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.80 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.80 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.80 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.80 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) 543.64/241.80 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.80 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.80 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.80 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.80 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.80 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.80 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.80 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.80 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.80 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.80 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.80 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.80 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.80 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.80 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.80 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.80 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.80 543.64/241.80 The TRS R consists of the following rules: 543.64/241.80 543.64/241.80 down(a) -> up(f(a)) 543.64/241.80 down(b) -> up(g(b)) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.80 down(f(a)) -> f_flat(down(a)) 543.64/241.80 down(f(b)) -> f_flat(down(b)) 543.64/241.80 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.80 down(f(c)) -> f_flat(down(c)) 543.64/241.80 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.80 down(g(a)) -> g_flat(down(a)) 543.64/241.80 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.80 down(g(b)) -> g_flat(down(b)) 543.64/241.80 down(g(c)) -> g_flat(down(c)) 543.64/241.80 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.80 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.80 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.80 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.80 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.80 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.80 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.80 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.80 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.80 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.80 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.80 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.80 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.80 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.80 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.80 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.80 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.80 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.80 543.64/241.80 The set Q consists of the following terms: 543.64/241.80 543.64/241.80 down(a) 543.64/241.80 down(b) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.80 down(f(a)) 543.64/241.80 down(f(b)) 543.64/241.80 down(f(g(x0))) 543.64/241.80 down(f(c)) 543.64/241.80 down(f(fresh_constant)) 543.64/241.80 down(g(a)) 543.64/241.80 down(g(f(x0))) 543.64/241.80 down(g(b)) 543.64/241.80 down(g(c)) 543.64/241.80 down(g(fresh_constant)) 543.64/241.80 down(f(f(a))) 543.64/241.80 down(f(f(b))) 543.64/241.80 down(f(f(g(x0)))) 543.64/241.80 down(f(f(c))) 543.64/241.80 down(f(f(fresh_constant))) 543.64/241.80 down(g(g(a))) 543.64/241.80 down(g(g(f(x0)))) 543.64/241.80 down(g(g(b))) 543.64/241.80 down(g(g(c))) 543.64/241.80 down(g(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) 543.64/241.80 down(f(f(f(g(x0))))) 543.64/241.80 down(f(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) 543.64/241.80 down(g(g(g(f(x0))))) 543.64/241.80 down(g(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(x0)))))) 543.64/241.80 down(f(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(x0)))))) 543.64/241.80 down(g(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(x0))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(x0))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 f_flat(up(x0)) 543.64/241.80 g_flat(up(x0)) 543.64/241.80 543.64/241.80 We have to consider all minimal (P,Q,R)-chains. 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (573) TransformationProof (EQUIVALENT) 543.64/241.80 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(a)))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.80 543.64/241.80 (TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))),TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.64/241.80 543.64/241.80 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (574) 543.64/241.80 Obligation: 543.64/241.80 Q DP problem: 543.64/241.80 The TRS P consists of the following rules: 543.64/241.80 543.64/241.80 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.80 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.80 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.80 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.80 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.80 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.80 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.80 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.80 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.80 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.80 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.80 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.80 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.80 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.80 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.80 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.80 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.80 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.80 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.80 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.80 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.80 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.80 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.80 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.80 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.80 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.80 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.80 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.80 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.80 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.80 543.64/241.80 The TRS R consists of the following rules: 543.64/241.80 543.64/241.80 down(a) -> up(f(a)) 543.64/241.80 down(b) -> up(g(b)) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.80 down(f(a)) -> f_flat(down(a)) 543.64/241.80 down(f(b)) -> f_flat(down(b)) 543.64/241.80 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.80 down(f(c)) -> f_flat(down(c)) 543.64/241.80 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.80 down(g(a)) -> g_flat(down(a)) 543.64/241.80 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.80 down(g(b)) -> g_flat(down(b)) 543.64/241.80 down(g(c)) -> g_flat(down(c)) 543.64/241.80 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.80 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.80 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.80 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.80 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.80 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.80 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.80 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.80 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.80 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.80 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.80 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.80 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.80 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.80 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.80 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.80 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.80 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.80 543.64/241.80 The set Q consists of the following terms: 543.64/241.80 543.64/241.80 down(a) 543.64/241.80 down(b) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.80 down(f(a)) 543.64/241.80 down(f(b)) 543.64/241.80 down(f(g(x0))) 543.64/241.80 down(f(c)) 543.64/241.80 down(f(fresh_constant)) 543.64/241.80 down(g(a)) 543.64/241.80 down(g(f(x0))) 543.64/241.80 down(g(b)) 543.64/241.80 down(g(c)) 543.64/241.80 down(g(fresh_constant)) 543.64/241.80 down(f(f(a))) 543.64/241.80 down(f(f(b))) 543.64/241.80 down(f(f(g(x0)))) 543.64/241.80 down(f(f(c))) 543.64/241.80 down(f(f(fresh_constant))) 543.64/241.80 down(g(g(a))) 543.64/241.80 down(g(g(f(x0)))) 543.64/241.80 down(g(g(b))) 543.64/241.80 down(g(g(c))) 543.64/241.80 down(g(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) 543.64/241.80 down(f(f(f(g(x0))))) 543.64/241.80 down(f(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) 543.64/241.80 down(g(g(g(f(x0))))) 543.64/241.80 down(g(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(x0)))))) 543.64/241.80 down(f(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(x0)))))) 543.64/241.80 down(g(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(x0))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(x0))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 f_flat(up(x0)) 543.64/241.80 g_flat(up(x0)) 543.64/241.80 543.64/241.80 We have to consider all minimal (P,Q,R)-chains. 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (575) TransformationProof (EQUIVALENT) 543.64/241.80 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(b)))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.80 543.64/241.80 (TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))),TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.64/241.80 543.64/241.80 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (576) 543.64/241.80 Obligation: 543.64/241.80 Q DP problem: 543.64/241.80 The TRS P consists of the following rules: 543.64/241.80 543.64/241.80 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.80 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.80 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.80 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.80 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.80 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.80 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.80 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.80 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.80 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.80 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.80 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.80 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.80 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.80 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.80 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.80 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.80 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.80 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.80 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.80 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.80 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.80 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.80 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.80 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.80 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.80 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.80 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.80 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.80 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.80 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.80 543.64/241.80 The TRS R consists of the following rules: 543.64/241.80 543.64/241.80 down(a) -> up(f(a)) 543.64/241.80 down(b) -> up(g(b)) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.80 down(f(a)) -> f_flat(down(a)) 543.64/241.80 down(f(b)) -> f_flat(down(b)) 543.64/241.80 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.80 down(f(c)) -> f_flat(down(c)) 543.64/241.80 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.80 down(g(a)) -> g_flat(down(a)) 543.64/241.80 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.80 down(g(b)) -> g_flat(down(b)) 543.64/241.80 down(g(c)) -> g_flat(down(c)) 543.64/241.80 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.80 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.80 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.80 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.80 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.80 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.80 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.80 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.80 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.80 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.80 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.80 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.80 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.80 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.80 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.80 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.80 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.80 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.80 543.64/241.80 The set Q consists of the following terms: 543.64/241.80 543.64/241.80 down(a) 543.64/241.80 down(b) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.80 down(f(a)) 543.64/241.80 down(f(b)) 543.64/241.80 down(f(g(x0))) 543.64/241.80 down(f(c)) 543.64/241.80 down(f(fresh_constant)) 543.64/241.80 down(g(a)) 543.64/241.80 down(g(f(x0))) 543.64/241.80 down(g(b)) 543.64/241.80 down(g(c)) 543.64/241.80 down(g(fresh_constant)) 543.64/241.80 down(f(f(a))) 543.64/241.80 down(f(f(b))) 543.64/241.80 down(f(f(g(x0)))) 543.64/241.80 down(f(f(c))) 543.64/241.80 down(f(f(fresh_constant))) 543.64/241.80 down(g(g(a))) 543.64/241.80 down(g(g(f(x0)))) 543.64/241.80 down(g(g(b))) 543.64/241.80 down(g(g(c))) 543.64/241.80 down(g(g(fresh_constant))) 543.64/241.80 down(f(f(f(a)))) 543.64/241.80 down(f(f(f(b)))) 543.64/241.80 down(f(f(f(g(x0))))) 543.64/241.80 down(f(f(f(c)))) 543.64/241.80 down(f(f(f(fresh_constant)))) 543.64/241.80 down(g(g(g(a)))) 543.64/241.80 down(g(g(g(f(x0))))) 543.64/241.80 down(g(g(g(b)))) 543.64/241.80 down(g(g(g(c)))) 543.64/241.80 down(g(g(g(fresh_constant)))) 543.64/241.80 down(f(f(f(f(a))))) 543.64/241.80 down(f(f(f(f(b))))) 543.64/241.80 down(f(f(f(f(g(x0)))))) 543.64/241.80 down(f(f(f(f(c))))) 543.64/241.80 down(f(f(f(f(fresh_constant))))) 543.64/241.80 down(g(g(g(g(a))))) 543.64/241.80 down(g(g(g(g(f(x0)))))) 543.64/241.80 down(g(g(g(g(b))))) 543.64/241.80 down(g(g(g(g(c))))) 543.64/241.80 down(g(g(g(g(fresh_constant))))) 543.64/241.80 down(f(f(f(f(f(a)))))) 543.64/241.80 down(f(f(f(f(f(b)))))) 543.64/241.80 down(f(f(f(f(f(g(x0))))))) 543.64/241.80 down(f(f(f(f(f(c)))))) 543.64/241.80 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.80 down(g(g(g(g(g(a)))))) 543.64/241.80 down(g(g(g(g(g(f(x0))))))) 543.64/241.80 down(g(g(g(g(g(b)))))) 543.64/241.80 down(g(g(g(g(g(c)))))) 543.64/241.80 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.80 down(f(f(f(f(f(f(a))))))) 543.64/241.80 down(f(f(f(f(f(f(b))))))) 543.64/241.80 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.80 down(f(f(f(f(f(f(c))))))) 543.64/241.80 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.80 down(g(g(g(g(g(g(a))))))) 543.64/241.80 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.80 down(g(g(g(g(g(g(b))))))) 543.64/241.80 down(g(g(g(g(g(g(c))))))) 543.64/241.80 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.80 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.80 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.80 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.80 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.80 f_flat(up(x0)) 543.64/241.80 g_flat(up(x0)) 543.64/241.80 543.64/241.80 We have to consider all minimal (P,Q,R)-chains. 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (577) TransformationProof (EQUIVALENT) 543.64/241.80 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(b))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.80 543.64/241.80 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b)))))))))))) 543.64/241.80 543.64/241.80 543.64/241.80 ---------------------------------------- 543.64/241.80 543.64/241.80 (578) 543.64/241.80 Obligation: 543.64/241.80 Q DP problem: 543.64/241.80 The TRS P consists of the following rules: 543.64/241.80 543.64/241.80 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.80 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.80 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.80 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.80 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.80 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.80 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.80 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.80 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.80 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.80 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.80 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.80 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.80 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.80 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.80 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.80 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.80 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.80 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.80 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.80 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.80 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.80 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.80 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.80 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.80 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.80 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.80 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.80 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.80 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.81 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.81 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.81 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.81 543.64/241.81 The TRS R consists of the following rules: 543.64/241.81 543.64/241.81 down(a) -> up(f(a)) 543.64/241.81 down(b) -> up(g(b)) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.81 down(f(a)) -> f_flat(down(a)) 543.64/241.81 down(f(b)) -> f_flat(down(b)) 543.64/241.81 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.81 down(f(c)) -> f_flat(down(c)) 543.64/241.81 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.81 down(g(a)) -> g_flat(down(a)) 543.64/241.81 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.81 down(g(b)) -> g_flat(down(b)) 543.64/241.81 down(g(c)) -> g_flat(down(c)) 543.64/241.81 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.81 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.81 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.81 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.81 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.81 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.81 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.81 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.81 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.81 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.81 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.81 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.81 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.81 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.81 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.81 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.81 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.81 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.81 543.64/241.81 The set Q consists of the following terms: 543.64/241.81 543.64/241.81 down(a) 543.64/241.81 down(b) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.81 down(f(a)) 543.64/241.81 down(f(b)) 543.64/241.81 down(f(g(x0))) 543.64/241.81 down(f(c)) 543.64/241.81 down(f(fresh_constant)) 543.64/241.81 down(g(a)) 543.64/241.81 down(g(f(x0))) 543.64/241.81 down(g(b)) 543.64/241.81 down(g(c)) 543.64/241.81 down(g(fresh_constant)) 543.64/241.81 down(f(f(a))) 543.64/241.81 down(f(f(b))) 543.64/241.81 down(f(f(g(x0)))) 543.64/241.81 down(f(f(c))) 543.64/241.81 down(f(f(fresh_constant))) 543.64/241.81 down(g(g(a))) 543.64/241.81 down(g(g(f(x0)))) 543.64/241.81 down(g(g(b))) 543.64/241.81 down(g(g(c))) 543.64/241.81 down(g(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) 543.64/241.81 down(f(f(f(g(x0))))) 543.64/241.81 down(f(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) 543.64/241.81 down(g(g(g(f(x0))))) 543.64/241.81 down(g(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(x0)))))) 543.64/241.81 down(f(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(x0)))))) 543.64/241.81 down(g(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(x0))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(x0))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 f_flat(up(x0)) 543.64/241.81 g_flat(up(x0)) 543.64/241.81 543.64/241.81 We have to consider all minimal (P,Q,R)-chains. 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (579) TransformationProof (EQUIVALENT) 543.64/241.81 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(c))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.81 543.64/241.81 (TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c)))))))))))) 543.64/241.81 543.64/241.81 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (580) 543.64/241.81 Obligation: 543.64/241.81 Q DP problem: 543.64/241.81 The TRS P consists of the following rules: 543.64/241.81 543.64/241.81 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.81 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.81 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.81 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.81 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.81 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.81 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.81 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.81 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.81 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.81 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.81 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.81 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.81 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.81 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.81 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.81 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.81 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.81 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.81 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.81 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.81 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.81 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.81 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.81 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.81 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.81 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.81 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.81 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.81 543.64/241.81 The TRS R consists of the following rules: 543.64/241.81 543.64/241.81 down(a) -> up(f(a)) 543.64/241.81 down(b) -> up(g(b)) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.81 down(f(a)) -> f_flat(down(a)) 543.64/241.81 down(f(b)) -> f_flat(down(b)) 543.64/241.81 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.81 down(f(c)) -> f_flat(down(c)) 543.64/241.81 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.81 down(g(a)) -> g_flat(down(a)) 543.64/241.81 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.81 down(g(b)) -> g_flat(down(b)) 543.64/241.81 down(g(c)) -> g_flat(down(c)) 543.64/241.81 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.81 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.81 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.81 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.81 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.81 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.81 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.81 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.81 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.81 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.81 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.81 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.81 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.81 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.81 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.81 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.81 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.81 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.81 543.64/241.81 The set Q consists of the following terms: 543.64/241.81 543.64/241.81 down(a) 543.64/241.81 down(b) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.81 down(f(a)) 543.64/241.81 down(f(b)) 543.64/241.81 down(f(g(x0))) 543.64/241.81 down(f(c)) 543.64/241.81 down(f(fresh_constant)) 543.64/241.81 down(g(a)) 543.64/241.81 down(g(f(x0))) 543.64/241.81 down(g(b)) 543.64/241.81 down(g(c)) 543.64/241.81 down(g(fresh_constant)) 543.64/241.81 down(f(f(a))) 543.64/241.81 down(f(f(b))) 543.64/241.81 down(f(f(g(x0)))) 543.64/241.81 down(f(f(c))) 543.64/241.81 down(f(f(fresh_constant))) 543.64/241.81 down(g(g(a))) 543.64/241.81 down(g(g(f(x0)))) 543.64/241.81 down(g(g(b))) 543.64/241.81 down(g(g(c))) 543.64/241.81 down(g(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) 543.64/241.81 down(f(f(f(g(x0))))) 543.64/241.81 down(f(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) 543.64/241.81 down(g(g(g(f(x0))))) 543.64/241.81 down(g(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(x0)))))) 543.64/241.81 down(f(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(x0)))))) 543.64/241.81 down(g(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(x0))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(x0))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 f_flat(up(x0)) 543.64/241.81 g_flat(up(x0)) 543.64/241.81 543.64/241.81 We have to consider all minimal (P,Q,R)-chains. 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (581) TransformationProof (EQUIVALENT) 543.64/241.81 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(down(g(g(g(g(g(g(fresh_constant))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.81 543.64/241.81 (TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant)))))))))))) 543.64/241.81 543.64/241.81 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (582) 543.64/241.81 Obligation: 543.64/241.81 Q DP problem: 543.64/241.81 The TRS P consists of the following rules: 543.64/241.81 543.64/241.81 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.81 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.81 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.81 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.81 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.81 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.81 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.81 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.81 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.81 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.81 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.81 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.81 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.81 TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) 543.64/241.81 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.81 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.81 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.81 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.81 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.81 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.81 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.81 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.81 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.81 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.81 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.81 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.81 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.81 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.81 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.81 543.64/241.81 The TRS R consists of the following rules: 543.64/241.81 543.64/241.81 down(a) -> up(f(a)) 543.64/241.81 down(b) -> up(g(b)) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.81 down(f(a)) -> f_flat(down(a)) 543.64/241.81 down(f(b)) -> f_flat(down(b)) 543.64/241.81 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.81 down(f(c)) -> f_flat(down(c)) 543.64/241.81 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.81 down(g(a)) -> g_flat(down(a)) 543.64/241.81 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.81 down(g(b)) -> g_flat(down(b)) 543.64/241.81 down(g(c)) -> g_flat(down(c)) 543.64/241.81 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.81 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.81 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.81 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.81 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.81 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.81 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.81 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.81 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.81 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.81 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.81 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.81 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.81 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.81 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.81 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.81 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.81 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.81 543.64/241.81 The set Q consists of the following terms: 543.64/241.81 543.64/241.81 down(a) 543.64/241.81 down(b) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.81 down(f(a)) 543.64/241.81 down(f(b)) 543.64/241.81 down(f(g(x0))) 543.64/241.81 down(f(c)) 543.64/241.81 down(f(fresh_constant)) 543.64/241.81 down(g(a)) 543.64/241.81 down(g(f(x0))) 543.64/241.81 down(g(b)) 543.64/241.81 down(g(c)) 543.64/241.81 down(g(fresh_constant)) 543.64/241.81 down(f(f(a))) 543.64/241.81 down(f(f(b))) 543.64/241.81 down(f(f(g(x0)))) 543.64/241.81 down(f(f(c))) 543.64/241.81 down(f(f(fresh_constant))) 543.64/241.81 down(g(g(a))) 543.64/241.81 down(g(g(f(x0)))) 543.64/241.81 down(g(g(b))) 543.64/241.81 down(g(g(c))) 543.64/241.81 down(g(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) 543.64/241.81 down(f(f(f(g(x0))))) 543.64/241.81 down(f(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) 543.64/241.81 down(g(g(g(f(x0))))) 543.64/241.81 down(g(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(x0)))))) 543.64/241.81 down(f(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(x0)))))) 543.64/241.81 down(g(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(x0))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(x0))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 f_flat(up(x0)) 543.64/241.81 g_flat(up(x0)) 543.64/241.81 543.64/241.81 We have to consider all minimal (P,Q,R)-chains. 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (583) TransformationProof (EQUIVALENT) 543.64/241.81 By rewriting [LPAR04] the rule TOP(up(g(g(a)))) -> TOP(g_flat(up(g(f(a))))) at position [0] we obtained the following new rules [LPAR04]: 543.64/241.81 543.64/241.81 (TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))),TOP(up(g(g(a)))) -> TOP(up(g(g(f(a)))))) 543.64/241.81 543.64/241.81 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (584) 543.64/241.81 Obligation: 543.64/241.81 Q DP problem: 543.64/241.81 The TRS P consists of the following rules: 543.64/241.81 543.64/241.81 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.81 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.81 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.81 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.81 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.81 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.81 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.81 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.81 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.81 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.81 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.81 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.81 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.81 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) 543.64/241.81 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.81 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.81 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.81 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.81 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.81 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.81 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.81 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.81 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.81 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.81 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.81 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.81 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.81 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.81 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.81 543.64/241.81 The TRS R consists of the following rules: 543.64/241.81 543.64/241.81 down(a) -> up(f(a)) 543.64/241.81 down(b) -> up(g(b)) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.81 down(f(a)) -> f_flat(down(a)) 543.64/241.81 down(f(b)) -> f_flat(down(b)) 543.64/241.81 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.81 down(f(c)) -> f_flat(down(c)) 543.64/241.81 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.81 down(g(a)) -> g_flat(down(a)) 543.64/241.81 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.81 down(g(b)) -> g_flat(down(b)) 543.64/241.81 down(g(c)) -> g_flat(down(c)) 543.64/241.81 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.81 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.81 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.81 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.81 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.81 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.81 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.81 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.81 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.81 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.81 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.81 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.81 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.81 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.81 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.81 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.81 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.81 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.81 543.64/241.81 The set Q consists of the following terms: 543.64/241.81 543.64/241.81 down(a) 543.64/241.81 down(b) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.81 down(f(a)) 543.64/241.81 down(f(b)) 543.64/241.81 down(f(g(x0))) 543.64/241.81 down(f(c)) 543.64/241.81 down(f(fresh_constant)) 543.64/241.81 down(g(a)) 543.64/241.81 down(g(f(x0))) 543.64/241.81 down(g(b)) 543.64/241.81 down(g(c)) 543.64/241.81 down(g(fresh_constant)) 543.64/241.81 down(f(f(a))) 543.64/241.81 down(f(f(b))) 543.64/241.81 down(f(f(g(x0)))) 543.64/241.81 down(f(f(c))) 543.64/241.81 down(f(f(fresh_constant))) 543.64/241.81 down(g(g(a))) 543.64/241.81 down(g(g(f(x0)))) 543.64/241.81 down(g(g(b))) 543.64/241.81 down(g(g(c))) 543.64/241.81 down(g(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) 543.64/241.81 down(f(f(f(g(x0))))) 543.64/241.81 down(f(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) 543.64/241.81 down(g(g(g(f(x0))))) 543.64/241.81 down(g(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(x0)))))) 543.64/241.81 down(f(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(x0)))))) 543.64/241.81 down(g(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(x0))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(x0))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 f_flat(up(x0)) 543.64/241.81 g_flat(up(x0)) 543.64/241.81 543.64/241.81 We have to consider all minimal (P,Q,R)-chains. 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (585) TransformationProof (EQUIVALENT) 543.64/241.81 By rewriting [LPAR04] the rule TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(g_flat(up(f(a)))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.81 543.64/241.81 (TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))),TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a))))))) 543.64/241.81 543.64/241.81 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (586) 543.64/241.81 Obligation: 543.64/241.81 Q DP problem: 543.64/241.81 The TRS P consists of the following rules: 543.64/241.81 543.64/241.81 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.81 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.81 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.81 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.81 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.81 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.81 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.81 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.81 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.81 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.81 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.81 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.81 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.81 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) 543.64/241.81 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.81 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.81 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.81 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.81 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.81 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.81 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.81 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.81 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.81 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.81 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.81 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.81 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.81 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.81 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.81 543.64/241.81 The TRS R consists of the following rules: 543.64/241.81 543.64/241.81 down(a) -> up(f(a)) 543.64/241.81 down(b) -> up(g(b)) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.81 down(f(a)) -> f_flat(down(a)) 543.64/241.81 down(f(b)) -> f_flat(down(b)) 543.64/241.81 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.81 down(f(c)) -> f_flat(down(c)) 543.64/241.81 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.81 down(g(a)) -> g_flat(down(a)) 543.64/241.81 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.81 down(g(b)) -> g_flat(down(b)) 543.64/241.81 down(g(c)) -> g_flat(down(c)) 543.64/241.81 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.81 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.81 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.81 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.81 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.81 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.81 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.81 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.81 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.81 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.81 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.81 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.81 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.81 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.81 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.81 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.81 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.81 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.81 543.64/241.81 The set Q consists of the following terms: 543.64/241.81 543.64/241.81 down(a) 543.64/241.81 down(b) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.81 down(f(a)) 543.64/241.81 down(f(b)) 543.64/241.81 down(f(g(x0))) 543.64/241.81 down(f(c)) 543.64/241.81 down(f(fresh_constant)) 543.64/241.81 down(g(a)) 543.64/241.81 down(g(f(x0))) 543.64/241.81 down(g(b)) 543.64/241.81 down(g(c)) 543.64/241.81 down(g(fresh_constant)) 543.64/241.81 down(f(f(a))) 543.64/241.81 down(f(f(b))) 543.64/241.81 down(f(f(g(x0)))) 543.64/241.81 down(f(f(c))) 543.64/241.81 down(f(f(fresh_constant))) 543.64/241.81 down(g(g(a))) 543.64/241.81 down(g(g(f(x0)))) 543.64/241.81 down(g(g(b))) 543.64/241.81 down(g(g(c))) 543.64/241.81 down(g(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) 543.64/241.81 down(f(f(f(g(x0))))) 543.64/241.81 down(f(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) 543.64/241.81 down(g(g(g(f(x0))))) 543.64/241.81 down(g(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(x0)))))) 543.64/241.81 down(f(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(x0)))))) 543.64/241.81 down(g(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(x0))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(x0))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 f_flat(up(x0)) 543.64/241.81 g_flat(up(x0)) 543.64/241.81 543.64/241.81 We have to consider all minimal (P,Q,R)-chains. 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (587) TransformationProof (EQUIVALENT) 543.64/241.81 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(a)))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.81 543.64/241.81 (TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))),TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.64/241.81 543.64/241.81 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (588) 543.64/241.81 Obligation: 543.64/241.81 Q DP problem: 543.64/241.81 The TRS P consists of the following rules: 543.64/241.81 543.64/241.81 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.81 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.81 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.81 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.81 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.81 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.81 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.81 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.81 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.81 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.81 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.81 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.81 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.81 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.81 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.81 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.81 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.81 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.81 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.81 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.81 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.81 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.81 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.81 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.81 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.81 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.81 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.81 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.81 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.81 543.64/241.81 The TRS R consists of the following rules: 543.64/241.81 543.64/241.81 down(a) -> up(f(a)) 543.64/241.81 down(b) -> up(g(b)) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.81 down(f(a)) -> f_flat(down(a)) 543.64/241.81 down(f(b)) -> f_flat(down(b)) 543.64/241.81 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.81 down(f(c)) -> f_flat(down(c)) 543.64/241.81 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.81 down(g(a)) -> g_flat(down(a)) 543.64/241.81 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.81 down(g(b)) -> g_flat(down(b)) 543.64/241.81 down(g(c)) -> g_flat(down(c)) 543.64/241.81 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.81 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.81 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.81 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.81 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.81 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.81 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.81 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.81 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.81 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.81 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.81 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.81 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.81 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.81 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.81 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.81 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.81 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.81 543.64/241.81 The set Q consists of the following terms: 543.64/241.81 543.64/241.81 down(a) 543.64/241.81 down(b) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.81 down(f(a)) 543.64/241.81 down(f(b)) 543.64/241.81 down(f(g(x0))) 543.64/241.81 down(f(c)) 543.64/241.81 down(f(fresh_constant)) 543.64/241.81 down(g(a)) 543.64/241.81 down(g(f(x0))) 543.64/241.81 down(g(b)) 543.64/241.81 down(g(c)) 543.64/241.81 down(g(fresh_constant)) 543.64/241.81 down(f(f(a))) 543.64/241.81 down(f(f(b))) 543.64/241.81 down(f(f(g(x0)))) 543.64/241.81 down(f(f(c))) 543.64/241.81 down(f(f(fresh_constant))) 543.64/241.81 down(g(g(a))) 543.64/241.81 down(g(g(f(x0)))) 543.64/241.81 down(g(g(b))) 543.64/241.81 down(g(g(c))) 543.64/241.81 down(g(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) 543.64/241.81 down(f(f(f(g(x0))))) 543.64/241.81 down(f(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) 543.64/241.81 down(g(g(g(f(x0))))) 543.64/241.81 down(g(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(x0)))))) 543.64/241.81 down(f(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(x0)))))) 543.64/241.81 down(g(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(x0))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(x0))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 f_flat(up(x0)) 543.64/241.81 g_flat(up(x0)) 543.64/241.81 543.64/241.81 We have to consider all minimal (P,Q,R)-chains. 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (589) TransformationProof (EQUIVALENT) 543.64/241.81 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(a))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.81 543.64/241.81 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.64/241.81 543.64/241.81 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (590) 543.64/241.81 Obligation: 543.64/241.81 Q DP problem: 543.64/241.81 The TRS P consists of the following rules: 543.64/241.81 543.64/241.81 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.81 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.81 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.81 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.81 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.81 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.81 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.81 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.81 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.81 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.81 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.81 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.81 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.81 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.81 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) 543.64/241.81 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.81 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.81 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.81 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.81 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.81 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.81 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.81 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.81 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.81 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.81 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.81 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.81 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.81 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.81 543.64/241.81 The TRS R consists of the following rules: 543.64/241.81 543.64/241.81 down(a) -> up(f(a)) 543.64/241.81 down(b) -> up(g(b)) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.81 down(f(a)) -> f_flat(down(a)) 543.64/241.81 down(f(b)) -> f_flat(down(b)) 543.64/241.81 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.81 down(f(c)) -> f_flat(down(c)) 543.64/241.81 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.81 down(g(a)) -> g_flat(down(a)) 543.64/241.81 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.81 down(g(b)) -> g_flat(down(b)) 543.64/241.81 down(g(c)) -> g_flat(down(c)) 543.64/241.81 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.81 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.81 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.81 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.81 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.81 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.81 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.81 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.81 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.81 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.81 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.81 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.81 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.81 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.81 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.81 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.81 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.81 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.81 543.64/241.81 The set Q consists of the following terms: 543.64/241.81 543.64/241.81 down(a) 543.64/241.81 down(b) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.81 down(f(a)) 543.64/241.81 down(f(b)) 543.64/241.81 down(f(g(x0))) 543.64/241.81 down(f(c)) 543.64/241.81 down(f(fresh_constant)) 543.64/241.81 down(g(a)) 543.64/241.81 down(g(f(x0))) 543.64/241.81 down(g(b)) 543.64/241.81 down(g(c)) 543.64/241.81 down(g(fresh_constant)) 543.64/241.81 down(f(f(a))) 543.64/241.81 down(f(f(b))) 543.64/241.81 down(f(f(g(x0)))) 543.64/241.81 down(f(f(c))) 543.64/241.81 down(f(f(fresh_constant))) 543.64/241.81 down(g(g(a))) 543.64/241.81 down(g(g(f(x0)))) 543.64/241.81 down(g(g(b))) 543.64/241.81 down(g(g(c))) 543.64/241.81 down(g(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) 543.64/241.81 down(f(f(f(g(x0))))) 543.64/241.81 down(f(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) 543.64/241.81 down(g(g(g(f(x0))))) 543.64/241.81 down(g(g(g(b)))) 543.64/241.81 down(g(g(g(c)))) 543.64/241.81 down(g(g(g(fresh_constant)))) 543.64/241.81 down(f(f(f(f(a))))) 543.64/241.81 down(f(f(f(f(b))))) 543.64/241.81 down(f(f(f(f(g(x0)))))) 543.64/241.81 down(f(f(f(f(c))))) 543.64/241.81 down(f(f(f(f(fresh_constant))))) 543.64/241.81 down(g(g(g(g(a))))) 543.64/241.81 down(g(g(g(g(f(x0)))))) 543.64/241.81 down(g(g(g(g(b))))) 543.64/241.81 down(g(g(g(g(c))))) 543.64/241.81 down(g(g(g(g(fresh_constant))))) 543.64/241.81 down(f(f(f(f(f(a)))))) 543.64/241.81 down(f(f(f(f(f(b)))))) 543.64/241.81 down(f(f(f(f(f(g(x0))))))) 543.64/241.81 down(f(f(f(f(f(c)))))) 543.64/241.81 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.81 down(g(g(g(g(g(a)))))) 543.64/241.81 down(g(g(g(g(g(f(x0))))))) 543.64/241.81 down(g(g(g(g(g(b)))))) 543.64/241.81 down(g(g(g(g(g(c)))))) 543.64/241.81 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.81 down(f(f(f(f(f(f(a))))))) 543.64/241.81 down(f(f(f(f(f(f(b))))))) 543.64/241.81 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.81 down(f(f(f(f(f(f(c))))))) 543.64/241.81 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.81 down(g(g(g(g(g(g(a))))))) 543.64/241.81 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.81 down(g(g(g(g(g(g(b))))))) 543.64/241.81 down(g(g(g(g(g(g(c))))))) 543.64/241.81 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.81 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.81 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 f_flat(up(x0)) 543.64/241.81 g_flat(up(x0)) 543.64/241.81 543.64/241.81 We have to consider all minimal (P,Q,R)-chains. 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (591) TransformationProof (EQUIVALENT) 543.64/241.81 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(b))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.81 543.64/241.81 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.64/241.81 543.64/241.81 543.64/241.81 ---------------------------------------- 543.64/241.81 543.64/241.81 (592) 543.64/241.81 Obligation: 543.64/241.81 Q DP problem: 543.64/241.81 The TRS P consists of the following rules: 543.64/241.81 543.64/241.81 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.81 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.81 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.81 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.81 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.81 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.81 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.81 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.81 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.81 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.81 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.81 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.81 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.81 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.81 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) 543.64/241.81 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.81 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.81 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.81 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.81 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.81 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.81 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.81 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.81 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.81 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.81 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.81 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.81 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.81 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.81 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.81 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.81 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.64/241.81 543.64/241.81 The TRS R consists of the following rules: 543.64/241.81 543.64/241.81 down(a) -> up(f(a)) 543.64/241.81 down(b) -> up(g(b)) 543.64/241.81 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.81 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.81 down(f(a)) -> f_flat(down(a)) 543.64/241.81 down(f(b)) -> f_flat(down(b)) 543.64/241.81 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.81 down(f(c)) -> f_flat(down(c)) 543.64/241.81 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.81 down(g(a)) -> g_flat(down(a)) 543.64/241.81 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.81 down(g(b)) -> g_flat(down(b)) 543.64/241.81 down(g(c)) -> g_flat(down(c)) 543.64/241.81 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.81 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.81 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.81 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.81 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.81 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.81 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.81 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.81 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.81 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.81 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.81 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.81 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.81 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.81 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.81 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.81 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.82 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.82 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.82 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.82 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.82 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.82 543.64/241.82 The set Q consists of the following terms: 543.64/241.82 543.64/241.82 down(a) 543.64/241.82 down(b) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.82 down(f(a)) 543.64/241.82 down(f(b)) 543.64/241.82 down(f(g(x0))) 543.64/241.82 down(f(c)) 543.64/241.82 down(f(fresh_constant)) 543.64/241.82 down(g(a)) 543.64/241.82 down(g(f(x0))) 543.64/241.82 down(g(b)) 543.64/241.82 down(g(c)) 543.64/241.82 down(g(fresh_constant)) 543.64/241.82 down(f(f(a))) 543.64/241.82 down(f(f(b))) 543.64/241.82 down(f(f(g(x0)))) 543.64/241.82 down(f(f(c))) 543.64/241.82 down(f(f(fresh_constant))) 543.64/241.82 down(g(g(a))) 543.64/241.82 down(g(g(f(x0)))) 543.64/241.82 down(g(g(b))) 543.64/241.82 down(g(g(c))) 543.64/241.82 down(g(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) 543.64/241.82 down(f(f(f(g(x0))))) 543.64/241.82 down(f(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) 543.64/241.82 down(g(g(g(f(x0))))) 543.64/241.82 down(g(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(x0)))))) 543.64/241.82 down(f(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(x0)))))) 543.64/241.82 down(g(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(x0))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(x0))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 f_flat(up(x0)) 543.64/241.82 g_flat(up(x0)) 543.64/241.82 543.64/241.82 We have to consider all minimal (P,Q,R)-chains. 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (593) TransformationProof (EQUIVALENT) 543.64/241.82 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.82 543.64/241.82 (TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))),TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.64/241.82 543.64/241.82 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (594) 543.64/241.82 Obligation: 543.64/241.82 Q DP problem: 543.64/241.82 The TRS P consists of the following rules: 543.64/241.82 543.64/241.82 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.82 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.82 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.82 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.82 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.82 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.82 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.82 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.82 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.82 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.82 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.82 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.82 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.82 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.82 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) 543.64/241.82 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.82 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.82 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.82 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.82 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.82 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.82 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.82 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.82 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.82 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.82 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.82 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.64/241.82 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.64/241.82 543.64/241.82 The TRS R consists of the following rules: 543.64/241.82 543.64/241.82 down(a) -> up(f(a)) 543.64/241.82 down(b) -> up(g(b)) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.82 down(f(a)) -> f_flat(down(a)) 543.64/241.82 down(f(b)) -> f_flat(down(b)) 543.64/241.82 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.82 down(f(c)) -> f_flat(down(c)) 543.64/241.82 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.82 down(g(a)) -> g_flat(down(a)) 543.64/241.82 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.82 down(g(b)) -> g_flat(down(b)) 543.64/241.82 down(g(c)) -> g_flat(down(c)) 543.64/241.82 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.82 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.82 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.82 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.82 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.82 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.82 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.82 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.82 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.82 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.82 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.82 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.82 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.82 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.82 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.82 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.82 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.82 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.82 543.64/241.82 The set Q consists of the following terms: 543.64/241.82 543.64/241.82 down(a) 543.64/241.82 down(b) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.82 down(f(a)) 543.64/241.82 down(f(b)) 543.64/241.82 down(f(g(x0))) 543.64/241.82 down(f(c)) 543.64/241.82 down(f(fresh_constant)) 543.64/241.82 down(g(a)) 543.64/241.82 down(g(f(x0))) 543.64/241.82 down(g(b)) 543.64/241.82 down(g(c)) 543.64/241.82 down(g(fresh_constant)) 543.64/241.82 down(f(f(a))) 543.64/241.82 down(f(f(b))) 543.64/241.82 down(f(f(g(x0)))) 543.64/241.82 down(f(f(c))) 543.64/241.82 down(f(f(fresh_constant))) 543.64/241.82 down(g(g(a))) 543.64/241.82 down(g(g(f(x0)))) 543.64/241.82 down(g(g(b))) 543.64/241.82 down(g(g(c))) 543.64/241.82 down(g(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) 543.64/241.82 down(f(f(f(g(x0))))) 543.64/241.82 down(f(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) 543.64/241.82 down(g(g(g(f(x0))))) 543.64/241.82 down(g(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(x0)))))) 543.64/241.82 down(f(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(x0)))))) 543.64/241.82 down(g(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(x0))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(x0))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 f_flat(up(x0)) 543.64/241.82 g_flat(up(x0)) 543.64/241.82 543.64/241.82 We have to consider all minimal (P,Q,R)-chains. 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (595) TransformationProof (EQUIVALENT) 543.64/241.82 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(b)))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.82 543.64/241.82 (TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(b))))))),TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))) 543.64/241.82 543.64/241.82 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (596) 543.64/241.82 Obligation: 543.64/241.82 Q DP problem: 543.64/241.82 The TRS P consists of the following rules: 543.64/241.82 543.64/241.82 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.82 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.82 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.82 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.82 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.82 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.82 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.82 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.82 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.82 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.82 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.82 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.82 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.82 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.82 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.82 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.82 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) 543.64/241.82 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.82 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.82 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.82 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.82 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.82 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.82 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.82 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.82 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.64/241.82 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.64/241.82 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(b))))))) 543.64/241.82 543.64/241.82 The TRS R consists of the following rules: 543.64/241.82 543.64/241.82 down(a) -> up(f(a)) 543.64/241.82 down(b) -> up(g(b)) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.82 down(f(a)) -> f_flat(down(a)) 543.64/241.82 down(f(b)) -> f_flat(down(b)) 543.64/241.82 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.82 down(f(c)) -> f_flat(down(c)) 543.64/241.82 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.82 down(g(a)) -> g_flat(down(a)) 543.64/241.82 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.82 down(g(b)) -> g_flat(down(b)) 543.64/241.82 down(g(c)) -> g_flat(down(c)) 543.64/241.82 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.82 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.82 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.82 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.82 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.82 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.82 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.82 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.82 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.82 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.82 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.82 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.82 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.82 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.82 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.82 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.82 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.82 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.82 543.64/241.82 The set Q consists of the following terms: 543.64/241.82 543.64/241.82 down(a) 543.64/241.82 down(b) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.82 down(f(a)) 543.64/241.82 down(f(b)) 543.64/241.82 down(f(g(x0))) 543.64/241.82 down(f(c)) 543.64/241.82 down(f(fresh_constant)) 543.64/241.82 down(g(a)) 543.64/241.82 down(g(f(x0))) 543.64/241.82 down(g(b)) 543.64/241.82 down(g(c)) 543.64/241.82 down(g(fresh_constant)) 543.64/241.82 down(f(f(a))) 543.64/241.82 down(f(f(b))) 543.64/241.82 down(f(f(g(x0)))) 543.64/241.82 down(f(f(c))) 543.64/241.82 down(f(f(fresh_constant))) 543.64/241.82 down(g(g(a))) 543.64/241.82 down(g(g(f(x0)))) 543.64/241.82 down(g(g(b))) 543.64/241.82 down(g(g(c))) 543.64/241.82 down(g(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) 543.64/241.82 down(f(f(f(g(x0))))) 543.64/241.82 down(f(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) 543.64/241.82 down(g(g(g(f(x0))))) 543.64/241.82 down(g(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(x0)))))) 543.64/241.82 down(f(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(x0)))))) 543.64/241.82 down(g(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(x0))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(x0))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 f_flat(up(x0)) 543.64/241.82 g_flat(up(x0)) 543.64/241.82 543.64/241.82 We have to consider all minimal (P,Q,R)-chains. 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (597) TransformationProof (EQUIVALENT) 543.64/241.82 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(a))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.82 543.64/241.82 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.64/241.82 543.64/241.82 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (598) 543.64/241.82 Obligation: 543.64/241.82 Q DP problem: 543.64/241.82 The TRS P consists of the following rules: 543.64/241.82 543.64/241.82 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.82 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.82 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.82 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.82 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.82 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.82 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.82 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.82 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.82 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.82 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.82 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.82 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.82 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.82 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.82 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.82 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.82 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.82 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.82 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.82 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.82 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.82 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.82 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.82 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.64/241.82 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.64/241.82 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.64/241.82 543.64/241.82 The TRS R consists of the following rules: 543.64/241.82 543.64/241.82 down(a) -> up(f(a)) 543.64/241.82 down(b) -> up(g(b)) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.82 down(f(a)) -> f_flat(down(a)) 543.64/241.82 down(f(b)) -> f_flat(down(b)) 543.64/241.82 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.82 down(f(c)) -> f_flat(down(c)) 543.64/241.82 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.82 down(g(a)) -> g_flat(down(a)) 543.64/241.82 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.82 down(g(b)) -> g_flat(down(b)) 543.64/241.82 down(g(c)) -> g_flat(down(c)) 543.64/241.82 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.82 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.82 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.82 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.82 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.82 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.82 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.82 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.82 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.82 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.82 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.82 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.82 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.82 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.82 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.82 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.82 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.82 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.82 543.64/241.82 The set Q consists of the following terms: 543.64/241.82 543.64/241.82 down(a) 543.64/241.82 down(b) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.82 down(f(a)) 543.64/241.82 down(f(b)) 543.64/241.82 down(f(g(x0))) 543.64/241.82 down(f(c)) 543.64/241.82 down(f(fresh_constant)) 543.64/241.82 down(g(a)) 543.64/241.82 down(g(f(x0))) 543.64/241.82 down(g(b)) 543.64/241.82 down(g(c)) 543.64/241.82 down(g(fresh_constant)) 543.64/241.82 down(f(f(a))) 543.64/241.82 down(f(f(b))) 543.64/241.82 down(f(f(g(x0)))) 543.64/241.82 down(f(f(c))) 543.64/241.82 down(f(f(fresh_constant))) 543.64/241.82 down(g(g(a))) 543.64/241.82 down(g(g(f(x0)))) 543.64/241.82 down(g(g(b))) 543.64/241.82 down(g(g(c))) 543.64/241.82 down(g(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) 543.64/241.82 down(f(f(f(g(x0))))) 543.64/241.82 down(f(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) 543.64/241.82 down(g(g(g(f(x0))))) 543.64/241.82 down(g(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(x0)))))) 543.64/241.82 down(f(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(x0)))))) 543.64/241.82 down(g(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(x0))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(x0))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 f_flat(up(x0)) 543.64/241.82 g_flat(up(x0)) 543.64/241.82 543.64/241.82 We have to consider all minimal (P,Q,R)-chains. 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (599) TransformationProof (EQUIVALENT) 543.64/241.82 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.82 543.64/241.82 (TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))),TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.64/241.82 543.64/241.82 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (600) 543.64/241.82 Obligation: 543.64/241.82 Q DP problem: 543.64/241.82 The TRS P consists of the following rules: 543.64/241.82 543.64/241.82 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.82 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.82 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.82 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.82 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.82 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.82 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.82 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.82 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.82 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.82 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.82 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.82 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.82 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.82 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.82 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.82 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) 543.64/241.82 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.82 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.82 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.82 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.82 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.82 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.82 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.82 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.64/241.82 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.64/241.82 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.64/241.82 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.64/241.82 543.64/241.82 The TRS R consists of the following rules: 543.64/241.82 543.64/241.82 down(a) -> up(f(a)) 543.64/241.82 down(b) -> up(g(b)) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.82 down(f(a)) -> f_flat(down(a)) 543.64/241.82 down(f(b)) -> f_flat(down(b)) 543.64/241.82 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.82 down(f(c)) -> f_flat(down(c)) 543.64/241.82 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.82 down(g(a)) -> g_flat(down(a)) 543.64/241.82 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.82 down(g(b)) -> g_flat(down(b)) 543.64/241.82 down(g(c)) -> g_flat(down(c)) 543.64/241.82 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.82 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.82 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.82 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.82 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.82 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.82 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.82 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.82 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.82 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.82 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.82 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.82 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.82 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.82 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.82 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.82 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.82 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.82 543.64/241.82 The set Q consists of the following terms: 543.64/241.82 543.64/241.82 down(a) 543.64/241.82 down(b) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.82 down(f(a)) 543.64/241.82 down(f(b)) 543.64/241.82 down(f(g(x0))) 543.64/241.82 down(f(c)) 543.64/241.82 down(f(fresh_constant)) 543.64/241.82 down(g(a)) 543.64/241.82 down(g(f(x0))) 543.64/241.82 down(g(b)) 543.64/241.82 down(g(c)) 543.64/241.82 down(g(fresh_constant)) 543.64/241.82 down(f(f(a))) 543.64/241.82 down(f(f(b))) 543.64/241.82 down(f(f(g(x0)))) 543.64/241.82 down(f(f(c))) 543.64/241.82 down(f(f(fresh_constant))) 543.64/241.82 down(g(g(a))) 543.64/241.82 down(g(g(f(x0)))) 543.64/241.82 down(g(g(b))) 543.64/241.82 down(g(g(c))) 543.64/241.82 down(g(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) 543.64/241.82 down(f(f(f(g(x0))))) 543.64/241.82 down(f(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) 543.64/241.82 down(g(g(g(f(x0))))) 543.64/241.82 down(g(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(x0)))))) 543.64/241.82 down(f(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(x0)))))) 543.64/241.82 down(g(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(x0))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(x0))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 f_flat(up(x0)) 543.64/241.82 g_flat(up(x0)) 543.64/241.82 543.64/241.82 We have to consider all minimal (P,Q,R)-chains. 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (601) TransformationProof (EQUIVALENT) 543.64/241.82 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(c))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.82 543.64/241.82 (TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(c))))))),TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(c)))))))) 543.64/241.82 543.64/241.82 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (602) 543.64/241.82 Obligation: 543.64/241.82 Q DP problem: 543.64/241.82 The TRS P consists of the following rules: 543.64/241.82 543.64/241.82 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.82 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.82 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.82 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.82 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.82 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.82 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.82 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.82 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.82 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.82 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.82 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.82 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.82 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.82 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.82 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.82 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.82 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.82 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.82 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.82 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.82 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.82 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.82 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.64/241.82 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.64/241.82 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.64/241.82 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(c))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(c))))))) 543.64/241.82 543.64/241.82 The TRS R consists of the following rules: 543.64/241.82 543.64/241.82 down(a) -> up(f(a)) 543.64/241.82 down(b) -> up(g(b)) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.82 down(f(a)) -> f_flat(down(a)) 543.64/241.82 down(f(b)) -> f_flat(down(b)) 543.64/241.82 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.82 down(f(c)) -> f_flat(down(c)) 543.64/241.82 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.82 down(g(a)) -> g_flat(down(a)) 543.64/241.82 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.82 down(g(b)) -> g_flat(down(b)) 543.64/241.82 down(g(c)) -> g_flat(down(c)) 543.64/241.82 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.82 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.82 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.82 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.82 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.82 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.82 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.82 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.82 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.82 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.82 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.82 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.82 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.82 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.82 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.82 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.82 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.82 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.82 543.64/241.82 The set Q consists of the following terms: 543.64/241.82 543.64/241.82 down(a) 543.64/241.82 down(b) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.82 down(f(a)) 543.64/241.82 down(f(b)) 543.64/241.82 down(f(g(x0))) 543.64/241.82 down(f(c)) 543.64/241.82 down(f(fresh_constant)) 543.64/241.82 down(g(a)) 543.64/241.82 down(g(f(x0))) 543.64/241.82 down(g(b)) 543.64/241.82 down(g(c)) 543.64/241.82 down(g(fresh_constant)) 543.64/241.82 down(f(f(a))) 543.64/241.82 down(f(f(b))) 543.64/241.82 down(f(f(g(x0)))) 543.64/241.82 down(f(f(c))) 543.64/241.82 down(f(f(fresh_constant))) 543.64/241.82 down(g(g(a))) 543.64/241.82 down(g(g(f(x0)))) 543.64/241.82 down(g(g(b))) 543.64/241.82 down(g(g(c))) 543.64/241.82 down(g(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) 543.64/241.82 down(f(f(f(g(x0))))) 543.64/241.82 down(f(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) 543.64/241.82 down(g(g(g(f(x0))))) 543.64/241.82 down(g(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(x0)))))) 543.64/241.82 down(f(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(x0)))))) 543.64/241.82 down(g(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(x0))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(x0))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 f_flat(up(x0)) 543.64/241.82 g_flat(up(x0)) 543.64/241.82 543.64/241.82 We have to consider all minimal (P,Q,R)-chains. 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (603) DependencyGraphProof (EQUIVALENT) 543.64/241.82 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (604) 543.64/241.82 Obligation: 543.64/241.82 Q DP problem: 543.64/241.82 The TRS P consists of the following rules: 543.64/241.82 543.64/241.82 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.82 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.82 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.82 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.82 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.82 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.82 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.82 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) 543.64/241.82 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.82 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.82 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.82 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.82 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.82 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.82 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.82 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.82 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.82 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.82 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.82 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.82 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.82 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.82 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.64/241.82 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.82 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.82 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.82 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.82 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.64/241.82 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.64/241.82 543.64/241.82 The TRS R consists of the following rules: 543.64/241.82 543.64/241.82 down(a) -> up(f(a)) 543.64/241.82 down(b) -> up(g(b)) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.82 down(f(a)) -> f_flat(down(a)) 543.64/241.82 down(f(b)) -> f_flat(down(b)) 543.64/241.82 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.82 down(f(c)) -> f_flat(down(c)) 543.64/241.82 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.82 down(g(a)) -> g_flat(down(a)) 543.64/241.82 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.82 down(g(b)) -> g_flat(down(b)) 543.64/241.82 down(g(c)) -> g_flat(down(c)) 543.64/241.82 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.82 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.82 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.82 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.82 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.82 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.82 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.82 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.82 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.82 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.82 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.82 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.82 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.82 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.82 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.82 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.82 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.82 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.82 543.64/241.82 The set Q consists of the following terms: 543.64/241.82 543.64/241.82 down(a) 543.64/241.82 down(b) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.82 down(f(a)) 543.64/241.82 down(f(b)) 543.64/241.82 down(f(g(x0))) 543.64/241.82 down(f(c)) 543.64/241.82 down(f(fresh_constant)) 543.64/241.82 down(g(a)) 543.64/241.82 down(g(f(x0))) 543.64/241.82 down(g(b)) 543.64/241.82 down(g(c)) 543.64/241.82 down(g(fresh_constant)) 543.64/241.82 down(f(f(a))) 543.64/241.82 down(f(f(b))) 543.64/241.82 down(f(f(g(x0)))) 543.64/241.82 down(f(f(c))) 543.64/241.82 down(f(f(fresh_constant))) 543.64/241.82 down(g(g(a))) 543.64/241.82 down(g(g(f(x0)))) 543.64/241.82 down(g(g(b))) 543.64/241.82 down(g(g(c))) 543.64/241.82 down(g(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) 543.64/241.82 down(f(f(f(g(x0))))) 543.64/241.82 down(f(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) 543.64/241.82 down(g(g(g(f(x0))))) 543.64/241.82 down(g(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(x0)))))) 543.64/241.82 down(f(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(x0)))))) 543.64/241.82 down(g(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(x0))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(x0))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) 543.64/241.82 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.82 down(f(f(f(f(f(f(c))))))) 543.64/241.82 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.82 down(g(g(g(g(g(g(a))))))) 543.64/241.82 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.82 down(g(g(g(g(g(g(b))))))) 543.64/241.82 down(g(g(g(g(g(g(c))))))) 543.64/241.82 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.82 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.82 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 f_flat(up(x0)) 543.64/241.82 g_flat(up(x0)) 543.64/241.82 543.64/241.82 We have to consider all minimal (P,Q,R)-chains. 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (605) TransformationProof (EQUIVALENT) 543.64/241.82 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(a))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.82 543.64/241.82 (TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(a))))))),TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(a)))))))) 543.64/241.82 543.64/241.82 543.64/241.82 ---------------------------------------- 543.64/241.82 543.64/241.82 (606) 543.64/241.82 Obligation: 543.64/241.82 Q DP problem: 543.64/241.82 The TRS P consists of the following rules: 543.64/241.82 543.64/241.82 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.82 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.82 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.82 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.82 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.82 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.82 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.82 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.82 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.82 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.82 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.82 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.82 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(b))))))) 543.64/241.82 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.82 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.82 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.82 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.82 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.82 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.82 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.82 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.82 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.82 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.82 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.82 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.82 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.64/241.82 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.82 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.82 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.82 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.82 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.82 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.64/241.82 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.64/241.82 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(a))))))) 543.64/241.82 543.64/241.82 The TRS R consists of the following rules: 543.64/241.82 543.64/241.82 down(a) -> up(f(a)) 543.64/241.82 down(b) -> up(g(b)) 543.64/241.82 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.82 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.82 down(f(a)) -> f_flat(down(a)) 543.64/241.82 down(f(b)) -> f_flat(down(b)) 543.64/241.82 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.82 down(f(c)) -> f_flat(down(c)) 543.64/241.82 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.82 down(g(a)) -> g_flat(down(a)) 543.64/241.82 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.82 down(g(b)) -> g_flat(down(b)) 543.64/241.82 down(g(c)) -> g_flat(down(c)) 543.64/241.82 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.82 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.82 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.82 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.82 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.82 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.82 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.82 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.82 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.82 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.82 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.82 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.82 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.82 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.82 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.82 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.82 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.82 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.82 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.82 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.82 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.82 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.82 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.82 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.82 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.82 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.82 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.82 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.82 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.82 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.82 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.82 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.82 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.82 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.82 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.82 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.82 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.82 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.82 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.82 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.82 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.82 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.82 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.83 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.83 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.83 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.83 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.83 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.83 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.83 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.83 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.83 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.83 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.83 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.83 543.64/241.83 The set Q consists of the following terms: 543.64/241.83 543.64/241.83 down(a) 543.64/241.83 down(b) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.83 down(f(a)) 543.64/241.83 down(f(b)) 543.64/241.83 down(f(g(x0))) 543.64/241.83 down(f(c)) 543.64/241.83 down(f(fresh_constant)) 543.64/241.83 down(g(a)) 543.64/241.83 down(g(f(x0))) 543.64/241.83 down(g(b)) 543.64/241.83 down(g(c)) 543.64/241.83 down(g(fresh_constant)) 543.64/241.83 down(f(f(a))) 543.64/241.83 down(f(f(b))) 543.64/241.83 down(f(f(g(x0)))) 543.64/241.83 down(f(f(c))) 543.64/241.83 down(f(f(fresh_constant))) 543.64/241.83 down(g(g(a))) 543.64/241.83 down(g(g(f(x0)))) 543.64/241.83 down(g(g(b))) 543.64/241.83 down(g(g(c))) 543.64/241.83 down(g(g(fresh_constant))) 543.64/241.83 down(f(f(f(a)))) 543.64/241.83 down(f(f(f(b)))) 543.64/241.83 down(f(f(f(g(x0))))) 543.64/241.83 down(f(f(f(c)))) 543.64/241.83 down(f(f(f(fresh_constant)))) 543.64/241.83 down(g(g(g(a)))) 543.64/241.83 down(g(g(g(f(x0))))) 543.64/241.83 down(g(g(g(b)))) 543.64/241.83 down(g(g(g(c)))) 543.64/241.83 down(g(g(g(fresh_constant)))) 543.64/241.83 down(f(f(f(f(a))))) 543.64/241.83 down(f(f(f(f(b))))) 543.64/241.83 down(f(f(f(f(g(x0)))))) 543.64/241.83 down(f(f(f(f(c))))) 543.64/241.83 down(f(f(f(f(fresh_constant))))) 543.64/241.83 down(g(g(g(g(a))))) 543.64/241.83 down(g(g(g(g(f(x0)))))) 543.64/241.83 down(g(g(g(g(b))))) 543.64/241.83 down(g(g(g(g(c))))) 543.64/241.83 down(g(g(g(g(fresh_constant))))) 543.64/241.83 down(f(f(f(f(f(a)))))) 543.64/241.83 down(f(f(f(f(f(b)))))) 543.64/241.83 down(f(f(f(f(f(g(x0))))))) 543.64/241.83 down(f(f(f(f(f(c)))))) 543.64/241.83 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.83 down(g(g(g(g(g(a)))))) 543.64/241.83 down(g(g(g(g(g(f(x0))))))) 543.64/241.83 down(g(g(g(g(g(b)))))) 543.64/241.83 down(g(g(g(g(g(c)))))) 543.64/241.83 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.83 down(f(f(f(f(f(f(a))))))) 543.64/241.83 down(f(f(f(f(f(f(b))))))) 543.64/241.83 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.83 down(f(f(f(f(f(f(c))))))) 543.64/241.83 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.83 down(g(g(g(g(g(g(a))))))) 543.64/241.83 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.83 down(g(g(g(g(g(g(b))))))) 543.64/241.83 down(g(g(g(g(g(g(c))))))) 543.64/241.83 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.83 down(f(f(f(f(f(f(f(a)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(b)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(g(x0))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(c)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(a)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(f(x0))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(b)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(c)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(a))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(b))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(c))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(a))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(b))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(c))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.83 f_flat(up(x0)) 543.64/241.83 g_flat(up(x0)) 543.64/241.83 543.64/241.83 We have to consider all minimal (P,Q,R)-chains. 543.64/241.83 ---------------------------------------- 543.64/241.83 543.64/241.83 (607) TransformationProof (EQUIVALENT) 543.64/241.83 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(b))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.64/241.83 543.64/241.83 (TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(b))))))),TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(b)))))))) 543.64/241.83 543.64/241.83 543.64/241.83 ---------------------------------------- 543.64/241.83 543.64/241.83 (608) 543.64/241.83 Obligation: 543.64/241.83 Q DP problem: 543.64/241.83 The TRS P consists of the following rules: 543.64/241.83 543.64/241.83 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.64/241.83 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.64/241.83 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.64/241.83 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.64/241.83 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.64/241.83 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.64/241.83 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.64/241.83 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.64/241.83 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.64/241.83 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.64/241.83 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.64/241.83 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.64/241.83 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.64/241.83 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.64/241.83 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.64/241.83 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.64/241.83 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.64/241.83 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.64/241.83 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.64/241.83 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.64/241.83 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.64/241.83 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.64/241.83 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.64/241.83 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.64/241.83 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.64/241.83 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.64/241.83 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.64/241.83 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.64/241.83 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.64/241.83 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.64/241.83 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.64/241.83 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.64/241.83 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(a))))))) 543.64/241.83 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(b))))))) 543.64/241.83 543.64/241.83 The TRS R consists of the following rules: 543.64/241.83 543.64/241.83 down(a) -> up(f(a)) 543.64/241.83 down(b) -> up(g(b)) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.64/241.83 down(f(a)) -> f_flat(down(a)) 543.64/241.83 down(f(b)) -> f_flat(down(b)) 543.64/241.83 down(f(g(y4))) -> f_flat(down(g(y4))) 543.64/241.83 down(f(c)) -> f_flat(down(c)) 543.64/241.83 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.64/241.83 down(g(a)) -> g_flat(down(a)) 543.64/241.83 down(g(f(y6))) -> g_flat(down(f(y6))) 543.64/241.83 down(g(b)) -> g_flat(down(b)) 543.64/241.83 down(g(c)) -> g_flat(down(c)) 543.64/241.83 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.64/241.83 down(f(f(a))) -> f_flat(down(f(a))) 543.64/241.83 down(f(f(b))) -> f_flat(down(f(b))) 543.64/241.83 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.64/241.83 down(f(f(c))) -> f_flat(down(f(c))) 543.64/241.83 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.64/241.83 down(g(g(a))) -> g_flat(down(g(a))) 543.64/241.83 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.64/241.83 down(g(g(b))) -> g_flat(down(g(b))) 543.64/241.83 down(g(g(c))) -> g_flat(down(g(c))) 543.64/241.83 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.64/241.83 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.64/241.83 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.64/241.83 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.64/241.83 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.64/241.83 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.64/241.83 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.64/241.83 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.64/241.83 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.64/241.83 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.64/241.83 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.64/241.83 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.64/241.83 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.64/241.83 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.64/241.83 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.64/241.83 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.64/241.83 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.64/241.83 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.64/241.83 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.64/241.83 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.64/241.83 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.64/241.83 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.64/241.83 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.64/241.83 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.64/241.83 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.64/241.83 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.64/241.83 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.64/241.83 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.64/241.83 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.64/241.83 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.64/241.83 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.64/241.83 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.64/241.83 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.64/241.83 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.64/241.83 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.64/241.83 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.64/241.83 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.64/241.83 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.64/241.83 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.64/241.83 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.64/241.83 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.64/241.83 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.64/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.64/241.83 g_flat(up(x_1)) -> up(g(x_1)) 543.64/241.83 f_flat(up(x_1)) -> up(f(x_1)) 543.64/241.83 543.64/241.83 The set Q consists of the following terms: 543.64/241.83 543.64/241.83 down(a) 543.64/241.83 down(b) 543.64/241.83 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.64/241.83 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.64/241.83 down(f(a)) 543.64/241.83 down(f(b)) 543.64/241.83 down(f(g(x0))) 543.64/241.83 down(f(c)) 543.64/241.83 down(f(fresh_constant)) 543.64/241.83 down(g(a)) 543.64/241.83 down(g(f(x0))) 543.64/241.83 down(g(b)) 543.64/241.83 down(g(c)) 543.64/241.83 down(g(fresh_constant)) 543.64/241.83 down(f(f(a))) 543.64/241.83 down(f(f(b))) 543.64/241.83 down(f(f(g(x0)))) 543.64/241.83 down(f(f(c))) 543.64/241.83 down(f(f(fresh_constant))) 543.64/241.83 down(g(g(a))) 543.64/241.83 down(g(g(f(x0)))) 543.64/241.83 down(g(g(b))) 543.64/241.83 down(g(g(c))) 543.64/241.83 down(g(g(fresh_constant))) 543.64/241.83 down(f(f(f(a)))) 543.64/241.83 down(f(f(f(b)))) 543.64/241.83 down(f(f(f(g(x0))))) 543.64/241.83 down(f(f(f(c)))) 543.64/241.83 down(f(f(f(fresh_constant)))) 543.64/241.83 down(g(g(g(a)))) 543.64/241.83 down(g(g(g(f(x0))))) 543.64/241.83 down(g(g(g(b)))) 543.64/241.83 down(g(g(g(c)))) 543.64/241.83 down(g(g(g(fresh_constant)))) 543.64/241.83 down(f(f(f(f(a))))) 543.64/241.83 down(f(f(f(f(b))))) 543.64/241.83 down(f(f(f(f(g(x0)))))) 543.64/241.83 down(f(f(f(f(c))))) 543.64/241.83 down(f(f(f(f(fresh_constant))))) 543.64/241.83 down(g(g(g(g(a))))) 543.64/241.83 down(g(g(g(g(f(x0)))))) 543.64/241.83 down(g(g(g(g(b))))) 543.64/241.83 down(g(g(g(g(c))))) 543.64/241.83 down(g(g(g(g(fresh_constant))))) 543.64/241.83 down(f(f(f(f(f(a)))))) 543.64/241.83 down(f(f(f(f(f(b)))))) 543.64/241.83 down(f(f(f(f(f(g(x0))))))) 543.64/241.83 down(f(f(f(f(f(c)))))) 543.64/241.83 down(f(f(f(f(f(fresh_constant)))))) 543.64/241.83 down(g(g(g(g(g(a)))))) 543.64/241.83 down(g(g(g(g(g(f(x0))))))) 543.64/241.83 down(g(g(g(g(g(b)))))) 543.64/241.83 down(g(g(g(g(g(c)))))) 543.64/241.83 down(g(g(g(g(g(fresh_constant)))))) 543.64/241.83 down(f(f(f(f(f(f(a))))))) 543.64/241.83 down(f(f(f(f(f(f(b))))))) 543.64/241.83 down(f(f(f(f(f(f(g(x0)))))))) 543.64/241.83 down(f(f(f(f(f(f(c))))))) 543.64/241.83 down(f(f(f(f(f(f(fresh_constant))))))) 543.64/241.83 down(g(g(g(g(g(g(a))))))) 543.64/241.83 down(g(g(g(g(g(g(f(x0)))))))) 543.64/241.83 down(g(g(g(g(g(g(b))))))) 543.64/241.83 down(g(g(g(g(g(g(c))))))) 543.64/241.83 down(g(g(g(g(g(g(fresh_constant))))))) 543.64/241.83 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 f_flat(up(x0)) 543.68/241.83 g_flat(up(x0)) 543.68/241.83 543.68/241.83 We have to consider all minimal (P,Q,R)-chains. 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (609) TransformationProof (EQUIVALENT) 543.68/241.83 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.68/241.83 543.68/241.83 (TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant))))))),TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant)))))))) 543.68/241.83 543.68/241.83 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (610) 543.68/241.83 Obligation: 543.68/241.83 Q DP problem: 543.68/241.83 The TRS P consists of the following rules: 543.68/241.83 543.68/241.83 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.83 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.83 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.83 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.83 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.83 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.83 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.83 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.83 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.83 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.83 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.83 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.83 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.83 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.83 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.83 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.68/241.83 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.68/241.83 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.83 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.83 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.83 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.83 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.83 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.83 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.83 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.83 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(fresh_constant))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant))))))) 543.68/241.83 543.68/241.83 The TRS R consists of the following rules: 543.68/241.83 543.68/241.83 down(a) -> up(f(a)) 543.68/241.83 down(b) -> up(g(b)) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.83 down(f(a)) -> f_flat(down(a)) 543.68/241.83 down(f(b)) -> f_flat(down(b)) 543.68/241.83 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.83 down(f(c)) -> f_flat(down(c)) 543.68/241.83 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.83 down(g(a)) -> g_flat(down(a)) 543.68/241.83 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.83 down(g(b)) -> g_flat(down(b)) 543.68/241.83 down(g(c)) -> g_flat(down(c)) 543.68/241.83 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.83 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.83 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.83 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.83 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.83 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.83 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.83 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.83 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.83 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.83 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.83 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.83 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.83 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.83 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.83 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.83 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.83 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.83 543.68/241.83 The set Q consists of the following terms: 543.68/241.83 543.68/241.83 down(a) 543.68/241.83 down(b) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.83 down(f(a)) 543.68/241.83 down(f(b)) 543.68/241.83 down(f(g(x0))) 543.68/241.83 down(f(c)) 543.68/241.83 down(f(fresh_constant)) 543.68/241.83 down(g(a)) 543.68/241.83 down(g(f(x0))) 543.68/241.83 down(g(b)) 543.68/241.83 down(g(c)) 543.68/241.83 down(g(fresh_constant)) 543.68/241.83 down(f(f(a))) 543.68/241.83 down(f(f(b))) 543.68/241.83 down(f(f(g(x0)))) 543.68/241.83 down(f(f(c))) 543.68/241.83 down(f(f(fresh_constant))) 543.68/241.83 down(g(g(a))) 543.68/241.83 down(g(g(f(x0)))) 543.68/241.83 down(g(g(b))) 543.68/241.83 down(g(g(c))) 543.68/241.83 down(g(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) 543.68/241.83 down(f(f(f(g(x0))))) 543.68/241.83 down(f(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) 543.68/241.83 down(g(g(g(f(x0))))) 543.68/241.83 down(g(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(x0)))))) 543.68/241.83 down(f(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(x0)))))) 543.68/241.83 down(g(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(x0))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(x0))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 f_flat(up(x0)) 543.68/241.83 g_flat(up(x0)) 543.68/241.83 543.68/241.83 We have to consider all minimal (P,Q,R)-chains. 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (611) DependencyGraphProof (EQUIVALENT) 543.68/241.83 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (612) 543.68/241.83 Obligation: 543.68/241.83 Q DP problem: 543.68/241.83 The TRS P consists of the following rules: 543.68/241.83 543.68/241.83 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.83 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.83 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.83 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.83 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.83 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.83 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.83 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(a))))))) 543.68/241.83 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.83 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.83 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.83 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.83 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.83 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(b))))))) 543.68/241.83 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.83 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.83 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.83 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.68/241.83 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.68/241.83 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.83 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.83 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.83 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.83 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.83 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.83 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.83 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.83 543.68/241.83 The TRS R consists of the following rules: 543.68/241.83 543.68/241.83 down(a) -> up(f(a)) 543.68/241.83 down(b) -> up(g(b)) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.83 down(f(a)) -> f_flat(down(a)) 543.68/241.83 down(f(b)) -> f_flat(down(b)) 543.68/241.83 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.83 down(f(c)) -> f_flat(down(c)) 543.68/241.83 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.83 down(g(a)) -> g_flat(down(a)) 543.68/241.83 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.83 down(g(b)) -> g_flat(down(b)) 543.68/241.83 down(g(c)) -> g_flat(down(c)) 543.68/241.83 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.83 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.83 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.83 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.83 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.83 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.83 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.83 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.83 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.83 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.83 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.83 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.83 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.83 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.83 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.83 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.83 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.83 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.83 543.68/241.83 The set Q consists of the following terms: 543.68/241.83 543.68/241.83 down(a) 543.68/241.83 down(b) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.83 down(f(a)) 543.68/241.83 down(f(b)) 543.68/241.83 down(f(g(x0))) 543.68/241.83 down(f(c)) 543.68/241.83 down(f(fresh_constant)) 543.68/241.83 down(g(a)) 543.68/241.83 down(g(f(x0))) 543.68/241.83 down(g(b)) 543.68/241.83 down(g(c)) 543.68/241.83 down(g(fresh_constant)) 543.68/241.83 down(f(f(a))) 543.68/241.83 down(f(f(b))) 543.68/241.83 down(f(f(g(x0)))) 543.68/241.83 down(f(f(c))) 543.68/241.83 down(f(f(fresh_constant))) 543.68/241.83 down(g(g(a))) 543.68/241.83 down(g(g(f(x0)))) 543.68/241.83 down(g(g(b))) 543.68/241.83 down(g(g(c))) 543.68/241.83 down(g(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) 543.68/241.83 down(f(f(f(g(x0))))) 543.68/241.83 down(f(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) 543.68/241.83 down(g(g(g(f(x0))))) 543.68/241.83 down(g(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(x0)))))) 543.68/241.83 down(f(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(x0)))))) 543.68/241.83 down(g(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(x0))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(x0))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 f_flat(up(x0)) 543.68/241.83 g_flat(up(x0)) 543.68/241.83 543.68/241.83 We have to consider all minimal (P,Q,R)-chains. 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (613) TransformationProof (EQUIVALENT) 543.68/241.83 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(a))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.68/241.83 543.68/241.83 (TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))),TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a)))))))) 543.68/241.83 543.68/241.83 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (614) 543.68/241.83 Obligation: 543.68/241.83 Q DP problem: 543.68/241.83 The TRS P consists of the following rules: 543.68/241.83 543.68/241.83 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.83 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.83 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.83 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.83 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.83 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.83 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.83 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.83 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.83 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.83 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.83 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.83 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(b))))))) 543.68/241.83 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.83 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.83 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.83 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.68/241.83 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.68/241.83 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.83 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.83 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.83 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.83 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.83 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.83 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.83 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.83 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))) 543.68/241.83 543.68/241.83 The TRS R consists of the following rules: 543.68/241.83 543.68/241.83 down(a) -> up(f(a)) 543.68/241.83 down(b) -> up(g(b)) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.83 down(f(a)) -> f_flat(down(a)) 543.68/241.83 down(f(b)) -> f_flat(down(b)) 543.68/241.83 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.83 down(f(c)) -> f_flat(down(c)) 543.68/241.83 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.83 down(g(a)) -> g_flat(down(a)) 543.68/241.83 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.83 down(g(b)) -> g_flat(down(b)) 543.68/241.83 down(g(c)) -> g_flat(down(c)) 543.68/241.83 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.83 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.83 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.83 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.83 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.83 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.83 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.83 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.83 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.83 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.83 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.83 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.83 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.83 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.83 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.83 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.83 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.83 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.83 543.68/241.83 The set Q consists of the following terms: 543.68/241.83 543.68/241.83 down(a) 543.68/241.83 down(b) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.83 down(f(a)) 543.68/241.83 down(f(b)) 543.68/241.83 down(f(g(x0))) 543.68/241.83 down(f(c)) 543.68/241.83 down(f(fresh_constant)) 543.68/241.83 down(g(a)) 543.68/241.83 down(g(f(x0))) 543.68/241.83 down(g(b)) 543.68/241.83 down(g(c)) 543.68/241.83 down(g(fresh_constant)) 543.68/241.83 down(f(f(a))) 543.68/241.83 down(f(f(b))) 543.68/241.83 down(f(f(g(x0)))) 543.68/241.83 down(f(f(c))) 543.68/241.83 down(f(f(fresh_constant))) 543.68/241.83 down(g(g(a))) 543.68/241.83 down(g(g(f(x0)))) 543.68/241.83 down(g(g(b))) 543.68/241.83 down(g(g(c))) 543.68/241.83 down(g(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) 543.68/241.83 down(f(f(f(g(x0))))) 543.68/241.83 down(f(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) 543.68/241.83 down(g(g(g(f(x0))))) 543.68/241.83 down(g(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(x0)))))) 543.68/241.83 down(f(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(x0)))))) 543.68/241.83 down(g(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(x0))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(x0))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 f_flat(up(x0)) 543.68/241.83 g_flat(up(x0)) 543.68/241.83 543.68/241.83 We have to consider all minimal (P,Q,R)-chains. 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (615) TransformationProof (EQUIVALENT) 543.68/241.83 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(b))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.68/241.83 543.68/241.83 (TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))),TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b)))))))) 543.68/241.83 543.68/241.83 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (616) 543.68/241.83 Obligation: 543.68/241.83 Q DP problem: 543.68/241.83 The TRS P consists of the following rules: 543.68/241.83 543.68/241.83 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.83 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.83 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.83 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.83 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.83 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.83 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.83 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.83 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.83 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.83 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.83 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.83 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.83 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.83 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.83 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.68/241.83 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.68/241.83 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.83 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.83 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.83 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.83 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.83 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.83 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.83 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.83 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))) 543.68/241.83 543.68/241.83 The TRS R consists of the following rules: 543.68/241.83 543.68/241.83 down(a) -> up(f(a)) 543.68/241.83 down(b) -> up(g(b)) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.83 down(f(a)) -> f_flat(down(a)) 543.68/241.83 down(f(b)) -> f_flat(down(b)) 543.68/241.83 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.83 down(f(c)) -> f_flat(down(c)) 543.68/241.83 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.83 down(g(a)) -> g_flat(down(a)) 543.68/241.83 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.83 down(g(b)) -> g_flat(down(b)) 543.68/241.83 down(g(c)) -> g_flat(down(c)) 543.68/241.83 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.83 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.83 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.83 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.83 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.83 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.83 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.83 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.83 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.83 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.83 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.83 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.83 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.83 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.83 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.83 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.83 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.83 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.83 543.68/241.83 The set Q consists of the following terms: 543.68/241.83 543.68/241.83 down(a) 543.68/241.83 down(b) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.83 down(f(a)) 543.68/241.83 down(f(b)) 543.68/241.83 down(f(g(x0))) 543.68/241.83 down(f(c)) 543.68/241.83 down(f(fresh_constant)) 543.68/241.83 down(g(a)) 543.68/241.83 down(g(f(x0))) 543.68/241.83 down(g(b)) 543.68/241.83 down(g(c)) 543.68/241.83 down(g(fresh_constant)) 543.68/241.83 down(f(f(a))) 543.68/241.83 down(f(f(b))) 543.68/241.83 down(f(f(g(x0)))) 543.68/241.83 down(f(f(c))) 543.68/241.83 down(f(f(fresh_constant))) 543.68/241.83 down(g(g(a))) 543.68/241.83 down(g(g(f(x0)))) 543.68/241.83 down(g(g(b))) 543.68/241.83 down(g(g(c))) 543.68/241.83 down(g(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) 543.68/241.83 down(f(f(f(g(x0))))) 543.68/241.83 down(f(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) 543.68/241.83 down(g(g(g(f(x0))))) 543.68/241.83 down(g(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(x0)))))) 543.68/241.83 down(f(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(x0)))))) 543.68/241.83 down(g(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(x0))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(x0))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 f_flat(up(x0)) 543.68/241.83 g_flat(up(x0)) 543.68/241.83 543.68/241.83 We have to consider all minimal (P,Q,R)-chains. 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (617) TransformationProof (EQUIVALENT) 543.68/241.83 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.68/241.83 543.68/241.83 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.68/241.83 543.68/241.83 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (618) 543.68/241.83 Obligation: 543.68/241.83 Q DP problem: 543.68/241.83 The TRS P consists of the following rules: 543.68/241.83 543.68/241.83 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.83 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.83 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.83 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.83 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.83 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.83 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.83 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.83 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.83 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.83 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.83 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.83 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.83 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.83 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.83 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.68/241.83 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.68/241.83 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.83 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.83 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.83 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.83 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.83 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.83 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.83 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.83 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.68/241.83 543.68/241.83 The TRS R consists of the following rules: 543.68/241.83 543.68/241.83 down(a) -> up(f(a)) 543.68/241.83 down(b) -> up(g(b)) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.83 down(f(a)) -> f_flat(down(a)) 543.68/241.83 down(f(b)) -> f_flat(down(b)) 543.68/241.83 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.83 down(f(c)) -> f_flat(down(c)) 543.68/241.83 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.83 down(g(a)) -> g_flat(down(a)) 543.68/241.83 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.83 down(g(b)) -> g_flat(down(b)) 543.68/241.83 down(g(c)) -> g_flat(down(c)) 543.68/241.83 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.83 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.83 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.83 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.83 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.83 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.83 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.83 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.83 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.83 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.83 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.83 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.83 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.83 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.83 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.83 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.83 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.83 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.83 543.68/241.83 The set Q consists of the following terms: 543.68/241.83 543.68/241.83 down(a) 543.68/241.83 down(b) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.83 down(f(a)) 543.68/241.83 down(f(b)) 543.68/241.83 down(f(g(x0))) 543.68/241.83 down(f(c)) 543.68/241.83 down(f(fresh_constant)) 543.68/241.83 down(g(a)) 543.68/241.83 down(g(f(x0))) 543.68/241.83 down(g(b)) 543.68/241.83 down(g(c)) 543.68/241.83 down(g(fresh_constant)) 543.68/241.83 down(f(f(a))) 543.68/241.83 down(f(f(b))) 543.68/241.83 down(f(f(g(x0)))) 543.68/241.83 down(f(f(c))) 543.68/241.83 down(f(f(fresh_constant))) 543.68/241.83 down(g(g(a))) 543.68/241.83 down(g(g(f(x0)))) 543.68/241.83 down(g(g(b))) 543.68/241.83 down(g(g(c))) 543.68/241.83 down(g(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) 543.68/241.83 down(f(f(f(g(x0))))) 543.68/241.83 down(f(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) 543.68/241.83 down(g(g(g(f(x0))))) 543.68/241.83 down(g(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(x0)))))) 543.68/241.83 down(f(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(x0)))))) 543.68/241.83 down(g(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(x0))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(x0))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 f_flat(up(x0)) 543.68/241.83 g_flat(up(x0)) 543.68/241.83 543.68/241.83 We have to consider all minimal (P,Q,R)-chains. 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (619) TransformationProof (EQUIVALENT) 543.68/241.83 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.68/241.83 543.68/241.83 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.68/241.83 543.68/241.83 543.68/241.83 ---------------------------------------- 543.68/241.83 543.68/241.83 (620) 543.68/241.83 Obligation: 543.68/241.83 Q DP problem: 543.68/241.83 The TRS P consists of the following rules: 543.68/241.83 543.68/241.83 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.83 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.83 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.83 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.83 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.83 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.83 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.83 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.83 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.83 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.83 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.83 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.83 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.83 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.83 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.83 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.68/241.83 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.68/241.83 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.83 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.83 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.83 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.83 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.83 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.83 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.83 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.83 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.83 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.83 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))) 543.68/241.83 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.68/241.83 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.68/241.83 543.68/241.83 The TRS R consists of the following rules: 543.68/241.83 543.68/241.83 down(a) -> up(f(a)) 543.68/241.83 down(b) -> up(g(b)) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.83 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.83 down(f(a)) -> f_flat(down(a)) 543.68/241.83 down(f(b)) -> f_flat(down(b)) 543.68/241.83 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.83 down(f(c)) -> f_flat(down(c)) 543.68/241.83 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.83 down(g(a)) -> g_flat(down(a)) 543.68/241.83 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.83 down(g(b)) -> g_flat(down(b)) 543.68/241.83 down(g(c)) -> g_flat(down(c)) 543.68/241.83 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.83 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.83 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.83 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.83 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.83 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.83 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.83 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.83 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.83 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.83 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.83 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.83 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.83 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.83 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.83 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.83 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.83 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.83 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.83 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.83 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.83 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.83 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.83 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.83 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.83 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.83 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.83 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.83 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.83 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.83 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.83 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.83 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.83 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.83 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.83 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.83 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.83 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.83 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.83 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.83 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.83 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.83 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.83 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.83 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.83 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.83 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.83 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.83 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.83 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.83 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.83 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.83 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.83 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.83 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.84 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.84 543.68/241.84 The set Q consists of the following terms: 543.68/241.84 543.68/241.84 down(a) 543.68/241.84 down(b) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.84 down(f(a)) 543.68/241.84 down(f(b)) 543.68/241.84 down(f(g(x0))) 543.68/241.84 down(f(c)) 543.68/241.84 down(f(fresh_constant)) 543.68/241.84 down(g(a)) 543.68/241.84 down(g(f(x0))) 543.68/241.84 down(g(b)) 543.68/241.84 down(g(c)) 543.68/241.84 down(g(fresh_constant)) 543.68/241.84 down(f(f(a))) 543.68/241.84 down(f(f(b))) 543.68/241.84 down(f(f(g(x0)))) 543.68/241.84 down(f(f(c))) 543.68/241.84 down(f(f(fresh_constant))) 543.68/241.84 down(g(g(a))) 543.68/241.84 down(g(g(f(x0)))) 543.68/241.84 down(g(g(b))) 543.68/241.84 down(g(g(c))) 543.68/241.84 down(g(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) 543.68/241.84 down(f(f(f(g(x0))))) 543.68/241.84 down(f(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) 543.68/241.84 down(g(g(g(f(x0))))) 543.68/241.84 down(g(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(x0)))))) 543.68/241.84 down(f(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(x0)))))) 543.68/241.84 down(g(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(x0))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(x0))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 f_flat(up(x0)) 543.68/241.84 g_flat(up(x0)) 543.68/241.84 543.68/241.84 We have to consider all minimal (P,Q,R)-chains. 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (621) TransformationProof (EQUIVALENT) 543.68/241.84 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.68/241.84 543.68/241.84 (TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))),TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.68/241.84 543.68/241.84 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (622) 543.68/241.84 Obligation: 543.68/241.84 Q DP problem: 543.68/241.84 The TRS P consists of the following rules: 543.68/241.84 543.68/241.84 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.84 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.84 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.84 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.84 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.84 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.84 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.84 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.84 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.84 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.84 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.84 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.84 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.84 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.84 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) 543.68/241.84 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.68/241.84 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.84 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.84 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.84 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.84 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.84 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.84 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.84 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.84 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.68/241.84 543.68/241.84 The TRS R consists of the following rules: 543.68/241.84 543.68/241.84 down(a) -> up(f(a)) 543.68/241.84 down(b) -> up(g(b)) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.84 down(f(a)) -> f_flat(down(a)) 543.68/241.84 down(f(b)) -> f_flat(down(b)) 543.68/241.84 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.84 down(f(c)) -> f_flat(down(c)) 543.68/241.84 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.84 down(g(a)) -> g_flat(down(a)) 543.68/241.84 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.84 down(g(b)) -> g_flat(down(b)) 543.68/241.84 down(g(c)) -> g_flat(down(c)) 543.68/241.84 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.84 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.84 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.84 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.84 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.84 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.84 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.84 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.84 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.84 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.84 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.84 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.84 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.84 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.84 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.84 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.84 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.84 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.84 543.68/241.84 The set Q consists of the following terms: 543.68/241.84 543.68/241.84 down(a) 543.68/241.84 down(b) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.84 down(f(a)) 543.68/241.84 down(f(b)) 543.68/241.84 down(f(g(x0))) 543.68/241.84 down(f(c)) 543.68/241.84 down(f(fresh_constant)) 543.68/241.84 down(g(a)) 543.68/241.84 down(g(f(x0))) 543.68/241.84 down(g(b)) 543.68/241.84 down(g(c)) 543.68/241.84 down(g(fresh_constant)) 543.68/241.84 down(f(f(a))) 543.68/241.84 down(f(f(b))) 543.68/241.84 down(f(f(g(x0)))) 543.68/241.84 down(f(f(c))) 543.68/241.84 down(f(f(fresh_constant))) 543.68/241.84 down(g(g(a))) 543.68/241.84 down(g(g(f(x0)))) 543.68/241.84 down(g(g(b))) 543.68/241.84 down(g(g(c))) 543.68/241.84 down(g(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) 543.68/241.84 down(f(f(f(g(x0))))) 543.68/241.84 down(f(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) 543.68/241.84 down(g(g(g(f(x0))))) 543.68/241.84 down(g(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(x0)))))) 543.68/241.84 down(f(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(x0)))))) 543.68/241.84 down(g(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(x0))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(x0))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 f_flat(up(x0)) 543.68/241.84 g_flat(up(x0)) 543.68/241.84 543.68/241.84 We have to consider all minimal (P,Q,R)-chains. 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (623) TransformationProof (EQUIVALENT) 543.68/241.84 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(b))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.68/241.84 543.68/241.84 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.68/241.84 543.68/241.84 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (624) 543.68/241.84 Obligation: 543.68/241.84 Q DP problem: 543.68/241.84 The TRS P consists of the following rules: 543.68/241.84 543.68/241.84 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.84 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.84 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.84 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.84 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.84 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.84 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.84 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.84 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.84 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.84 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.84 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.84 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.84 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.84 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) 543.68/241.84 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.84 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.84 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.84 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.84 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.84 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.84 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.84 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.84 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.68/241.84 543.68/241.84 The TRS R consists of the following rules: 543.68/241.84 543.68/241.84 down(a) -> up(f(a)) 543.68/241.84 down(b) -> up(g(b)) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.84 down(f(a)) -> f_flat(down(a)) 543.68/241.84 down(f(b)) -> f_flat(down(b)) 543.68/241.84 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.84 down(f(c)) -> f_flat(down(c)) 543.68/241.84 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.84 down(g(a)) -> g_flat(down(a)) 543.68/241.84 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.84 down(g(b)) -> g_flat(down(b)) 543.68/241.84 down(g(c)) -> g_flat(down(c)) 543.68/241.84 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.84 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.84 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.84 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.84 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.84 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.84 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.84 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.84 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.84 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.84 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.84 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.84 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.84 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.84 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.84 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.84 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.84 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.84 543.68/241.84 The set Q consists of the following terms: 543.68/241.84 543.68/241.84 down(a) 543.68/241.84 down(b) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.84 down(f(a)) 543.68/241.84 down(f(b)) 543.68/241.84 down(f(g(x0))) 543.68/241.84 down(f(c)) 543.68/241.84 down(f(fresh_constant)) 543.68/241.84 down(g(a)) 543.68/241.84 down(g(f(x0))) 543.68/241.84 down(g(b)) 543.68/241.84 down(g(c)) 543.68/241.84 down(g(fresh_constant)) 543.68/241.84 down(f(f(a))) 543.68/241.84 down(f(f(b))) 543.68/241.84 down(f(f(g(x0)))) 543.68/241.84 down(f(f(c))) 543.68/241.84 down(f(f(fresh_constant))) 543.68/241.84 down(g(g(a))) 543.68/241.84 down(g(g(f(x0)))) 543.68/241.84 down(g(g(b))) 543.68/241.84 down(g(g(c))) 543.68/241.84 down(g(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) 543.68/241.84 down(f(f(f(g(x0))))) 543.68/241.84 down(f(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) 543.68/241.84 down(g(g(g(f(x0))))) 543.68/241.84 down(g(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(x0)))))) 543.68/241.84 down(f(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(x0)))))) 543.68/241.84 down(g(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(x0))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(x0))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 f_flat(up(x0)) 543.68/241.84 g_flat(up(x0)) 543.68/241.84 543.68/241.84 We have to consider all minimal (P,Q,R)-chains. 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (625) TransformationProof (EQUIVALENT) 543.68/241.84 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(c))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.68/241.84 543.68/241.84 (TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(c))))))),TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(c)))))))) 543.68/241.84 543.68/241.84 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (626) 543.68/241.84 Obligation: 543.68/241.84 Q DP problem: 543.68/241.84 The TRS P consists of the following rules: 543.68/241.84 543.68/241.84 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.84 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.84 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.84 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.84 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.84 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.84 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.84 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.84 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.84 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.84 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.84 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.84 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.84 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.84 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.84 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.84 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.84 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.84 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.84 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.84 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.84 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.84 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.68/241.84 TOP(up(g(g(g(g(g(c))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(c))))))) 543.68/241.84 543.68/241.84 The TRS R consists of the following rules: 543.68/241.84 543.68/241.84 down(a) -> up(f(a)) 543.68/241.84 down(b) -> up(g(b)) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.84 down(f(a)) -> f_flat(down(a)) 543.68/241.84 down(f(b)) -> f_flat(down(b)) 543.68/241.84 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.84 down(f(c)) -> f_flat(down(c)) 543.68/241.84 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.84 down(g(a)) -> g_flat(down(a)) 543.68/241.84 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.84 down(g(b)) -> g_flat(down(b)) 543.68/241.84 down(g(c)) -> g_flat(down(c)) 543.68/241.84 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.84 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.84 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.84 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.84 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.84 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.84 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.84 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.84 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.84 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.84 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.84 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.84 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.84 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.84 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.84 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.84 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.84 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.84 543.68/241.84 The set Q consists of the following terms: 543.68/241.84 543.68/241.84 down(a) 543.68/241.84 down(b) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.84 down(f(a)) 543.68/241.84 down(f(b)) 543.68/241.84 down(f(g(x0))) 543.68/241.84 down(f(c)) 543.68/241.84 down(f(fresh_constant)) 543.68/241.84 down(g(a)) 543.68/241.84 down(g(f(x0))) 543.68/241.84 down(g(b)) 543.68/241.84 down(g(c)) 543.68/241.84 down(g(fresh_constant)) 543.68/241.84 down(f(f(a))) 543.68/241.84 down(f(f(b))) 543.68/241.84 down(f(f(g(x0)))) 543.68/241.84 down(f(f(c))) 543.68/241.84 down(f(f(fresh_constant))) 543.68/241.84 down(g(g(a))) 543.68/241.84 down(g(g(f(x0)))) 543.68/241.84 down(g(g(b))) 543.68/241.84 down(g(g(c))) 543.68/241.84 down(g(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) 543.68/241.84 down(f(f(f(g(x0))))) 543.68/241.84 down(f(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) 543.68/241.84 down(g(g(g(f(x0))))) 543.68/241.84 down(g(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(x0)))))) 543.68/241.84 down(f(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(x0)))))) 543.68/241.84 down(g(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(x0))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(x0))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 f_flat(up(x0)) 543.68/241.84 g_flat(up(x0)) 543.68/241.84 543.68/241.84 We have to consider all minimal (P,Q,R)-chains. 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (627) DependencyGraphProof (EQUIVALENT) 543.68/241.84 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (628) 543.68/241.84 Obligation: 543.68/241.84 Q DP problem: 543.68/241.84 The TRS P consists of the following rules: 543.68/241.84 543.68/241.84 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.84 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.84 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.84 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.84 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.84 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.84 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.84 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))) 543.68/241.84 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.84 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.84 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.84 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.84 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.84 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))) 543.68/241.84 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.84 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.84 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.84 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.84 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.84 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.84 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.84 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.84 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.84 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.68/241.84 543.68/241.84 The TRS R consists of the following rules: 543.68/241.84 543.68/241.84 down(a) -> up(f(a)) 543.68/241.84 down(b) -> up(g(b)) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.84 down(f(a)) -> f_flat(down(a)) 543.68/241.84 down(f(b)) -> f_flat(down(b)) 543.68/241.84 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.84 down(f(c)) -> f_flat(down(c)) 543.68/241.84 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.84 down(g(a)) -> g_flat(down(a)) 543.68/241.84 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.84 down(g(b)) -> g_flat(down(b)) 543.68/241.84 down(g(c)) -> g_flat(down(c)) 543.68/241.84 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.84 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.84 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.84 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.84 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.84 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.84 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.84 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.84 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.84 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.84 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.84 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.84 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.84 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.84 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.84 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.84 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.84 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.84 543.68/241.84 The set Q consists of the following terms: 543.68/241.84 543.68/241.84 down(a) 543.68/241.84 down(b) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.84 down(f(a)) 543.68/241.84 down(f(b)) 543.68/241.84 down(f(g(x0))) 543.68/241.84 down(f(c)) 543.68/241.84 down(f(fresh_constant)) 543.68/241.84 down(g(a)) 543.68/241.84 down(g(f(x0))) 543.68/241.84 down(g(b)) 543.68/241.84 down(g(c)) 543.68/241.84 down(g(fresh_constant)) 543.68/241.84 down(f(f(a))) 543.68/241.84 down(f(f(b))) 543.68/241.84 down(f(f(g(x0)))) 543.68/241.84 down(f(f(c))) 543.68/241.84 down(f(f(fresh_constant))) 543.68/241.84 down(g(g(a))) 543.68/241.84 down(g(g(f(x0)))) 543.68/241.84 down(g(g(b))) 543.68/241.84 down(g(g(c))) 543.68/241.84 down(g(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) 543.68/241.84 down(f(f(f(g(x0))))) 543.68/241.84 down(f(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) 543.68/241.84 down(g(g(g(f(x0))))) 543.68/241.84 down(g(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(x0)))))) 543.68/241.84 down(f(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(x0)))))) 543.68/241.84 down(g(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(x0))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(x0))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 f_flat(up(x0)) 543.68/241.84 g_flat(up(x0)) 543.68/241.84 543.68/241.84 We have to consider all minimal (P,Q,R)-chains. 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (629) TransformationProof (EQUIVALENT) 543.68/241.84 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(f_flat(up(f(f(f(a))))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.68/241.84 543.68/241.84 (TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(up(f(f(f(f(a))))))),TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(up(f(f(f(f(a)))))))) 543.68/241.84 543.68/241.84 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (630) 543.68/241.84 Obligation: 543.68/241.84 Q DP problem: 543.68/241.84 The TRS P consists of the following rules: 543.68/241.84 543.68/241.84 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.84 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.84 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.84 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.84 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.84 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.84 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.84 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.84 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.84 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.84 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.84 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.84 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))) 543.68/241.84 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.84 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.84 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.84 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.84 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.84 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.84 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.84 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.84 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.84 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(up(f(f(f(f(a))))))) 543.68/241.84 543.68/241.84 The TRS R consists of the following rules: 543.68/241.84 543.68/241.84 down(a) -> up(f(a)) 543.68/241.84 down(b) -> up(g(b)) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.84 down(f(a)) -> f_flat(down(a)) 543.68/241.84 down(f(b)) -> f_flat(down(b)) 543.68/241.84 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.84 down(f(c)) -> f_flat(down(c)) 543.68/241.84 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.84 down(g(a)) -> g_flat(down(a)) 543.68/241.84 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.84 down(g(b)) -> g_flat(down(b)) 543.68/241.84 down(g(c)) -> g_flat(down(c)) 543.68/241.84 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.84 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.84 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.84 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.84 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.84 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.84 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.84 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.84 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.84 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.84 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.84 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.84 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.84 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.84 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.84 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.84 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.84 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.84 543.68/241.84 The set Q consists of the following terms: 543.68/241.84 543.68/241.84 down(a) 543.68/241.84 down(b) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.84 down(f(a)) 543.68/241.84 down(f(b)) 543.68/241.84 down(f(g(x0))) 543.68/241.84 down(f(c)) 543.68/241.84 down(f(fresh_constant)) 543.68/241.84 down(g(a)) 543.68/241.84 down(g(f(x0))) 543.68/241.84 down(g(b)) 543.68/241.84 down(g(c)) 543.68/241.84 down(g(fresh_constant)) 543.68/241.84 down(f(f(a))) 543.68/241.84 down(f(f(b))) 543.68/241.84 down(f(f(g(x0)))) 543.68/241.84 down(f(f(c))) 543.68/241.84 down(f(f(fresh_constant))) 543.68/241.84 down(g(g(a))) 543.68/241.84 down(g(g(f(x0)))) 543.68/241.84 down(g(g(b))) 543.68/241.84 down(g(g(c))) 543.68/241.84 down(g(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) 543.68/241.84 down(f(f(f(g(x0))))) 543.68/241.84 down(f(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) 543.68/241.84 down(g(g(g(f(x0))))) 543.68/241.84 down(g(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(x0)))))) 543.68/241.84 down(f(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(x0)))))) 543.68/241.84 down(g(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(x0))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(x0))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 f_flat(up(x0)) 543.68/241.84 g_flat(up(x0)) 543.68/241.84 543.68/241.84 We have to consider all minimal (P,Q,R)-chains. 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (631) TransformationProof (EQUIVALENT) 543.68/241.84 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(g_flat(up(g(g(g(b))))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.68/241.84 543.68/241.84 (TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(up(g(g(g(g(b))))))),TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(up(g(g(g(g(b)))))))) 543.68/241.84 543.68/241.84 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (632) 543.68/241.84 Obligation: 543.68/241.84 Q DP problem: 543.68/241.84 The TRS P consists of the following rules: 543.68/241.84 543.68/241.84 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.84 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.84 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.84 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.84 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.84 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.84 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.84 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.84 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.84 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.84 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.84 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.84 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.84 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.84 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.84 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.84 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.84 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.84 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.84 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.84 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.84 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(up(f(f(f(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(up(g(g(g(g(b))))))) 543.68/241.84 543.68/241.84 The TRS R consists of the following rules: 543.68/241.84 543.68/241.84 down(a) -> up(f(a)) 543.68/241.84 down(b) -> up(g(b)) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.84 down(f(a)) -> f_flat(down(a)) 543.68/241.84 down(f(b)) -> f_flat(down(b)) 543.68/241.84 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.84 down(f(c)) -> f_flat(down(c)) 543.68/241.84 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.84 down(g(a)) -> g_flat(down(a)) 543.68/241.84 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.84 down(g(b)) -> g_flat(down(b)) 543.68/241.84 down(g(c)) -> g_flat(down(c)) 543.68/241.84 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.84 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.84 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.84 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.84 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.84 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.84 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.84 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.84 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.84 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.84 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.84 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.84 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.84 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.84 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.84 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.84 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 g_flat(up(x_1)) -> up(g(x_1)) 543.68/241.84 f_flat(up(x_1)) -> up(f(x_1)) 543.68/241.84 543.68/241.84 The set Q consists of the following terms: 543.68/241.84 543.68/241.84 down(a) 543.68/241.84 down(b) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.68/241.84 down(f(a)) 543.68/241.84 down(f(b)) 543.68/241.84 down(f(g(x0))) 543.68/241.84 down(f(c)) 543.68/241.84 down(f(fresh_constant)) 543.68/241.84 down(g(a)) 543.68/241.84 down(g(f(x0))) 543.68/241.84 down(g(b)) 543.68/241.84 down(g(c)) 543.68/241.84 down(g(fresh_constant)) 543.68/241.84 down(f(f(a))) 543.68/241.84 down(f(f(b))) 543.68/241.84 down(f(f(g(x0)))) 543.68/241.84 down(f(f(c))) 543.68/241.84 down(f(f(fresh_constant))) 543.68/241.84 down(g(g(a))) 543.68/241.84 down(g(g(f(x0)))) 543.68/241.84 down(g(g(b))) 543.68/241.84 down(g(g(c))) 543.68/241.84 down(g(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) 543.68/241.84 down(f(f(f(g(x0))))) 543.68/241.84 down(f(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) 543.68/241.84 down(g(g(g(f(x0))))) 543.68/241.84 down(g(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(x0)))))) 543.68/241.84 down(f(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(x0)))))) 543.68/241.84 down(g(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(x0))))))) 543.68/241.84 down(f(f(f(f(f(c)))))) 543.68/241.84 down(f(f(f(f(f(fresh_constant)))))) 543.68/241.84 down(g(g(g(g(g(a)))))) 543.68/241.84 down(g(g(g(g(g(f(x0))))))) 543.68/241.84 down(g(g(g(g(g(b)))))) 543.68/241.84 down(g(g(g(g(g(c)))))) 543.68/241.84 down(g(g(g(g(g(fresh_constant)))))) 543.68/241.84 down(f(f(f(f(f(f(a))))))) 543.68/241.84 down(f(f(f(f(f(f(b))))))) 543.68/241.84 down(f(f(f(f(f(f(g(x0)))))))) 543.68/241.84 down(f(f(f(f(f(f(c))))))) 543.68/241.84 down(f(f(f(f(f(f(fresh_constant))))))) 543.68/241.84 down(g(g(g(g(g(g(a))))))) 543.68/241.84 down(g(g(g(g(g(g(f(x0)))))))) 543.68/241.84 down(g(g(g(g(g(g(b))))))) 543.68/241.84 down(g(g(g(g(g(g(c))))))) 543.68/241.84 down(g(g(g(g(g(g(fresh_constant))))))) 543.68/241.84 down(f(f(f(f(f(f(f(a)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(b)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(g(x0))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(c)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(a)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(f(x0))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(b)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(c)))))))) 543.68/241.84 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(a))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(b))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(c))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(a))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(b))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(c))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 f_flat(up(x0)) 543.68/241.84 g_flat(up(x0)) 543.68/241.84 543.68/241.84 We have to consider all minimal (P,Q,R)-chains. 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (633) TransformationProof (EQUIVALENT) 543.68/241.84 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.68/241.84 543.68/241.84 (TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant))))))),TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant)))))))) 543.68/241.84 543.68/241.84 543.68/241.84 ---------------------------------------- 543.68/241.84 543.68/241.84 (634) 543.68/241.84 Obligation: 543.68/241.84 Q DP problem: 543.68/241.84 The TRS P consists of the following rules: 543.68/241.84 543.68/241.84 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.68/241.84 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.68/241.84 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.68/241.84 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.68/241.84 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.68/241.84 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.68/241.84 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.68/241.84 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.68/241.84 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.68/241.84 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.68/241.84 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.68/241.84 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.68/241.84 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.68/241.84 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.68/241.84 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.68/241.84 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.68/241.84 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.68/241.84 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.68/241.84 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.68/241.84 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.68/241.84 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.68/241.84 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.68/241.84 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.68/241.84 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.68/241.84 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.68/241.84 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(up(f(f(f(f(a))))))) 543.68/241.84 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(up(g(g(g(g(b))))))) 543.68/241.84 TOP(up(g(g(g(g(g(fresh_constant))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant))))))) 543.68/241.84 543.68/241.84 The TRS R consists of the following rules: 543.68/241.84 543.68/241.84 down(a) -> up(f(a)) 543.68/241.84 down(b) -> up(g(b)) 543.68/241.84 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.68/241.84 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.68/241.84 down(f(a)) -> f_flat(down(a)) 543.68/241.84 down(f(b)) -> f_flat(down(b)) 543.68/241.84 down(f(g(y4))) -> f_flat(down(g(y4))) 543.68/241.84 down(f(c)) -> f_flat(down(c)) 543.68/241.84 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.68/241.84 down(g(a)) -> g_flat(down(a)) 543.68/241.84 down(g(f(y6))) -> g_flat(down(f(y6))) 543.68/241.84 down(g(b)) -> g_flat(down(b)) 543.68/241.84 down(g(c)) -> g_flat(down(c)) 543.68/241.84 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.68/241.84 down(f(f(a))) -> f_flat(down(f(a))) 543.68/241.84 down(f(f(b))) -> f_flat(down(f(b))) 543.68/241.84 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.68/241.84 down(f(f(c))) -> f_flat(down(f(c))) 543.68/241.84 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.68/241.84 down(g(g(a))) -> g_flat(down(g(a))) 543.68/241.84 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.68/241.84 down(g(g(b))) -> g_flat(down(g(b))) 543.68/241.84 down(g(g(c))) -> g_flat(down(g(c))) 543.68/241.84 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.68/241.84 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.68/241.84 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.68/241.84 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.68/241.84 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.68/241.84 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.68/241.84 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.68/241.84 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.68/241.84 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.68/241.84 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.68/241.84 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.68/241.84 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.68/241.84 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.68/241.84 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.68/241.84 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.68/241.84 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.68/241.84 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.68/241.84 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.68/241.84 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.68/241.84 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.68/241.84 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.68/241.84 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.68/241.84 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.68/241.84 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.68/241.85 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.68/241.85 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.68/241.85 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.68/241.85 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.68/241.85 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.68/241.85 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.68/241.85 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.68/241.85 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.68/241.85 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.68/241.85 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.68/241.85 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.68/241.85 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.68/241.85 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.68/241.85 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.68/241.85 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.68/241.85 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.68/241.85 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.68/241.85 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.68/241.85 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.68/241.85 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.68/241.85 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.68/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.68/241.85 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.68/241.85 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.68/241.85 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.68/241.85 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.68/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.68/241.85 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.68/241.85 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.68/241.85 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.68/241.85 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.68/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.68/241.85 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.68/241.85 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.68/241.85 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.68/241.85 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.68/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.68/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.68/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.68/241.85 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.68/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.85 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.85 543.70/241.85 The set Q consists of the following terms: 543.70/241.85 543.70/241.85 down(a) 543.70/241.85 down(b) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.85 down(f(a)) 543.70/241.85 down(f(b)) 543.70/241.85 down(f(g(x0))) 543.70/241.85 down(f(c)) 543.70/241.85 down(f(fresh_constant)) 543.70/241.85 down(g(a)) 543.70/241.85 down(g(f(x0))) 543.70/241.85 down(g(b)) 543.70/241.85 down(g(c)) 543.70/241.85 down(g(fresh_constant)) 543.70/241.85 down(f(f(a))) 543.70/241.85 down(f(f(b))) 543.70/241.85 down(f(f(g(x0)))) 543.70/241.85 down(f(f(c))) 543.70/241.85 down(f(f(fresh_constant))) 543.70/241.85 down(g(g(a))) 543.70/241.85 down(g(g(f(x0)))) 543.70/241.85 down(g(g(b))) 543.70/241.85 down(g(g(c))) 543.70/241.85 down(g(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) 543.70/241.85 down(f(f(f(g(x0))))) 543.70/241.85 down(f(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) 543.70/241.85 down(g(g(g(f(x0))))) 543.70/241.85 down(g(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(x0)))))) 543.70/241.85 down(f(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(x0)))))) 543.70/241.85 down(g(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(x0))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(x0))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 f_flat(up(x0)) 543.70/241.85 g_flat(up(x0)) 543.70/241.85 543.70/241.85 We have to consider all minimal (P,Q,R)-chains. 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (635) DependencyGraphProof (EQUIVALENT) 543.70/241.85 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (636) 543.70/241.85 Obligation: 543.70/241.85 Q DP problem: 543.70/241.85 The TRS P consists of the following rules: 543.70/241.85 543.70/241.85 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.85 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.85 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.85 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.85 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.85 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.85 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.85 TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(up(f(f(f(f(a))))))) 543.70/241.85 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.85 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.85 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.85 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.85 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.85 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(up(g(g(g(g(b))))))) 543.70/241.85 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.85 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.85 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.85 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.85 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.85 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.85 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.85 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.85 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.85 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.85 543.70/241.85 The TRS R consists of the following rules: 543.70/241.85 543.70/241.85 down(a) -> up(f(a)) 543.70/241.85 down(b) -> up(g(b)) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.85 down(f(a)) -> f_flat(down(a)) 543.70/241.85 down(f(b)) -> f_flat(down(b)) 543.70/241.85 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.85 down(f(c)) -> f_flat(down(c)) 543.70/241.85 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.85 down(g(a)) -> g_flat(down(a)) 543.70/241.85 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.85 down(g(b)) -> g_flat(down(b)) 543.70/241.85 down(g(c)) -> g_flat(down(c)) 543.70/241.85 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.85 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.85 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.85 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.85 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.85 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.85 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.85 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.85 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.85 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.85 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.85 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.85 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.85 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.85 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.85 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.85 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.85 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.85 543.70/241.85 The set Q consists of the following terms: 543.70/241.85 543.70/241.85 down(a) 543.70/241.85 down(b) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.85 down(f(a)) 543.70/241.85 down(f(b)) 543.70/241.85 down(f(g(x0))) 543.70/241.85 down(f(c)) 543.70/241.85 down(f(fresh_constant)) 543.70/241.85 down(g(a)) 543.70/241.85 down(g(f(x0))) 543.70/241.85 down(g(b)) 543.70/241.85 down(g(c)) 543.70/241.85 down(g(fresh_constant)) 543.70/241.85 down(f(f(a))) 543.70/241.85 down(f(f(b))) 543.70/241.85 down(f(f(g(x0)))) 543.70/241.85 down(f(f(c))) 543.70/241.85 down(f(f(fresh_constant))) 543.70/241.85 down(g(g(a))) 543.70/241.85 down(g(g(f(x0)))) 543.70/241.85 down(g(g(b))) 543.70/241.85 down(g(g(c))) 543.70/241.85 down(g(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) 543.70/241.85 down(f(f(f(g(x0))))) 543.70/241.85 down(f(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) 543.70/241.85 down(g(g(g(f(x0))))) 543.70/241.85 down(g(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(x0)))))) 543.70/241.85 down(f(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(x0)))))) 543.70/241.85 down(g(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(x0))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(x0))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 f_flat(up(x0)) 543.70/241.85 g_flat(up(x0)) 543.70/241.85 543.70/241.85 We have to consider all minimal (P,Q,R)-chains. 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (637) TransformationProof (EQUIVALENT) 543.70/241.85 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(a)))))) -> TOP(f_flat(up(f(f(f(f(a))))))) at position [0] we obtained the following new rules [LPAR04]: 543.70/241.85 543.70/241.85 (TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))),TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a)))))))) 543.70/241.85 543.70/241.85 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (638) 543.70/241.85 Obligation: 543.70/241.85 Q DP problem: 543.70/241.85 The TRS P consists of the following rules: 543.70/241.85 543.70/241.85 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.85 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.85 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.85 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.85 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.85 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.85 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.85 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.85 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.85 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.85 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.85 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.85 TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(up(g(g(g(g(b))))))) 543.70/241.85 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.85 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.85 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.85 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.85 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.85 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.85 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.85 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.85 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.85 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.85 543.70/241.85 The TRS R consists of the following rules: 543.70/241.85 543.70/241.85 down(a) -> up(f(a)) 543.70/241.85 down(b) -> up(g(b)) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.85 down(f(a)) -> f_flat(down(a)) 543.70/241.85 down(f(b)) -> f_flat(down(b)) 543.70/241.85 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.85 down(f(c)) -> f_flat(down(c)) 543.70/241.85 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.85 down(g(a)) -> g_flat(down(a)) 543.70/241.85 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.85 down(g(b)) -> g_flat(down(b)) 543.70/241.85 down(g(c)) -> g_flat(down(c)) 543.70/241.85 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.85 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.85 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.85 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.85 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.85 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.85 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.85 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.85 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.85 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.85 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.85 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.85 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.85 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.85 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.85 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.85 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.85 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.85 543.70/241.85 The set Q consists of the following terms: 543.70/241.85 543.70/241.85 down(a) 543.70/241.85 down(b) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.85 down(f(a)) 543.70/241.85 down(f(b)) 543.70/241.85 down(f(g(x0))) 543.70/241.85 down(f(c)) 543.70/241.85 down(f(fresh_constant)) 543.70/241.85 down(g(a)) 543.70/241.85 down(g(f(x0))) 543.70/241.85 down(g(b)) 543.70/241.85 down(g(c)) 543.70/241.85 down(g(fresh_constant)) 543.70/241.85 down(f(f(a))) 543.70/241.85 down(f(f(b))) 543.70/241.85 down(f(f(g(x0)))) 543.70/241.85 down(f(f(c))) 543.70/241.85 down(f(f(fresh_constant))) 543.70/241.85 down(g(g(a))) 543.70/241.85 down(g(g(f(x0)))) 543.70/241.85 down(g(g(b))) 543.70/241.85 down(g(g(c))) 543.70/241.85 down(g(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) 543.70/241.85 down(f(f(f(g(x0))))) 543.70/241.85 down(f(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) 543.70/241.85 down(g(g(g(f(x0))))) 543.70/241.85 down(g(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(x0)))))) 543.70/241.85 down(f(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(x0)))))) 543.70/241.85 down(g(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(x0))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(x0))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 f_flat(up(x0)) 543.70/241.85 g_flat(up(x0)) 543.70/241.85 543.70/241.85 We have to consider all minimal (P,Q,R)-chains. 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (639) TransformationProof (EQUIVALENT) 543.70/241.85 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(b)))))) -> TOP(g_flat(up(g(g(g(g(b))))))) at position [0] we obtained the following new rules [LPAR04]: 543.70/241.85 543.70/241.85 (TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))),TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b)))))))) 543.70/241.85 543.70/241.85 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (640) 543.70/241.85 Obligation: 543.70/241.85 Q DP problem: 543.70/241.85 The TRS P consists of the following rules: 543.70/241.85 543.70/241.85 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.85 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.85 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.85 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.85 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.85 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.85 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.85 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.85 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.85 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.85 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.85 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.85 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.85 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.85 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.85 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.85 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.85 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.85 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.85 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.85 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.85 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.85 543.70/241.85 The TRS R consists of the following rules: 543.70/241.85 543.70/241.85 down(a) -> up(f(a)) 543.70/241.85 down(b) -> up(g(b)) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.85 down(f(a)) -> f_flat(down(a)) 543.70/241.85 down(f(b)) -> f_flat(down(b)) 543.70/241.85 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.85 down(f(c)) -> f_flat(down(c)) 543.70/241.85 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.85 down(g(a)) -> g_flat(down(a)) 543.70/241.85 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.85 down(g(b)) -> g_flat(down(b)) 543.70/241.85 down(g(c)) -> g_flat(down(c)) 543.70/241.85 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.85 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.85 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.85 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.85 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.85 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.85 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.85 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.85 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.85 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.85 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.85 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.85 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.85 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.85 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.85 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.85 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.85 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.85 543.70/241.85 The set Q consists of the following terms: 543.70/241.85 543.70/241.85 down(a) 543.70/241.85 down(b) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.85 down(f(a)) 543.70/241.85 down(f(b)) 543.70/241.85 down(f(g(x0))) 543.70/241.85 down(f(c)) 543.70/241.85 down(f(fresh_constant)) 543.70/241.85 down(g(a)) 543.70/241.85 down(g(f(x0))) 543.70/241.85 down(g(b)) 543.70/241.85 down(g(c)) 543.70/241.85 down(g(fresh_constant)) 543.70/241.85 down(f(f(a))) 543.70/241.85 down(f(f(b))) 543.70/241.85 down(f(f(g(x0)))) 543.70/241.85 down(f(f(c))) 543.70/241.85 down(f(f(fresh_constant))) 543.70/241.85 down(g(g(a))) 543.70/241.85 down(g(g(f(x0)))) 543.70/241.85 down(g(g(b))) 543.70/241.85 down(g(g(c))) 543.70/241.85 down(g(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) 543.70/241.85 down(f(f(f(g(x0))))) 543.70/241.85 down(f(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) 543.70/241.85 down(g(g(g(f(x0))))) 543.70/241.85 down(g(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(x0)))))) 543.70/241.85 down(f(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(x0)))))) 543.70/241.85 down(g(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(x0))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(x0))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 f_flat(up(x0)) 543.70/241.85 g_flat(up(x0)) 543.70/241.85 543.70/241.85 We have to consider all minimal (P,Q,R)-chains. 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (641) TransformationProof (EQUIVALENT) 543.70/241.85 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.85 543.70/241.85 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.70/241.85 543.70/241.85 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (642) 543.70/241.85 Obligation: 543.70/241.85 Q DP problem: 543.70/241.85 The TRS P consists of the following rules: 543.70/241.85 543.70/241.85 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.85 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.85 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.85 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.85 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.85 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.85 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.85 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.85 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.85 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.85 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.85 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.85 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.85 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.85 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.85 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.85 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.85 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.85 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.85 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.85 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.85 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.85 543.70/241.85 The TRS R consists of the following rules: 543.70/241.85 543.70/241.85 down(a) -> up(f(a)) 543.70/241.85 down(b) -> up(g(b)) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.85 down(f(a)) -> f_flat(down(a)) 543.70/241.85 down(f(b)) -> f_flat(down(b)) 543.70/241.85 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.85 down(f(c)) -> f_flat(down(c)) 543.70/241.85 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.85 down(g(a)) -> g_flat(down(a)) 543.70/241.85 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.85 down(g(b)) -> g_flat(down(b)) 543.70/241.85 down(g(c)) -> g_flat(down(c)) 543.70/241.85 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.85 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.85 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.85 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.85 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.85 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.85 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.85 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.85 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.85 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.85 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.85 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.85 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.85 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.85 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.85 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.85 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.85 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.85 543.70/241.85 The set Q consists of the following terms: 543.70/241.85 543.70/241.85 down(a) 543.70/241.85 down(b) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.85 down(f(a)) 543.70/241.85 down(f(b)) 543.70/241.85 down(f(g(x0))) 543.70/241.85 down(f(c)) 543.70/241.85 down(f(fresh_constant)) 543.70/241.85 down(g(a)) 543.70/241.85 down(g(f(x0))) 543.70/241.85 down(g(b)) 543.70/241.85 down(g(c)) 543.70/241.85 down(g(fresh_constant)) 543.70/241.85 down(f(f(a))) 543.70/241.85 down(f(f(b))) 543.70/241.85 down(f(f(g(x0)))) 543.70/241.85 down(f(f(c))) 543.70/241.85 down(f(f(fresh_constant))) 543.70/241.85 down(g(g(a))) 543.70/241.85 down(g(g(f(x0)))) 543.70/241.85 down(g(g(b))) 543.70/241.85 down(g(g(c))) 543.70/241.85 down(g(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) 543.70/241.85 down(f(f(f(g(x0))))) 543.70/241.85 down(f(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) 543.70/241.85 down(g(g(g(f(x0))))) 543.70/241.85 down(g(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(x0)))))) 543.70/241.85 down(f(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(x0)))))) 543.70/241.85 down(g(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(x0))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(x0))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 f_flat(up(x0)) 543.70/241.85 g_flat(up(x0)) 543.70/241.85 543.70/241.85 We have to consider all minimal (P,Q,R)-chains. 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (643) TransformationProof (EQUIVALENT) 543.70/241.85 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.85 543.70/241.85 (TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))),TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.70/241.85 543.70/241.85 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (644) 543.70/241.85 Obligation: 543.70/241.85 Q DP problem: 543.70/241.85 The TRS P consists of the following rules: 543.70/241.85 543.70/241.85 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.85 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.85 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.85 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.85 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.85 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.85 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.85 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.85 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.85 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.85 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.85 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.85 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.85 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.85 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.85 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.85 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.85 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.85 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.85 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.85 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.85 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.85 543.70/241.85 The TRS R consists of the following rules: 543.70/241.85 543.70/241.85 down(a) -> up(f(a)) 543.70/241.85 down(b) -> up(g(b)) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.85 down(f(a)) -> f_flat(down(a)) 543.70/241.85 down(f(b)) -> f_flat(down(b)) 543.70/241.85 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.85 down(f(c)) -> f_flat(down(c)) 543.70/241.85 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.85 down(g(a)) -> g_flat(down(a)) 543.70/241.85 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.85 down(g(b)) -> g_flat(down(b)) 543.70/241.85 down(g(c)) -> g_flat(down(c)) 543.70/241.85 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.85 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.85 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.85 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.85 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.85 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.85 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.85 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.85 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.85 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.85 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.85 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.85 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.85 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.85 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.85 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.85 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.85 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.85 543.70/241.85 The set Q consists of the following terms: 543.70/241.85 543.70/241.85 down(a) 543.70/241.85 down(b) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.85 down(f(a)) 543.70/241.85 down(f(b)) 543.70/241.85 down(f(g(x0))) 543.70/241.85 down(f(c)) 543.70/241.85 down(f(fresh_constant)) 543.70/241.85 down(g(a)) 543.70/241.85 down(g(f(x0))) 543.70/241.85 down(g(b)) 543.70/241.85 down(g(c)) 543.70/241.85 down(g(fresh_constant)) 543.70/241.85 down(f(f(a))) 543.70/241.85 down(f(f(b))) 543.70/241.85 down(f(f(g(x0)))) 543.70/241.85 down(f(f(c))) 543.70/241.85 down(f(f(fresh_constant))) 543.70/241.85 down(g(g(a))) 543.70/241.85 down(g(g(f(x0)))) 543.70/241.85 down(g(g(b))) 543.70/241.85 down(g(g(c))) 543.70/241.85 down(g(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) 543.70/241.85 down(f(f(f(g(x0))))) 543.70/241.85 down(f(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) 543.70/241.85 down(g(g(g(f(x0))))) 543.70/241.85 down(g(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(x0)))))) 543.70/241.85 down(f(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(x0)))))) 543.70/241.85 down(g(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(x0))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(x0))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 f_flat(up(x0)) 543.70/241.85 g_flat(up(x0)) 543.70/241.85 543.70/241.85 We have to consider all minimal (P,Q,R)-chains. 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (645) TransformationProof (EQUIVALENT) 543.70/241.85 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.85 543.70/241.85 (TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))),TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.70/241.85 543.70/241.85 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (646) 543.70/241.85 Obligation: 543.70/241.85 Q DP problem: 543.70/241.85 The TRS P consists of the following rules: 543.70/241.85 543.70/241.85 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.85 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.85 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.85 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.85 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.85 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.85 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.85 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.85 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.85 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.85 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.85 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.85 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.85 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.85 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.85 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.85 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.85 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.85 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.85 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.85 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.85 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.85 543.70/241.85 The TRS R consists of the following rules: 543.70/241.85 543.70/241.85 down(a) -> up(f(a)) 543.70/241.85 down(b) -> up(g(b)) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.85 down(f(a)) -> f_flat(down(a)) 543.70/241.85 down(f(b)) -> f_flat(down(b)) 543.70/241.85 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.85 down(f(c)) -> f_flat(down(c)) 543.70/241.85 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.85 down(g(a)) -> g_flat(down(a)) 543.70/241.85 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.85 down(g(b)) -> g_flat(down(b)) 543.70/241.85 down(g(c)) -> g_flat(down(c)) 543.70/241.85 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.85 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.85 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.85 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.85 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.85 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.85 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.85 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.85 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.85 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.85 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.85 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.85 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.85 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.85 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.85 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.85 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.85 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.85 543.70/241.85 The set Q consists of the following terms: 543.70/241.85 543.70/241.85 down(a) 543.70/241.85 down(b) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.85 down(f(a)) 543.70/241.85 down(f(b)) 543.70/241.85 down(f(g(x0))) 543.70/241.85 down(f(c)) 543.70/241.85 down(f(fresh_constant)) 543.70/241.85 down(g(a)) 543.70/241.85 down(g(f(x0))) 543.70/241.85 down(g(b)) 543.70/241.85 down(g(c)) 543.70/241.85 down(g(fresh_constant)) 543.70/241.85 down(f(f(a))) 543.70/241.85 down(f(f(b))) 543.70/241.85 down(f(f(g(x0)))) 543.70/241.85 down(f(f(c))) 543.70/241.85 down(f(f(fresh_constant))) 543.70/241.85 down(g(g(a))) 543.70/241.85 down(g(g(f(x0)))) 543.70/241.85 down(g(g(b))) 543.70/241.85 down(g(g(c))) 543.70/241.85 down(g(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) 543.70/241.85 down(f(f(f(g(x0))))) 543.70/241.85 down(f(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) 543.70/241.85 down(g(g(g(f(x0))))) 543.70/241.85 down(g(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(x0)))))) 543.70/241.85 down(f(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(x0)))))) 543.70/241.85 down(g(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(x0))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(x0))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 f_flat(up(x0)) 543.70/241.85 g_flat(up(x0)) 543.70/241.85 543.70/241.85 We have to consider all minimal (P,Q,R)-chains. 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (647) TransformationProof (EQUIVALENT) 543.70/241.85 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.85 543.70/241.85 (TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))),TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.70/241.85 543.70/241.85 543.70/241.85 ---------------------------------------- 543.70/241.85 543.70/241.85 (648) 543.70/241.85 Obligation: 543.70/241.85 Q DP problem: 543.70/241.85 The TRS P consists of the following rules: 543.70/241.85 543.70/241.85 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.85 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.85 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.85 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.85 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.85 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.85 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.85 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.85 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.85 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.85 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.85 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.85 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.85 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.85 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.85 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.85 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.85 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.85 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.85 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.85 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.85 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.85 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.85 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.85 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.85 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.85 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.85 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.85 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.85 543.70/241.85 The TRS R consists of the following rules: 543.70/241.85 543.70/241.85 down(a) -> up(f(a)) 543.70/241.85 down(b) -> up(g(b)) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.85 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.85 down(f(a)) -> f_flat(down(a)) 543.70/241.85 down(f(b)) -> f_flat(down(b)) 543.70/241.85 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.85 down(f(c)) -> f_flat(down(c)) 543.70/241.85 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.85 down(g(a)) -> g_flat(down(a)) 543.70/241.85 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.85 down(g(b)) -> g_flat(down(b)) 543.70/241.85 down(g(c)) -> g_flat(down(c)) 543.70/241.85 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.85 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.85 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.85 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.85 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.85 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.85 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.85 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.85 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.85 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.85 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.85 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.85 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.85 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.85 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.85 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.85 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.85 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.85 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.85 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.85 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.85 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.85 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.85 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.85 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.85 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.85 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.85 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.85 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.85 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.85 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.85 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.85 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.85 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.85 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.85 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.85 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.85 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.85 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.85 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.85 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.85 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.85 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.85 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.85 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.85 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.85 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.85 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.85 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.85 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.85 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.85 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.85 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.85 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.85 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.86 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.86 543.70/241.86 The set Q consists of the following terms: 543.70/241.86 543.70/241.86 down(a) 543.70/241.86 down(b) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.86 down(f(a)) 543.70/241.86 down(f(b)) 543.70/241.86 down(f(g(x0))) 543.70/241.86 down(f(c)) 543.70/241.86 down(f(fresh_constant)) 543.70/241.86 down(g(a)) 543.70/241.86 down(g(f(x0))) 543.70/241.86 down(g(b)) 543.70/241.86 down(g(c)) 543.70/241.86 down(g(fresh_constant)) 543.70/241.86 down(f(f(a))) 543.70/241.86 down(f(f(b))) 543.70/241.86 down(f(f(g(x0)))) 543.70/241.86 down(f(f(c))) 543.70/241.86 down(f(f(fresh_constant))) 543.70/241.86 down(g(g(a))) 543.70/241.86 down(g(g(f(x0)))) 543.70/241.86 down(g(g(b))) 543.70/241.86 down(g(g(c))) 543.70/241.86 down(g(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) 543.70/241.86 down(f(f(f(g(x0))))) 543.70/241.86 down(f(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) 543.70/241.86 down(g(g(g(f(x0))))) 543.70/241.86 down(g(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(x0)))))) 543.70/241.86 down(f(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(x0)))))) 543.70/241.86 down(g(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(x0))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(x0))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 f_flat(up(x0)) 543.70/241.86 g_flat(up(x0)) 543.70/241.86 543.70/241.86 We have to consider all minimal (P,Q,R)-chains. 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (649) TransformationProof (EQUIVALENT) 543.70/241.86 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.86 543.70/241.86 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.70/241.86 543.70/241.86 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (650) 543.70/241.86 Obligation: 543.70/241.86 Q DP problem: 543.70/241.86 The TRS P consists of the following rules: 543.70/241.86 543.70/241.86 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.86 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.86 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.86 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.86 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.86 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.86 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.86 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.86 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.86 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.86 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.86 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.86 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.86 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.86 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.86 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.86 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.86 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.86 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.86 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.86 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.86 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.86 543.70/241.86 The TRS R consists of the following rules: 543.70/241.86 543.70/241.86 down(a) -> up(f(a)) 543.70/241.86 down(b) -> up(g(b)) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.86 down(f(a)) -> f_flat(down(a)) 543.70/241.86 down(f(b)) -> f_flat(down(b)) 543.70/241.86 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.86 down(f(c)) -> f_flat(down(c)) 543.70/241.86 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.86 down(g(a)) -> g_flat(down(a)) 543.70/241.86 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.86 down(g(b)) -> g_flat(down(b)) 543.70/241.86 down(g(c)) -> g_flat(down(c)) 543.70/241.86 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.86 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.86 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.86 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.86 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.86 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.86 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.86 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.86 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.86 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.86 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.86 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.86 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.86 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.86 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.86 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.86 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.86 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.86 543.70/241.86 The set Q consists of the following terms: 543.70/241.86 543.70/241.86 down(a) 543.70/241.86 down(b) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.86 down(f(a)) 543.70/241.86 down(f(b)) 543.70/241.86 down(f(g(x0))) 543.70/241.86 down(f(c)) 543.70/241.86 down(f(fresh_constant)) 543.70/241.86 down(g(a)) 543.70/241.86 down(g(f(x0))) 543.70/241.86 down(g(b)) 543.70/241.86 down(g(c)) 543.70/241.86 down(g(fresh_constant)) 543.70/241.86 down(f(f(a))) 543.70/241.86 down(f(f(b))) 543.70/241.86 down(f(f(g(x0)))) 543.70/241.86 down(f(f(c))) 543.70/241.86 down(f(f(fresh_constant))) 543.70/241.86 down(g(g(a))) 543.70/241.86 down(g(g(f(x0)))) 543.70/241.86 down(g(g(b))) 543.70/241.86 down(g(g(c))) 543.70/241.86 down(g(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) 543.70/241.86 down(f(f(f(g(x0))))) 543.70/241.86 down(f(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) 543.70/241.86 down(g(g(g(f(x0))))) 543.70/241.86 down(g(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(x0)))))) 543.70/241.86 down(f(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(x0)))))) 543.70/241.86 down(g(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(x0))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(x0))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 f_flat(up(x0)) 543.70/241.86 g_flat(up(x0)) 543.70/241.86 543.70/241.86 We have to consider all minimal (P,Q,R)-chains. 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (651) TransformationProof (EQUIVALENT) 543.70/241.86 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.86 543.70/241.86 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.70/241.86 543.70/241.86 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (652) 543.70/241.86 Obligation: 543.70/241.86 Q DP problem: 543.70/241.86 The TRS P consists of the following rules: 543.70/241.86 543.70/241.86 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.86 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.86 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.86 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.86 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.86 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.86 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.86 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.86 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.86 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.86 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.86 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.86 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.86 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.86 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.86 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.86 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.86 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.86 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.86 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.86 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.86 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.86 543.70/241.86 The TRS R consists of the following rules: 543.70/241.86 543.70/241.86 down(a) -> up(f(a)) 543.70/241.86 down(b) -> up(g(b)) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.86 down(f(a)) -> f_flat(down(a)) 543.70/241.86 down(f(b)) -> f_flat(down(b)) 543.70/241.86 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.86 down(f(c)) -> f_flat(down(c)) 543.70/241.86 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.86 down(g(a)) -> g_flat(down(a)) 543.70/241.86 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.86 down(g(b)) -> g_flat(down(b)) 543.70/241.86 down(g(c)) -> g_flat(down(c)) 543.70/241.86 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.86 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.86 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.86 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.86 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.86 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.86 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.86 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.86 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.86 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.86 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.86 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.86 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.86 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.86 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.86 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.86 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.86 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.86 543.70/241.86 The set Q consists of the following terms: 543.70/241.86 543.70/241.86 down(a) 543.70/241.86 down(b) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.86 down(f(a)) 543.70/241.86 down(f(b)) 543.70/241.86 down(f(g(x0))) 543.70/241.86 down(f(c)) 543.70/241.86 down(f(fresh_constant)) 543.70/241.86 down(g(a)) 543.70/241.86 down(g(f(x0))) 543.70/241.86 down(g(b)) 543.70/241.86 down(g(c)) 543.70/241.86 down(g(fresh_constant)) 543.70/241.86 down(f(f(a))) 543.70/241.86 down(f(f(b))) 543.70/241.86 down(f(f(g(x0)))) 543.70/241.86 down(f(f(c))) 543.70/241.86 down(f(f(fresh_constant))) 543.70/241.86 down(g(g(a))) 543.70/241.86 down(g(g(f(x0)))) 543.70/241.86 down(g(g(b))) 543.70/241.86 down(g(g(c))) 543.70/241.86 down(g(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) 543.70/241.86 down(f(f(f(g(x0))))) 543.70/241.86 down(f(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) 543.70/241.86 down(g(g(g(f(x0))))) 543.70/241.86 down(g(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(x0)))))) 543.70/241.86 down(f(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(x0)))))) 543.70/241.86 down(g(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(x0))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(x0))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 f_flat(up(x0)) 543.70/241.86 g_flat(up(x0)) 543.70/241.86 543.70/241.86 We have to consider all minimal (P,Q,R)-chains. 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (653) TransformationProof (EQUIVALENT) 543.70/241.86 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.86 543.70/241.86 (TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))),TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.70/241.86 543.70/241.86 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (654) 543.70/241.86 Obligation: 543.70/241.86 Q DP problem: 543.70/241.86 The TRS P consists of the following rules: 543.70/241.86 543.70/241.86 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.86 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.86 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.86 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.86 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.86 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.86 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.86 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.86 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.86 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.86 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.86 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.86 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.86 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.86 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.86 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.86 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.86 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.86 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.86 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.86 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.86 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.86 543.70/241.86 The TRS R consists of the following rules: 543.70/241.86 543.70/241.86 down(a) -> up(f(a)) 543.70/241.86 down(b) -> up(g(b)) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.86 down(f(a)) -> f_flat(down(a)) 543.70/241.86 down(f(b)) -> f_flat(down(b)) 543.70/241.86 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.86 down(f(c)) -> f_flat(down(c)) 543.70/241.86 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.86 down(g(a)) -> g_flat(down(a)) 543.70/241.86 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.86 down(g(b)) -> g_flat(down(b)) 543.70/241.86 down(g(c)) -> g_flat(down(c)) 543.70/241.86 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.86 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.86 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.86 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.86 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.86 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.86 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.86 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.86 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.86 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.86 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.86 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.86 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.86 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.86 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.86 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.86 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.86 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.86 543.70/241.86 The set Q consists of the following terms: 543.70/241.86 543.70/241.86 down(a) 543.70/241.86 down(b) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.86 down(f(a)) 543.70/241.86 down(f(b)) 543.70/241.86 down(f(g(x0))) 543.70/241.86 down(f(c)) 543.70/241.86 down(f(fresh_constant)) 543.70/241.86 down(g(a)) 543.70/241.86 down(g(f(x0))) 543.70/241.86 down(g(b)) 543.70/241.86 down(g(c)) 543.70/241.86 down(g(fresh_constant)) 543.70/241.86 down(f(f(a))) 543.70/241.86 down(f(f(b))) 543.70/241.86 down(f(f(g(x0)))) 543.70/241.86 down(f(f(c))) 543.70/241.86 down(f(f(fresh_constant))) 543.70/241.86 down(g(g(a))) 543.70/241.86 down(g(g(f(x0)))) 543.70/241.86 down(g(g(b))) 543.70/241.86 down(g(g(c))) 543.70/241.86 down(g(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) 543.70/241.86 down(f(f(f(g(x0))))) 543.70/241.86 down(f(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) 543.70/241.86 down(g(g(g(f(x0))))) 543.70/241.86 down(g(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(x0)))))) 543.70/241.86 down(f(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(x0)))))) 543.70/241.86 down(g(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(x0))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(x0))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 f_flat(up(x0)) 543.70/241.86 g_flat(up(x0)) 543.70/241.86 543.70/241.86 We have to consider all minimal (P,Q,R)-chains. 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (655) TransformationProof (EQUIVALENT) 543.70/241.86 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.86 543.70/241.86 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.70/241.86 543.70/241.86 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (656) 543.70/241.86 Obligation: 543.70/241.86 Q DP problem: 543.70/241.86 The TRS P consists of the following rules: 543.70/241.86 543.70/241.86 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.86 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.86 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.86 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.86 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.86 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.86 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.86 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.86 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.86 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.86 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.86 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.86 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.86 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.86 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.86 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.86 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.86 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.86 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.86 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.86 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.86 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.86 543.70/241.86 The TRS R consists of the following rules: 543.70/241.86 543.70/241.86 down(a) -> up(f(a)) 543.70/241.86 down(b) -> up(g(b)) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.86 down(f(a)) -> f_flat(down(a)) 543.70/241.86 down(f(b)) -> f_flat(down(b)) 543.70/241.86 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.86 down(f(c)) -> f_flat(down(c)) 543.70/241.86 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.86 down(g(a)) -> g_flat(down(a)) 543.70/241.86 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.86 down(g(b)) -> g_flat(down(b)) 543.70/241.86 down(g(c)) -> g_flat(down(c)) 543.70/241.86 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.86 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.86 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.86 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.86 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.86 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.86 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.86 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.86 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.86 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.86 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.86 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.86 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.86 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.86 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.86 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.86 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.86 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.86 543.70/241.86 The set Q consists of the following terms: 543.70/241.86 543.70/241.86 down(a) 543.70/241.86 down(b) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.86 down(f(a)) 543.70/241.86 down(f(b)) 543.70/241.86 down(f(g(x0))) 543.70/241.86 down(f(c)) 543.70/241.86 down(f(fresh_constant)) 543.70/241.86 down(g(a)) 543.70/241.86 down(g(f(x0))) 543.70/241.86 down(g(b)) 543.70/241.86 down(g(c)) 543.70/241.86 down(g(fresh_constant)) 543.70/241.86 down(f(f(a))) 543.70/241.86 down(f(f(b))) 543.70/241.86 down(f(f(g(x0)))) 543.70/241.86 down(f(f(c))) 543.70/241.86 down(f(f(fresh_constant))) 543.70/241.86 down(g(g(a))) 543.70/241.86 down(g(g(f(x0)))) 543.70/241.86 down(g(g(b))) 543.70/241.86 down(g(g(c))) 543.70/241.86 down(g(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) 543.70/241.86 down(f(f(f(g(x0))))) 543.70/241.86 down(f(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) 543.70/241.86 down(g(g(g(f(x0))))) 543.70/241.86 down(g(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(x0)))))) 543.70/241.86 down(f(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(x0)))))) 543.70/241.86 down(g(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(x0))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(x0))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 f_flat(up(x0)) 543.70/241.86 g_flat(up(x0)) 543.70/241.86 543.70/241.86 We have to consider all minimal (P,Q,R)-chains. 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (657) TransformationProof (EQUIVALENT) 543.70/241.86 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.86 543.70/241.86 (TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))),TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.70/241.86 543.70/241.86 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (658) 543.70/241.86 Obligation: 543.70/241.86 Q DP problem: 543.70/241.86 The TRS P consists of the following rules: 543.70/241.86 543.70/241.86 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.86 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.86 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.86 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.86 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.86 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.86 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.86 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.86 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.86 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.86 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.86 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.86 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.86 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.86 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.86 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.86 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.86 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.86 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.86 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.86 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.86 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.86 543.70/241.86 The TRS R consists of the following rules: 543.70/241.86 543.70/241.86 down(a) -> up(f(a)) 543.70/241.86 down(b) -> up(g(b)) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.86 down(f(a)) -> f_flat(down(a)) 543.70/241.86 down(f(b)) -> f_flat(down(b)) 543.70/241.86 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.86 down(f(c)) -> f_flat(down(c)) 543.70/241.86 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.86 down(g(a)) -> g_flat(down(a)) 543.70/241.86 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.86 down(g(b)) -> g_flat(down(b)) 543.70/241.86 down(g(c)) -> g_flat(down(c)) 543.70/241.86 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.86 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.86 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.86 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.86 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.86 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.86 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.86 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.86 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.86 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.86 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.86 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.86 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.86 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.86 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.86 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.86 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.86 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.86 543.70/241.86 The set Q consists of the following terms: 543.70/241.86 543.70/241.86 down(a) 543.70/241.86 down(b) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.86 down(f(a)) 543.70/241.86 down(f(b)) 543.70/241.86 down(f(g(x0))) 543.70/241.86 down(f(c)) 543.70/241.86 down(f(fresh_constant)) 543.70/241.86 down(g(a)) 543.70/241.86 down(g(f(x0))) 543.70/241.86 down(g(b)) 543.70/241.86 down(g(c)) 543.70/241.86 down(g(fresh_constant)) 543.70/241.86 down(f(f(a))) 543.70/241.86 down(f(f(b))) 543.70/241.86 down(f(f(g(x0)))) 543.70/241.86 down(f(f(c))) 543.70/241.86 down(f(f(fresh_constant))) 543.70/241.86 down(g(g(a))) 543.70/241.86 down(g(g(f(x0)))) 543.70/241.86 down(g(g(b))) 543.70/241.86 down(g(g(c))) 543.70/241.86 down(g(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) 543.70/241.86 down(f(f(f(g(x0))))) 543.70/241.86 down(f(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) 543.70/241.86 down(g(g(g(f(x0))))) 543.70/241.86 down(g(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(x0)))))) 543.70/241.86 down(f(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(x0)))))) 543.70/241.86 down(g(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(x0))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(x0))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 f_flat(up(x0)) 543.70/241.86 g_flat(up(x0)) 543.70/241.86 543.70/241.86 We have to consider all minimal (P,Q,R)-chains. 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (659) TransformationProof (EQUIVALENT) 543.70/241.86 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.86 543.70/241.86 (TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))),TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.70/241.86 543.70/241.86 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (660) 543.70/241.86 Obligation: 543.70/241.86 Q DP problem: 543.70/241.86 The TRS P consists of the following rules: 543.70/241.86 543.70/241.86 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.86 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.86 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.86 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.86 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.86 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.86 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.86 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.86 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.86 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.86 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.86 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.86 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.86 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.86 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.86 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.86 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.86 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.86 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.86 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.86 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.86 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.86 543.70/241.86 The TRS R consists of the following rules: 543.70/241.86 543.70/241.86 down(a) -> up(f(a)) 543.70/241.86 down(b) -> up(g(b)) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.86 down(f(a)) -> f_flat(down(a)) 543.70/241.86 down(f(b)) -> f_flat(down(b)) 543.70/241.86 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.86 down(f(c)) -> f_flat(down(c)) 543.70/241.86 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.86 down(g(a)) -> g_flat(down(a)) 543.70/241.86 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.86 down(g(b)) -> g_flat(down(b)) 543.70/241.86 down(g(c)) -> g_flat(down(c)) 543.70/241.86 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.86 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.86 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.86 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.86 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.86 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.86 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.86 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.86 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.86 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.86 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.86 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.86 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.86 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.86 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.86 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.86 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.86 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.86 543.70/241.86 The set Q consists of the following terms: 543.70/241.86 543.70/241.86 down(a) 543.70/241.86 down(b) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.86 down(f(a)) 543.70/241.86 down(f(b)) 543.70/241.86 down(f(g(x0))) 543.70/241.86 down(f(c)) 543.70/241.86 down(f(fresh_constant)) 543.70/241.86 down(g(a)) 543.70/241.86 down(g(f(x0))) 543.70/241.86 down(g(b)) 543.70/241.86 down(g(c)) 543.70/241.86 down(g(fresh_constant)) 543.70/241.86 down(f(f(a))) 543.70/241.86 down(f(f(b))) 543.70/241.86 down(f(f(g(x0)))) 543.70/241.86 down(f(f(c))) 543.70/241.86 down(f(f(fresh_constant))) 543.70/241.86 down(g(g(a))) 543.70/241.86 down(g(g(f(x0)))) 543.70/241.86 down(g(g(b))) 543.70/241.86 down(g(g(c))) 543.70/241.86 down(g(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) 543.70/241.86 down(f(f(f(g(x0))))) 543.70/241.86 down(f(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) 543.70/241.86 down(g(g(g(f(x0))))) 543.70/241.86 down(g(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(x0)))))) 543.70/241.86 down(f(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(x0)))))) 543.70/241.86 down(g(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(x0))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(x0))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 f_flat(up(x0)) 543.70/241.86 g_flat(up(x0)) 543.70/241.86 543.70/241.86 We have to consider all minimal (P,Q,R)-chains. 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (661) TransformationProof (EQUIVALENT) 543.70/241.86 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.86 543.70/241.86 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.70/241.86 543.70/241.86 543.70/241.86 ---------------------------------------- 543.70/241.86 543.70/241.86 (662) 543.70/241.86 Obligation: 543.70/241.86 Q DP problem: 543.70/241.86 The TRS P consists of the following rules: 543.70/241.86 543.70/241.86 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.86 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.86 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.86 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.86 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.86 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.86 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.86 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.86 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.86 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.86 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.86 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.86 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.86 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.86 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.86 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.86 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.86 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.86 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.86 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.86 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.86 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.86 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.86 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.86 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.86 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.86 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.86 543.70/241.86 The TRS R consists of the following rules: 543.70/241.86 543.70/241.86 down(a) -> up(f(a)) 543.70/241.86 down(b) -> up(g(b)) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.86 down(f(a)) -> f_flat(down(a)) 543.70/241.86 down(f(b)) -> f_flat(down(b)) 543.70/241.86 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.86 down(f(c)) -> f_flat(down(c)) 543.70/241.86 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.86 down(g(a)) -> g_flat(down(a)) 543.70/241.86 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.86 down(g(b)) -> g_flat(down(b)) 543.70/241.86 down(g(c)) -> g_flat(down(c)) 543.70/241.86 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.86 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.86 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.86 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.86 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.86 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.86 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.86 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.86 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.86 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.86 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.86 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.86 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.86 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.86 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.86 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.86 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.86 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.86 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.86 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.86 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.86 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.86 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.86 543.70/241.86 The set Q consists of the following terms: 543.70/241.86 543.70/241.86 down(a) 543.70/241.86 down(b) 543.70/241.86 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.86 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.86 down(f(a)) 543.70/241.86 down(f(b)) 543.70/241.86 down(f(g(x0))) 543.70/241.86 down(f(c)) 543.70/241.86 down(f(fresh_constant)) 543.70/241.86 down(g(a)) 543.70/241.86 down(g(f(x0))) 543.70/241.86 down(g(b)) 543.70/241.86 down(g(c)) 543.70/241.86 down(g(fresh_constant)) 543.70/241.86 down(f(f(a))) 543.70/241.86 down(f(f(b))) 543.70/241.86 down(f(f(g(x0)))) 543.70/241.86 down(f(f(c))) 543.70/241.86 down(f(f(fresh_constant))) 543.70/241.86 down(g(g(a))) 543.70/241.86 down(g(g(f(x0)))) 543.70/241.86 down(g(g(b))) 543.70/241.86 down(g(g(c))) 543.70/241.86 down(g(g(fresh_constant))) 543.70/241.86 down(f(f(f(a)))) 543.70/241.86 down(f(f(f(b)))) 543.70/241.86 down(f(f(f(g(x0))))) 543.70/241.86 down(f(f(f(c)))) 543.70/241.86 down(f(f(f(fresh_constant)))) 543.70/241.86 down(g(g(g(a)))) 543.70/241.86 down(g(g(g(f(x0))))) 543.70/241.86 down(g(g(g(b)))) 543.70/241.86 down(g(g(g(c)))) 543.70/241.86 down(g(g(g(fresh_constant)))) 543.70/241.86 down(f(f(f(f(a))))) 543.70/241.86 down(f(f(f(f(b))))) 543.70/241.86 down(f(f(f(f(g(x0)))))) 543.70/241.86 down(f(f(f(f(c))))) 543.70/241.86 down(f(f(f(f(fresh_constant))))) 543.70/241.86 down(g(g(g(g(a))))) 543.70/241.86 down(g(g(g(g(f(x0)))))) 543.70/241.86 down(g(g(g(g(b))))) 543.70/241.86 down(g(g(g(g(c))))) 543.70/241.86 down(g(g(g(g(fresh_constant))))) 543.70/241.86 down(f(f(f(f(f(a)))))) 543.70/241.86 down(f(f(f(f(f(b)))))) 543.70/241.86 down(f(f(f(f(f(g(x0))))))) 543.70/241.86 down(f(f(f(f(f(c)))))) 543.70/241.86 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.86 down(g(g(g(g(g(a)))))) 543.70/241.86 down(g(g(g(g(g(f(x0))))))) 543.70/241.86 down(g(g(g(g(g(b)))))) 543.70/241.86 down(g(g(g(g(g(c)))))) 543.70/241.86 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.86 down(f(f(f(f(f(f(a))))))) 543.70/241.86 down(f(f(f(f(f(f(b))))))) 543.70/241.86 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.86 down(f(f(f(f(f(f(c))))))) 543.70/241.86 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.86 down(g(g(g(g(g(g(a))))))) 543.70/241.86 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.86 down(g(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 f_flat(up(x0)) 543.70/241.87 g_flat(up(x0)) 543.70/241.87 543.70/241.87 We have to consider all minimal (P,Q,R)-chains. 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (663) TransformationProof (EQUIVALENT) 543.70/241.87 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.87 543.70/241.87 (TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))),TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.70/241.87 543.70/241.87 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (664) 543.70/241.87 Obligation: 543.70/241.87 Q DP problem: 543.70/241.87 The TRS P consists of the following rules: 543.70/241.87 543.70/241.87 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.87 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.87 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.87 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.87 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.87 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.87 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.87 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.87 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.87 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.87 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.87 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.87 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.87 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.87 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.87 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.87 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.87 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.87 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.87 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.87 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.87 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.87 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.87 543.70/241.87 The TRS R consists of the following rules: 543.70/241.87 543.70/241.87 down(a) -> up(f(a)) 543.70/241.87 down(b) -> up(g(b)) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.87 down(f(a)) -> f_flat(down(a)) 543.70/241.87 down(f(b)) -> f_flat(down(b)) 543.70/241.87 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.87 down(f(c)) -> f_flat(down(c)) 543.70/241.87 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.87 down(g(a)) -> g_flat(down(a)) 543.70/241.87 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.87 down(g(b)) -> g_flat(down(b)) 543.70/241.87 down(g(c)) -> g_flat(down(c)) 543.70/241.87 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.87 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.87 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.87 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.87 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.87 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.87 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.87 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.87 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.87 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.87 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.87 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.87 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.87 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.87 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.87 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.87 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.87 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.87 543.70/241.87 The set Q consists of the following terms: 543.70/241.87 543.70/241.87 down(a) 543.70/241.87 down(b) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.87 down(f(a)) 543.70/241.87 down(f(b)) 543.70/241.87 down(f(g(x0))) 543.70/241.87 down(f(c)) 543.70/241.87 down(f(fresh_constant)) 543.70/241.87 down(g(a)) 543.70/241.87 down(g(f(x0))) 543.70/241.87 down(g(b)) 543.70/241.87 down(g(c)) 543.70/241.87 down(g(fresh_constant)) 543.70/241.87 down(f(f(a))) 543.70/241.87 down(f(f(b))) 543.70/241.87 down(f(f(g(x0)))) 543.70/241.87 down(f(f(c))) 543.70/241.87 down(f(f(fresh_constant))) 543.70/241.87 down(g(g(a))) 543.70/241.87 down(g(g(f(x0)))) 543.70/241.87 down(g(g(b))) 543.70/241.87 down(g(g(c))) 543.70/241.87 down(g(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) 543.70/241.87 down(f(f(f(g(x0))))) 543.70/241.87 down(f(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) 543.70/241.87 down(g(g(g(f(x0))))) 543.70/241.87 down(g(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(x0)))))) 543.70/241.87 down(f(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(x0)))))) 543.70/241.87 down(g(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(x0))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(x0))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 f_flat(up(x0)) 543.70/241.87 g_flat(up(x0)) 543.70/241.87 543.70/241.87 We have to consider all minimal (P,Q,R)-chains. 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (665) TransformationProof (EQUIVALENT) 543.70/241.87 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.87 543.70/241.87 (TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))),TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.70/241.87 543.70/241.87 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (666) 543.70/241.87 Obligation: 543.70/241.87 Q DP problem: 543.70/241.87 The TRS P consists of the following rules: 543.70/241.87 543.70/241.87 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.87 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.87 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.87 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.87 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.87 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.87 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.87 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.87 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.87 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.87 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.87 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.87 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.87 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.87 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.87 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.87 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.87 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.87 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.87 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.87 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.87 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.87 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.87 543.70/241.87 The TRS R consists of the following rules: 543.70/241.87 543.70/241.87 down(a) -> up(f(a)) 543.70/241.87 down(b) -> up(g(b)) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.87 down(f(a)) -> f_flat(down(a)) 543.70/241.87 down(f(b)) -> f_flat(down(b)) 543.70/241.87 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.87 down(f(c)) -> f_flat(down(c)) 543.70/241.87 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.87 down(g(a)) -> g_flat(down(a)) 543.70/241.87 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.87 down(g(b)) -> g_flat(down(b)) 543.70/241.87 down(g(c)) -> g_flat(down(c)) 543.70/241.87 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.87 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.87 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.87 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.87 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.87 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.87 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.87 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.87 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.87 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.87 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.87 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.87 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.87 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.87 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.87 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.87 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.87 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.87 543.70/241.87 The set Q consists of the following terms: 543.70/241.87 543.70/241.87 down(a) 543.70/241.87 down(b) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.87 down(f(a)) 543.70/241.87 down(f(b)) 543.70/241.87 down(f(g(x0))) 543.70/241.87 down(f(c)) 543.70/241.87 down(f(fresh_constant)) 543.70/241.87 down(g(a)) 543.70/241.87 down(g(f(x0))) 543.70/241.87 down(g(b)) 543.70/241.87 down(g(c)) 543.70/241.87 down(g(fresh_constant)) 543.70/241.87 down(f(f(a))) 543.70/241.87 down(f(f(b))) 543.70/241.87 down(f(f(g(x0)))) 543.70/241.87 down(f(f(c))) 543.70/241.87 down(f(f(fresh_constant))) 543.70/241.87 down(g(g(a))) 543.70/241.87 down(g(g(f(x0)))) 543.70/241.87 down(g(g(b))) 543.70/241.87 down(g(g(c))) 543.70/241.87 down(g(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) 543.70/241.87 down(f(f(f(g(x0))))) 543.70/241.87 down(f(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) 543.70/241.87 down(g(g(g(f(x0))))) 543.70/241.87 down(g(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(x0)))))) 543.70/241.87 down(f(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(x0)))))) 543.70/241.87 down(g(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(x0))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(x0))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 f_flat(up(x0)) 543.70/241.87 g_flat(up(x0)) 543.70/241.87 543.70/241.87 We have to consider all minimal (P,Q,R)-chains. 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (667) TransformationProof (EQUIVALENT) 543.70/241.87 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.87 543.70/241.87 (TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))),TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.70/241.87 543.70/241.87 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (668) 543.70/241.87 Obligation: 543.70/241.87 Q DP problem: 543.70/241.87 The TRS P consists of the following rules: 543.70/241.87 543.70/241.87 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.87 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.87 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.87 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.87 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.87 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.87 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.87 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.87 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.87 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.87 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.87 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.87 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.87 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.87 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.87 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.87 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.87 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.87 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.87 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.87 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.87 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.87 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.87 543.70/241.87 The TRS R consists of the following rules: 543.70/241.87 543.70/241.87 down(a) -> up(f(a)) 543.70/241.87 down(b) -> up(g(b)) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.87 down(f(a)) -> f_flat(down(a)) 543.70/241.87 down(f(b)) -> f_flat(down(b)) 543.70/241.87 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.87 down(f(c)) -> f_flat(down(c)) 543.70/241.87 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.87 down(g(a)) -> g_flat(down(a)) 543.70/241.87 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.87 down(g(b)) -> g_flat(down(b)) 543.70/241.87 down(g(c)) -> g_flat(down(c)) 543.70/241.87 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.87 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.87 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.87 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.87 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.87 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.87 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.87 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.87 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.87 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.87 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.87 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.87 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.87 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.87 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.87 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.87 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.87 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.87 543.70/241.87 The set Q consists of the following terms: 543.70/241.87 543.70/241.87 down(a) 543.70/241.87 down(b) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.87 down(f(a)) 543.70/241.87 down(f(b)) 543.70/241.87 down(f(g(x0))) 543.70/241.87 down(f(c)) 543.70/241.87 down(f(fresh_constant)) 543.70/241.87 down(g(a)) 543.70/241.87 down(g(f(x0))) 543.70/241.87 down(g(b)) 543.70/241.87 down(g(c)) 543.70/241.87 down(g(fresh_constant)) 543.70/241.87 down(f(f(a))) 543.70/241.87 down(f(f(b))) 543.70/241.87 down(f(f(g(x0)))) 543.70/241.87 down(f(f(c))) 543.70/241.87 down(f(f(fresh_constant))) 543.70/241.87 down(g(g(a))) 543.70/241.87 down(g(g(f(x0)))) 543.70/241.87 down(g(g(b))) 543.70/241.87 down(g(g(c))) 543.70/241.87 down(g(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) 543.70/241.87 down(f(f(f(g(x0))))) 543.70/241.87 down(f(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) 543.70/241.87 down(g(g(g(f(x0))))) 543.70/241.87 down(g(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(x0)))))) 543.70/241.87 down(f(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(x0)))))) 543.70/241.87 down(g(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(x0))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(x0))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 f_flat(up(x0)) 543.70/241.87 g_flat(up(x0)) 543.70/241.87 543.70/241.87 We have to consider all minimal (P,Q,R)-chains. 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (669) TransformationProof (EQUIVALENT) 543.70/241.87 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.87 543.70/241.87 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.70/241.87 543.70/241.87 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (670) 543.70/241.87 Obligation: 543.70/241.87 Q DP problem: 543.70/241.87 The TRS P consists of the following rules: 543.70/241.87 543.70/241.87 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.87 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.87 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.87 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.87 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.87 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.87 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.87 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.87 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.87 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.87 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.87 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.87 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.87 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.87 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.87 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.87 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.87 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.87 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.87 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.87 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.87 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.87 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.87 543.70/241.87 The TRS R consists of the following rules: 543.70/241.87 543.70/241.87 down(a) -> up(f(a)) 543.70/241.87 down(b) -> up(g(b)) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.87 down(f(a)) -> f_flat(down(a)) 543.70/241.87 down(f(b)) -> f_flat(down(b)) 543.70/241.87 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.87 down(f(c)) -> f_flat(down(c)) 543.70/241.87 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.87 down(g(a)) -> g_flat(down(a)) 543.70/241.87 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.87 down(g(b)) -> g_flat(down(b)) 543.70/241.87 down(g(c)) -> g_flat(down(c)) 543.70/241.87 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.87 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.87 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.87 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.87 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.87 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.87 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.87 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.87 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.87 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.87 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.87 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.87 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.87 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.87 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.87 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.87 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.87 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.87 543.70/241.87 The set Q consists of the following terms: 543.70/241.87 543.70/241.87 down(a) 543.70/241.87 down(b) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.87 down(f(a)) 543.70/241.87 down(f(b)) 543.70/241.87 down(f(g(x0))) 543.70/241.87 down(f(c)) 543.70/241.87 down(f(fresh_constant)) 543.70/241.87 down(g(a)) 543.70/241.87 down(g(f(x0))) 543.70/241.87 down(g(b)) 543.70/241.87 down(g(c)) 543.70/241.87 down(g(fresh_constant)) 543.70/241.87 down(f(f(a))) 543.70/241.87 down(f(f(b))) 543.70/241.87 down(f(f(g(x0)))) 543.70/241.87 down(f(f(c))) 543.70/241.87 down(f(f(fresh_constant))) 543.70/241.87 down(g(g(a))) 543.70/241.87 down(g(g(f(x0)))) 543.70/241.87 down(g(g(b))) 543.70/241.87 down(g(g(c))) 543.70/241.87 down(g(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) 543.70/241.87 down(f(f(f(g(x0))))) 543.70/241.87 down(f(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) 543.70/241.87 down(g(g(g(f(x0))))) 543.70/241.87 down(g(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(x0)))))) 543.70/241.87 down(f(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(x0)))))) 543.70/241.87 down(g(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(x0))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(x0))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 f_flat(up(x0)) 543.70/241.87 g_flat(up(x0)) 543.70/241.87 543.70/241.87 We have to consider all minimal (P,Q,R)-chains. 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (671) TransformationProof (EQUIVALENT) 543.70/241.87 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.87 543.70/241.87 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.70/241.87 543.70/241.87 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (672) 543.70/241.87 Obligation: 543.70/241.87 Q DP problem: 543.70/241.87 The TRS P consists of the following rules: 543.70/241.87 543.70/241.87 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.87 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.87 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.87 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.87 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.87 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.87 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.87 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.87 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.87 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.87 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.87 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.87 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.87 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.87 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.87 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.87 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.87 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.87 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.87 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.87 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.87 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.87 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.87 543.70/241.87 The TRS R consists of the following rules: 543.70/241.87 543.70/241.87 down(a) -> up(f(a)) 543.70/241.87 down(b) -> up(g(b)) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.87 down(f(a)) -> f_flat(down(a)) 543.70/241.87 down(f(b)) -> f_flat(down(b)) 543.70/241.87 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.87 down(f(c)) -> f_flat(down(c)) 543.70/241.87 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.87 down(g(a)) -> g_flat(down(a)) 543.70/241.87 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.87 down(g(b)) -> g_flat(down(b)) 543.70/241.87 down(g(c)) -> g_flat(down(c)) 543.70/241.87 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.87 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.87 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.87 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.87 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.87 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.87 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.87 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.87 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.87 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.87 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.87 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.87 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.87 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.87 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.87 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.87 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.87 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.87 543.70/241.87 The set Q consists of the following terms: 543.70/241.87 543.70/241.87 down(a) 543.70/241.87 down(b) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.87 down(f(a)) 543.70/241.87 down(f(b)) 543.70/241.87 down(f(g(x0))) 543.70/241.87 down(f(c)) 543.70/241.87 down(f(fresh_constant)) 543.70/241.87 down(g(a)) 543.70/241.87 down(g(f(x0))) 543.70/241.87 down(g(b)) 543.70/241.87 down(g(c)) 543.70/241.87 down(g(fresh_constant)) 543.70/241.87 down(f(f(a))) 543.70/241.87 down(f(f(b))) 543.70/241.87 down(f(f(g(x0)))) 543.70/241.87 down(f(f(c))) 543.70/241.87 down(f(f(fresh_constant))) 543.70/241.87 down(g(g(a))) 543.70/241.87 down(g(g(f(x0)))) 543.70/241.87 down(g(g(b))) 543.70/241.87 down(g(g(c))) 543.70/241.87 down(g(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) 543.70/241.87 down(f(f(f(g(x0))))) 543.70/241.87 down(f(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) 543.70/241.87 down(g(g(g(f(x0))))) 543.70/241.87 down(g(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(x0)))))) 543.70/241.87 down(f(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(x0)))))) 543.70/241.87 down(g(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(x0))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(x0))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 f_flat(up(x0)) 543.70/241.87 g_flat(up(x0)) 543.70/241.87 543.70/241.87 We have to consider all minimal (P,Q,R)-chains. 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (673) TransformationProof (EQUIVALENT) 543.70/241.87 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.87 543.70/241.87 (TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))),TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.70/241.87 543.70/241.87 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (674) 543.70/241.87 Obligation: 543.70/241.87 Q DP problem: 543.70/241.87 The TRS P consists of the following rules: 543.70/241.87 543.70/241.87 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.87 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.87 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.87 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.87 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.87 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.87 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.87 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.87 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.87 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.87 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.87 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.87 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.87 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.87 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.87 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.87 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.87 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.87 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.87 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.87 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.87 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.87 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.87 543.70/241.87 The TRS R consists of the following rules: 543.70/241.87 543.70/241.87 down(a) -> up(f(a)) 543.70/241.87 down(b) -> up(g(b)) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.87 down(f(a)) -> f_flat(down(a)) 543.70/241.87 down(f(b)) -> f_flat(down(b)) 543.70/241.87 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.87 down(f(c)) -> f_flat(down(c)) 543.70/241.87 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.87 down(g(a)) -> g_flat(down(a)) 543.70/241.87 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.87 down(g(b)) -> g_flat(down(b)) 543.70/241.87 down(g(c)) -> g_flat(down(c)) 543.70/241.87 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.87 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.87 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.87 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.87 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.87 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.87 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.87 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.87 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.87 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.87 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.87 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.87 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.87 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.87 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.87 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.87 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.87 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.87 543.70/241.87 The set Q consists of the following terms: 543.70/241.87 543.70/241.87 down(a) 543.70/241.87 down(b) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.87 down(f(a)) 543.70/241.87 down(f(b)) 543.70/241.87 down(f(g(x0))) 543.70/241.87 down(f(c)) 543.70/241.87 down(f(fresh_constant)) 543.70/241.87 down(g(a)) 543.70/241.87 down(g(f(x0))) 543.70/241.87 down(g(b)) 543.70/241.87 down(g(c)) 543.70/241.87 down(g(fresh_constant)) 543.70/241.87 down(f(f(a))) 543.70/241.87 down(f(f(b))) 543.70/241.87 down(f(f(g(x0)))) 543.70/241.87 down(f(f(c))) 543.70/241.87 down(f(f(fresh_constant))) 543.70/241.87 down(g(g(a))) 543.70/241.87 down(g(g(f(x0)))) 543.70/241.87 down(g(g(b))) 543.70/241.87 down(g(g(c))) 543.70/241.87 down(g(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) 543.70/241.87 down(f(f(f(g(x0))))) 543.70/241.87 down(f(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) 543.70/241.87 down(g(g(g(f(x0))))) 543.70/241.87 down(g(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(x0)))))) 543.70/241.87 down(f(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(x0)))))) 543.70/241.87 down(g(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(x0))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(x0))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 f_flat(up(x0)) 543.70/241.87 g_flat(up(x0)) 543.70/241.87 543.70/241.87 We have to consider all minimal (P,Q,R)-chains. 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (675) TransformationProof (EQUIVALENT) 543.70/241.87 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.87 543.70/241.87 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.70/241.87 543.70/241.87 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (676) 543.70/241.87 Obligation: 543.70/241.87 Q DP problem: 543.70/241.87 The TRS P consists of the following rules: 543.70/241.87 543.70/241.87 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.87 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.87 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.87 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.87 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.87 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.87 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.87 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.87 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.87 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.87 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.87 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.87 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.87 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.87 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.87 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.87 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.87 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.87 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.87 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.87 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.87 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.87 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.87 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.87 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.87 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.87 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.87 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.87 543.70/241.87 The TRS R consists of the following rules: 543.70/241.87 543.70/241.87 down(a) -> up(f(a)) 543.70/241.87 down(b) -> up(g(b)) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.87 down(f(a)) -> f_flat(down(a)) 543.70/241.87 down(f(b)) -> f_flat(down(b)) 543.70/241.87 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.87 down(f(c)) -> f_flat(down(c)) 543.70/241.87 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.87 down(g(a)) -> g_flat(down(a)) 543.70/241.87 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.87 down(g(b)) -> g_flat(down(b)) 543.70/241.87 down(g(c)) -> g_flat(down(c)) 543.70/241.87 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.87 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.87 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.87 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.87 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.87 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.87 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.87 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.87 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.87 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.87 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.87 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.87 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.87 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.87 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.87 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.87 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.87 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.87 543.70/241.87 The set Q consists of the following terms: 543.70/241.87 543.70/241.87 down(a) 543.70/241.87 down(b) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.87 down(f(a)) 543.70/241.87 down(f(b)) 543.70/241.87 down(f(g(x0))) 543.70/241.87 down(f(c)) 543.70/241.87 down(f(fresh_constant)) 543.70/241.87 down(g(a)) 543.70/241.87 down(g(f(x0))) 543.70/241.87 down(g(b)) 543.70/241.87 down(g(c)) 543.70/241.87 down(g(fresh_constant)) 543.70/241.87 down(f(f(a))) 543.70/241.87 down(f(f(b))) 543.70/241.87 down(f(f(g(x0)))) 543.70/241.87 down(f(f(c))) 543.70/241.87 down(f(f(fresh_constant))) 543.70/241.87 down(g(g(a))) 543.70/241.87 down(g(g(f(x0)))) 543.70/241.87 down(g(g(b))) 543.70/241.87 down(g(g(c))) 543.70/241.87 down(g(g(fresh_constant))) 543.70/241.87 down(f(f(f(a)))) 543.70/241.87 down(f(f(f(b)))) 543.70/241.87 down(f(f(f(g(x0))))) 543.70/241.87 down(f(f(f(c)))) 543.70/241.87 down(f(f(f(fresh_constant)))) 543.70/241.87 down(g(g(g(a)))) 543.70/241.87 down(g(g(g(f(x0))))) 543.70/241.87 down(g(g(g(b)))) 543.70/241.87 down(g(g(g(c)))) 543.70/241.87 down(g(g(g(fresh_constant)))) 543.70/241.87 down(f(f(f(f(a))))) 543.70/241.87 down(f(f(f(f(b))))) 543.70/241.87 down(f(f(f(f(g(x0)))))) 543.70/241.87 down(f(f(f(f(c))))) 543.70/241.87 down(f(f(f(f(fresh_constant))))) 543.70/241.87 down(g(g(g(g(a))))) 543.70/241.87 down(g(g(g(g(f(x0)))))) 543.70/241.87 down(g(g(g(g(b))))) 543.70/241.87 down(g(g(g(g(c))))) 543.70/241.87 down(g(g(g(g(fresh_constant))))) 543.70/241.87 down(f(f(f(f(f(a)))))) 543.70/241.87 down(f(f(f(f(f(b)))))) 543.70/241.87 down(f(f(f(f(f(g(x0))))))) 543.70/241.87 down(f(f(f(f(f(c)))))) 543.70/241.87 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.87 down(g(g(g(g(g(a)))))) 543.70/241.87 down(g(g(g(g(g(f(x0))))))) 543.70/241.87 down(g(g(g(g(g(b)))))) 543.70/241.87 down(g(g(g(g(g(c)))))) 543.70/241.87 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.87 down(f(f(f(f(f(f(a))))))) 543.70/241.87 down(f(f(f(f(f(f(b))))))) 543.70/241.87 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.87 down(f(f(f(f(f(f(c))))))) 543.70/241.87 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.87 down(g(g(g(g(g(g(a))))))) 543.70/241.87 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.87 down(g(g(g(g(g(g(b))))))) 543.70/241.87 down(g(g(g(g(g(g(c))))))) 543.70/241.87 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.87 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.87 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.87 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.87 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.87 f_flat(up(x0)) 543.70/241.87 g_flat(up(x0)) 543.70/241.87 543.70/241.87 We have to consider all minimal (P,Q,R)-chains. 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (677) TransformationProof (EQUIVALENT) 543.70/241.87 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.87 543.70/241.87 (TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))),TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.70/241.87 543.70/241.87 543.70/241.87 ---------------------------------------- 543.70/241.87 543.70/241.87 (678) 543.70/241.87 Obligation: 543.70/241.87 Q DP problem: 543.70/241.88 The TRS P consists of the following rules: 543.70/241.88 543.70/241.88 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.88 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.88 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.88 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.88 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.88 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.88 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.88 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.88 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.88 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.88 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.88 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.88 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.88 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.88 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.88 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.88 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.88 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.88 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.88 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.88 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.88 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.88 543.70/241.88 The TRS R consists of the following rules: 543.70/241.88 543.70/241.88 down(a) -> up(f(a)) 543.70/241.88 down(b) -> up(g(b)) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.88 down(f(a)) -> f_flat(down(a)) 543.70/241.88 down(f(b)) -> f_flat(down(b)) 543.70/241.88 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.88 down(f(c)) -> f_flat(down(c)) 543.70/241.88 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.88 down(g(a)) -> g_flat(down(a)) 543.70/241.88 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.88 down(g(b)) -> g_flat(down(b)) 543.70/241.88 down(g(c)) -> g_flat(down(c)) 543.70/241.88 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.88 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.88 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.88 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.88 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.88 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.88 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.88 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.88 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.88 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.88 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.88 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.88 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.88 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.88 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.88 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.88 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.88 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.88 543.70/241.88 The set Q consists of the following terms: 543.70/241.88 543.70/241.88 down(a) 543.70/241.88 down(b) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.88 down(f(a)) 543.70/241.88 down(f(b)) 543.70/241.88 down(f(g(x0))) 543.70/241.88 down(f(c)) 543.70/241.88 down(f(fresh_constant)) 543.70/241.88 down(g(a)) 543.70/241.88 down(g(f(x0))) 543.70/241.88 down(g(b)) 543.70/241.88 down(g(c)) 543.70/241.88 down(g(fresh_constant)) 543.70/241.88 down(f(f(a))) 543.70/241.88 down(f(f(b))) 543.70/241.88 down(f(f(g(x0)))) 543.70/241.88 down(f(f(c))) 543.70/241.88 down(f(f(fresh_constant))) 543.70/241.88 down(g(g(a))) 543.70/241.88 down(g(g(f(x0)))) 543.70/241.88 down(g(g(b))) 543.70/241.88 down(g(g(c))) 543.70/241.88 down(g(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) 543.70/241.88 down(f(f(f(g(x0))))) 543.70/241.88 down(f(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) 543.70/241.88 down(g(g(g(f(x0))))) 543.70/241.88 down(g(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(x0)))))) 543.70/241.88 down(f(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(x0)))))) 543.70/241.88 down(g(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(x0))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(x0))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 f_flat(up(x0)) 543.70/241.88 g_flat(up(x0)) 543.70/241.88 543.70/241.88 We have to consider all minimal (P,Q,R)-chains. 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (679) TransformationProof (EQUIVALENT) 543.70/241.88 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.88 543.70/241.88 (TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))),TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.70/241.88 543.70/241.88 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (680) 543.70/241.88 Obligation: 543.70/241.88 Q DP problem: 543.70/241.88 The TRS P consists of the following rules: 543.70/241.88 543.70/241.88 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.88 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.88 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.88 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.88 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.88 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.88 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.88 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.88 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.88 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.88 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.88 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.88 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.88 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.88 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.88 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.88 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.88 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.88 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.88 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.88 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.88 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.88 543.70/241.88 The TRS R consists of the following rules: 543.70/241.88 543.70/241.88 down(a) -> up(f(a)) 543.70/241.88 down(b) -> up(g(b)) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.88 down(f(a)) -> f_flat(down(a)) 543.70/241.88 down(f(b)) -> f_flat(down(b)) 543.70/241.88 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.88 down(f(c)) -> f_flat(down(c)) 543.70/241.88 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.88 down(g(a)) -> g_flat(down(a)) 543.70/241.88 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.88 down(g(b)) -> g_flat(down(b)) 543.70/241.88 down(g(c)) -> g_flat(down(c)) 543.70/241.88 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.88 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.88 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.88 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.88 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.88 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.88 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.88 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.88 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.88 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.88 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.88 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.88 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.88 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.88 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.88 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.88 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.88 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.88 543.70/241.88 The set Q consists of the following terms: 543.70/241.88 543.70/241.88 down(a) 543.70/241.88 down(b) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.88 down(f(a)) 543.70/241.88 down(f(b)) 543.70/241.88 down(f(g(x0))) 543.70/241.88 down(f(c)) 543.70/241.88 down(f(fresh_constant)) 543.70/241.88 down(g(a)) 543.70/241.88 down(g(f(x0))) 543.70/241.88 down(g(b)) 543.70/241.88 down(g(c)) 543.70/241.88 down(g(fresh_constant)) 543.70/241.88 down(f(f(a))) 543.70/241.88 down(f(f(b))) 543.70/241.88 down(f(f(g(x0)))) 543.70/241.88 down(f(f(c))) 543.70/241.88 down(f(f(fresh_constant))) 543.70/241.88 down(g(g(a))) 543.70/241.88 down(g(g(f(x0)))) 543.70/241.88 down(g(g(b))) 543.70/241.88 down(g(g(c))) 543.70/241.88 down(g(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) 543.70/241.88 down(f(f(f(g(x0))))) 543.70/241.88 down(f(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) 543.70/241.88 down(g(g(g(f(x0))))) 543.70/241.88 down(g(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(x0)))))) 543.70/241.88 down(f(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(x0)))))) 543.70/241.88 down(g(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(x0))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(x0))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 f_flat(up(x0)) 543.70/241.88 g_flat(up(x0)) 543.70/241.88 543.70/241.88 We have to consider all minimal (P,Q,R)-chains. 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (681) TransformationProof (EQUIVALENT) 543.70/241.88 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.88 543.70/241.88 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.70/241.88 543.70/241.88 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (682) 543.70/241.88 Obligation: 543.70/241.88 Q DP problem: 543.70/241.88 The TRS P consists of the following rules: 543.70/241.88 543.70/241.88 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.88 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.88 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.88 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.88 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.88 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.88 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.88 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.88 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.88 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.88 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.88 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.88 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.88 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.88 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.88 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.88 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.88 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.88 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.88 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.88 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.88 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.88 543.70/241.88 The TRS R consists of the following rules: 543.70/241.88 543.70/241.88 down(a) -> up(f(a)) 543.70/241.88 down(b) -> up(g(b)) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.88 down(f(a)) -> f_flat(down(a)) 543.70/241.88 down(f(b)) -> f_flat(down(b)) 543.70/241.88 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.88 down(f(c)) -> f_flat(down(c)) 543.70/241.88 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.88 down(g(a)) -> g_flat(down(a)) 543.70/241.88 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.88 down(g(b)) -> g_flat(down(b)) 543.70/241.88 down(g(c)) -> g_flat(down(c)) 543.70/241.88 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.88 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.88 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.88 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.88 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.88 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.88 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.88 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.88 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.88 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.88 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.88 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.88 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.88 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.88 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.88 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.88 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.88 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.88 543.70/241.88 The set Q consists of the following terms: 543.70/241.88 543.70/241.88 down(a) 543.70/241.88 down(b) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.88 down(f(a)) 543.70/241.88 down(f(b)) 543.70/241.88 down(f(g(x0))) 543.70/241.88 down(f(c)) 543.70/241.88 down(f(fresh_constant)) 543.70/241.88 down(g(a)) 543.70/241.88 down(g(f(x0))) 543.70/241.88 down(g(b)) 543.70/241.88 down(g(c)) 543.70/241.88 down(g(fresh_constant)) 543.70/241.88 down(f(f(a))) 543.70/241.88 down(f(f(b))) 543.70/241.88 down(f(f(g(x0)))) 543.70/241.88 down(f(f(c))) 543.70/241.88 down(f(f(fresh_constant))) 543.70/241.88 down(g(g(a))) 543.70/241.88 down(g(g(f(x0)))) 543.70/241.88 down(g(g(b))) 543.70/241.88 down(g(g(c))) 543.70/241.88 down(g(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) 543.70/241.88 down(f(f(f(g(x0))))) 543.70/241.88 down(f(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) 543.70/241.88 down(g(g(g(f(x0))))) 543.70/241.88 down(g(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(x0)))))) 543.70/241.88 down(f(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(x0)))))) 543.70/241.88 down(g(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(x0))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(x0))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 f_flat(up(x0)) 543.70/241.88 g_flat(up(x0)) 543.70/241.88 543.70/241.88 We have to consider all minimal (P,Q,R)-chains. 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (683) TransformationProof (EQUIVALENT) 543.70/241.88 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.88 543.70/241.88 (TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))),TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.70/241.88 543.70/241.88 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (684) 543.70/241.88 Obligation: 543.70/241.88 Q DP problem: 543.70/241.88 The TRS P consists of the following rules: 543.70/241.88 543.70/241.88 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.88 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.88 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.88 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.88 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.88 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.88 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.88 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.88 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.88 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.88 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.88 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.88 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.88 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.88 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.88 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.88 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.88 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.88 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.88 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.88 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.88 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.88 543.70/241.88 The TRS R consists of the following rules: 543.70/241.88 543.70/241.88 down(a) -> up(f(a)) 543.70/241.88 down(b) -> up(g(b)) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.88 down(f(a)) -> f_flat(down(a)) 543.70/241.88 down(f(b)) -> f_flat(down(b)) 543.70/241.88 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.88 down(f(c)) -> f_flat(down(c)) 543.70/241.88 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.88 down(g(a)) -> g_flat(down(a)) 543.70/241.88 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.88 down(g(b)) -> g_flat(down(b)) 543.70/241.88 down(g(c)) -> g_flat(down(c)) 543.70/241.88 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.88 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.88 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.88 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.88 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.88 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.88 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.88 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.88 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.88 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.88 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.88 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.88 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.88 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.88 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.88 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.88 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.88 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.88 543.70/241.88 The set Q consists of the following terms: 543.70/241.88 543.70/241.88 down(a) 543.70/241.88 down(b) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.88 down(f(a)) 543.70/241.88 down(f(b)) 543.70/241.88 down(f(g(x0))) 543.70/241.88 down(f(c)) 543.70/241.88 down(f(fresh_constant)) 543.70/241.88 down(g(a)) 543.70/241.88 down(g(f(x0))) 543.70/241.88 down(g(b)) 543.70/241.88 down(g(c)) 543.70/241.88 down(g(fresh_constant)) 543.70/241.88 down(f(f(a))) 543.70/241.88 down(f(f(b))) 543.70/241.88 down(f(f(g(x0)))) 543.70/241.88 down(f(f(c))) 543.70/241.88 down(f(f(fresh_constant))) 543.70/241.88 down(g(g(a))) 543.70/241.88 down(g(g(f(x0)))) 543.70/241.88 down(g(g(b))) 543.70/241.88 down(g(g(c))) 543.70/241.88 down(g(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) 543.70/241.88 down(f(f(f(g(x0))))) 543.70/241.88 down(f(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) 543.70/241.88 down(g(g(g(f(x0))))) 543.70/241.88 down(g(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(x0)))))) 543.70/241.88 down(f(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(x0)))))) 543.70/241.88 down(g(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(x0))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(x0))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 f_flat(up(x0)) 543.70/241.88 g_flat(up(x0)) 543.70/241.88 543.70/241.88 We have to consider all minimal (P,Q,R)-chains. 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (685) TransformationProof (EQUIVALENT) 543.70/241.88 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.88 543.70/241.88 (TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))),TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.70/241.88 543.70/241.88 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (686) 543.70/241.88 Obligation: 543.70/241.88 Q DP problem: 543.70/241.88 The TRS P consists of the following rules: 543.70/241.88 543.70/241.88 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.88 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.88 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.88 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.88 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.88 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.88 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.88 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.88 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.88 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.88 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.88 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.88 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.88 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.88 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.88 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.88 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.88 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.88 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.88 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.88 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.88 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.88 543.70/241.88 The TRS R consists of the following rules: 543.70/241.88 543.70/241.88 down(a) -> up(f(a)) 543.70/241.88 down(b) -> up(g(b)) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.88 down(f(a)) -> f_flat(down(a)) 543.70/241.88 down(f(b)) -> f_flat(down(b)) 543.70/241.88 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.88 down(f(c)) -> f_flat(down(c)) 543.70/241.88 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.88 down(g(a)) -> g_flat(down(a)) 543.70/241.88 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.88 down(g(b)) -> g_flat(down(b)) 543.70/241.88 down(g(c)) -> g_flat(down(c)) 543.70/241.88 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.88 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.88 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.88 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.88 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.88 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.88 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.88 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.88 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.88 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.88 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.88 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.88 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.88 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.88 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.88 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.88 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.88 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.88 543.70/241.88 The set Q consists of the following terms: 543.70/241.88 543.70/241.88 down(a) 543.70/241.88 down(b) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.88 down(f(a)) 543.70/241.88 down(f(b)) 543.70/241.88 down(f(g(x0))) 543.70/241.88 down(f(c)) 543.70/241.88 down(f(fresh_constant)) 543.70/241.88 down(g(a)) 543.70/241.88 down(g(f(x0))) 543.70/241.88 down(g(b)) 543.70/241.88 down(g(c)) 543.70/241.88 down(g(fresh_constant)) 543.70/241.88 down(f(f(a))) 543.70/241.88 down(f(f(b))) 543.70/241.88 down(f(f(g(x0)))) 543.70/241.88 down(f(f(c))) 543.70/241.88 down(f(f(fresh_constant))) 543.70/241.88 down(g(g(a))) 543.70/241.88 down(g(g(f(x0)))) 543.70/241.88 down(g(g(b))) 543.70/241.88 down(g(g(c))) 543.70/241.88 down(g(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) 543.70/241.88 down(f(f(f(g(x0))))) 543.70/241.88 down(f(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) 543.70/241.88 down(g(g(g(f(x0))))) 543.70/241.88 down(g(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(x0)))))) 543.70/241.88 down(f(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(x0)))))) 543.70/241.88 down(g(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(x0))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(x0))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 f_flat(up(x0)) 543.70/241.88 g_flat(up(x0)) 543.70/241.88 543.70/241.88 We have to consider all minimal (P,Q,R)-chains. 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (687) TransformationProof (EQUIVALENT) 543.70/241.88 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.88 543.70/241.88 (TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))),TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.70/241.88 543.70/241.88 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (688) 543.70/241.88 Obligation: 543.70/241.88 Q DP problem: 543.70/241.88 The TRS P consists of the following rules: 543.70/241.88 543.70/241.88 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.88 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.88 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.88 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.88 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.88 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.88 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.88 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.88 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.88 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.88 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.88 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.88 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.88 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.88 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.88 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.88 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.88 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.88 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.88 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.88 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.88 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.88 543.70/241.88 The TRS R consists of the following rules: 543.70/241.88 543.70/241.88 down(a) -> up(f(a)) 543.70/241.88 down(b) -> up(g(b)) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.88 down(f(a)) -> f_flat(down(a)) 543.70/241.88 down(f(b)) -> f_flat(down(b)) 543.70/241.88 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.88 down(f(c)) -> f_flat(down(c)) 543.70/241.88 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.88 down(g(a)) -> g_flat(down(a)) 543.70/241.88 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.88 down(g(b)) -> g_flat(down(b)) 543.70/241.88 down(g(c)) -> g_flat(down(c)) 543.70/241.88 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.88 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.88 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.88 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.88 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.88 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.88 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.88 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.88 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.88 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.88 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.88 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.88 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.88 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.88 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.88 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.88 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.88 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.88 543.70/241.88 The set Q consists of the following terms: 543.70/241.88 543.70/241.88 down(a) 543.70/241.88 down(b) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.88 down(f(a)) 543.70/241.88 down(f(b)) 543.70/241.88 down(f(g(x0))) 543.70/241.88 down(f(c)) 543.70/241.88 down(f(fresh_constant)) 543.70/241.88 down(g(a)) 543.70/241.88 down(g(f(x0))) 543.70/241.88 down(g(b)) 543.70/241.88 down(g(c)) 543.70/241.88 down(g(fresh_constant)) 543.70/241.88 down(f(f(a))) 543.70/241.88 down(f(f(b))) 543.70/241.88 down(f(f(g(x0)))) 543.70/241.88 down(f(f(c))) 543.70/241.88 down(f(f(fresh_constant))) 543.70/241.88 down(g(g(a))) 543.70/241.88 down(g(g(f(x0)))) 543.70/241.88 down(g(g(b))) 543.70/241.88 down(g(g(c))) 543.70/241.88 down(g(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) 543.70/241.88 down(f(f(f(g(x0))))) 543.70/241.88 down(f(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) 543.70/241.88 down(g(g(g(f(x0))))) 543.70/241.88 down(g(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(x0)))))) 543.70/241.88 down(f(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(x0)))))) 543.70/241.88 down(g(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(x0))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(x0))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 f_flat(up(x0)) 543.70/241.88 g_flat(up(x0)) 543.70/241.88 543.70/241.88 We have to consider all minimal (P,Q,R)-chains. 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (689) TransformationProof (EQUIVALENT) 543.70/241.88 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(a))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.88 543.70/241.88 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a)))))))))))) 543.70/241.88 543.70/241.88 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (690) 543.70/241.88 Obligation: 543.70/241.88 Q DP problem: 543.70/241.88 The TRS P consists of the following rules: 543.70/241.88 543.70/241.88 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.88 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.88 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.88 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.88 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.88 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.88 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.88 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.88 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.88 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.88 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.88 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.88 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.88 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.88 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.88 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.88 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.88 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.88 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.88 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.88 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.88 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.88 543.70/241.88 The TRS R consists of the following rules: 543.70/241.88 543.70/241.88 down(a) -> up(f(a)) 543.70/241.88 down(b) -> up(g(b)) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.88 down(f(a)) -> f_flat(down(a)) 543.70/241.88 down(f(b)) -> f_flat(down(b)) 543.70/241.88 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.88 down(f(c)) -> f_flat(down(c)) 543.70/241.88 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.88 down(g(a)) -> g_flat(down(a)) 543.70/241.88 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.88 down(g(b)) -> g_flat(down(b)) 543.70/241.88 down(g(c)) -> g_flat(down(c)) 543.70/241.88 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.88 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.88 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.88 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.88 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.88 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.88 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.88 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.88 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.88 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.88 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.88 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.88 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.88 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.88 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.88 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.88 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.88 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.88 543.70/241.88 The set Q consists of the following terms: 543.70/241.88 543.70/241.88 down(a) 543.70/241.88 down(b) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.88 down(f(a)) 543.70/241.88 down(f(b)) 543.70/241.88 down(f(g(x0))) 543.70/241.88 down(f(c)) 543.70/241.88 down(f(fresh_constant)) 543.70/241.88 down(g(a)) 543.70/241.88 down(g(f(x0))) 543.70/241.88 down(g(b)) 543.70/241.88 down(g(c)) 543.70/241.88 down(g(fresh_constant)) 543.70/241.88 down(f(f(a))) 543.70/241.88 down(f(f(b))) 543.70/241.88 down(f(f(g(x0)))) 543.70/241.88 down(f(f(c))) 543.70/241.88 down(f(f(fresh_constant))) 543.70/241.88 down(g(g(a))) 543.70/241.88 down(g(g(f(x0)))) 543.70/241.88 down(g(g(b))) 543.70/241.88 down(g(g(c))) 543.70/241.88 down(g(g(fresh_constant))) 543.70/241.88 down(f(f(f(a)))) 543.70/241.88 down(f(f(f(b)))) 543.70/241.88 down(f(f(f(g(x0))))) 543.70/241.88 down(f(f(f(c)))) 543.70/241.88 down(f(f(f(fresh_constant)))) 543.70/241.88 down(g(g(g(a)))) 543.70/241.88 down(g(g(g(f(x0))))) 543.70/241.88 down(g(g(g(b)))) 543.70/241.88 down(g(g(g(c)))) 543.70/241.88 down(g(g(g(fresh_constant)))) 543.70/241.88 down(f(f(f(f(a))))) 543.70/241.88 down(f(f(f(f(b))))) 543.70/241.88 down(f(f(f(f(g(x0)))))) 543.70/241.88 down(f(f(f(f(c))))) 543.70/241.88 down(f(f(f(f(fresh_constant))))) 543.70/241.88 down(g(g(g(g(a))))) 543.70/241.88 down(g(g(g(g(f(x0)))))) 543.70/241.88 down(g(g(g(g(b))))) 543.70/241.88 down(g(g(g(g(c))))) 543.70/241.88 down(g(g(g(g(fresh_constant))))) 543.70/241.88 down(f(f(f(f(f(a)))))) 543.70/241.88 down(f(f(f(f(f(b)))))) 543.70/241.88 down(f(f(f(f(f(g(x0))))))) 543.70/241.88 down(f(f(f(f(f(c)))))) 543.70/241.88 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.88 down(g(g(g(g(g(a)))))) 543.70/241.88 down(g(g(g(g(g(f(x0))))))) 543.70/241.88 down(g(g(g(g(g(b)))))) 543.70/241.88 down(g(g(g(g(g(c)))))) 543.70/241.88 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.88 down(f(f(f(f(f(f(a))))))) 543.70/241.88 down(f(f(f(f(f(f(b))))))) 543.70/241.88 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.88 down(f(f(f(f(f(f(c))))))) 543.70/241.88 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.88 down(g(g(g(g(g(g(a))))))) 543.70/241.88 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.88 down(g(g(g(g(g(g(b))))))) 543.70/241.88 down(g(g(g(g(g(g(c))))))) 543.70/241.88 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.88 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.88 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.88 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.88 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 f_flat(up(x0)) 543.70/241.88 g_flat(up(x0)) 543.70/241.88 543.70/241.88 We have to consider all minimal (P,Q,R)-chains. 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (691) TransformationProof (EQUIVALENT) 543.70/241.88 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(b))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.88 543.70/241.88 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b)))))))))))) 543.70/241.88 543.70/241.88 543.70/241.88 ---------------------------------------- 543.70/241.88 543.70/241.88 (692) 543.70/241.88 Obligation: 543.70/241.88 Q DP problem: 543.70/241.88 The TRS P consists of the following rules: 543.70/241.88 543.70/241.88 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.88 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.88 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.88 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.88 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.88 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.88 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.88 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.88 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.88 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.88 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.88 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.88 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.88 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.88 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.88 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.88 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.88 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.88 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.88 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.88 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.88 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.88 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.88 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.88 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.88 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.88 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.88 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.88 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.89 543.70/241.89 The TRS R consists of the following rules: 543.70/241.89 543.70/241.89 down(a) -> up(f(a)) 543.70/241.89 down(b) -> up(g(b)) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.89 down(f(a)) -> f_flat(down(a)) 543.70/241.89 down(f(b)) -> f_flat(down(b)) 543.70/241.89 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.89 down(f(c)) -> f_flat(down(c)) 543.70/241.89 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.89 down(g(a)) -> g_flat(down(a)) 543.70/241.89 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.89 down(g(b)) -> g_flat(down(b)) 543.70/241.89 down(g(c)) -> g_flat(down(c)) 543.70/241.89 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.89 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.89 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.89 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.89 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.89 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.89 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.89 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.89 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.89 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.89 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.89 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.89 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.89 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.89 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.89 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.89 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.89 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.89 543.70/241.89 The set Q consists of the following terms: 543.70/241.89 543.70/241.89 down(a) 543.70/241.89 down(b) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.89 down(f(a)) 543.70/241.89 down(f(b)) 543.70/241.89 down(f(g(x0))) 543.70/241.89 down(f(c)) 543.70/241.89 down(f(fresh_constant)) 543.70/241.89 down(g(a)) 543.70/241.89 down(g(f(x0))) 543.70/241.89 down(g(b)) 543.70/241.89 down(g(c)) 543.70/241.89 down(g(fresh_constant)) 543.70/241.89 down(f(f(a))) 543.70/241.89 down(f(f(b))) 543.70/241.89 down(f(f(g(x0)))) 543.70/241.89 down(f(f(c))) 543.70/241.89 down(f(f(fresh_constant))) 543.70/241.89 down(g(g(a))) 543.70/241.89 down(g(g(f(x0)))) 543.70/241.89 down(g(g(b))) 543.70/241.89 down(g(g(c))) 543.70/241.89 down(g(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) 543.70/241.89 down(f(f(f(g(x0))))) 543.70/241.89 down(f(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) 543.70/241.89 down(g(g(g(f(x0))))) 543.70/241.89 down(g(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(x0)))))) 543.70/241.89 down(f(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(x0)))))) 543.70/241.89 down(g(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(x0))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(x0))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 f_flat(up(x0)) 543.70/241.89 g_flat(up(x0)) 543.70/241.89 543.70/241.89 We have to consider all minimal (P,Q,R)-chains. 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (693) TransformationProof (EQUIVALENT) 543.70/241.89 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(g(x0)))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.89 543.70/241.89 (TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0))))))))))))) 543.70/241.89 543.70/241.89 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (694) 543.70/241.89 Obligation: 543.70/241.89 Q DP problem: 543.70/241.89 The TRS P consists of the following rules: 543.70/241.89 543.70/241.89 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.89 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.89 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.89 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.89 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.89 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.89 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.89 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.89 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.89 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.89 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.89 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.89 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.89 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.89 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.89 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.89 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.89 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.89 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.89 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.89 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.89 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.89 543.70/241.89 The TRS R consists of the following rules: 543.70/241.89 543.70/241.89 down(a) -> up(f(a)) 543.70/241.89 down(b) -> up(g(b)) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.89 down(f(a)) -> f_flat(down(a)) 543.70/241.89 down(f(b)) -> f_flat(down(b)) 543.70/241.89 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.89 down(f(c)) -> f_flat(down(c)) 543.70/241.89 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.89 down(g(a)) -> g_flat(down(a)) 543.70/241.89 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.89 down(g(b)) -> g_flat(down(b)) 543.70/241.89 down(g(c)) -> g_flat(down(c)) 543.70/241.89 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.89 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.89 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.89 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.89 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.89 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.89 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.89 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.89 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.89 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.89 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.89 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.89 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.89 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.89 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.89 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.89 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.89 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.89 543.70/241.89 The set Q consists of the following terms: 543.70/241.89 543.70/241.89 down(a) 543.70/241.89 down(b) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.89 down(f(a)) 543.70/241.89 down(f(b)) 543.70/241.89 down(f(g(x0))) 543.70/241.89 down(f(c)) 543.70/241.89 down(f(fresh_constant)) 543.70/241.89 down(g(a)) 543.70/241.89 down(g(f(x0))) 543.70/241.89 down(g(b)) 543.70/241.89 down(g(c)) 543.70/241.89 down(g(fresh_constant)) 543.70/241.89 down(f(f(a))) 543.70/241.89 down(f(f(b))) 543.70/241.89 down(f(f(g(x0)))) 543.70/241.89 down(f(f(c))) 543.70/241.89 down(f(f(fresh_constant))) 543.70/241.89 down(g(g(a))) 543.70/241.89 down(g(g(f(x0)))) 543.70/241.89 down(g(g(b))) 543.70/241.89 down(g(g(c))) 543.70/241.89 down(g(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) 543.70/241.89 down(f(f(f(g(x0))))) 543.70/241.89 down(f(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) 543.70/241.89 down(g(g(g(f(x0))))) 543.70/241.89 down(g(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(x0)))))) 543.70/241.89 down(f(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(x0)))))) 543.70/241.89 down(g(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(x0))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(x0))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 f_flat(up(x0)) 543.70/241.89 g_flat(up(x0)) 543.70/241.89 543.70/241.89 We have to consider all minimal (P,Q,R)-chains. 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (695) TransformationProof (EQUIVALENT) 543.70/241.89 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.89 543.70/241.89 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.70/241.89 543.70/241.89 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (696) 543.70/241.89 Obligation: 543.70/241.89 Q DP problem: 543.70/241.89 The TRS P consists of the following rules: 543.70/241.89 543.70/241.89 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.89 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.89 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.89 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.89 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.89 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.89 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.89 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.89 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.89 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.89 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.89 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.89 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.89 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.89 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.89 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.89 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.89 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.89 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.89 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.89 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.89 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.89 543.70/241.89 The TRS R consists of the following rules: 543.70/241.89 543.70/241.89 down(a) -> up(f(a)) 543.70/241.89 down(b) -> up(g(b)) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.89 down(f(a)) -> f_flat(down(a)) 543.70/241.89 down(f(b)) -> f_flat(down(b)) 543.70/241.89 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.89 down(f(c)) -> f_flat(down(c)) 543.70/241.89 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.89 down(g(a)) -> g_flat(down(a)) 543.70/241.89 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.89 down(g(b)) -> g_flat(down(b)) 543.70/241.89 down(g(c)) -> g_flat(down(c)) 543.70/241.89 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.89 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.89 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.89 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.89 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.89 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.89 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.89 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.89 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.89 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.89 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.89 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.89 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.89 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.89 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.89 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.89 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.89 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.89 543.70/241.89 The set Q consists of the following terms: 543.70/241.89 543.70/241.89 down(a) 543.70/241.89 down(b) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.89 down(f(a)) 543.70/241.89 down(f(b)) 543.70/241.89 down(f(g(x0))) 543.70/241.89 down(f(c)) 543.70/241.89 down(f(fresh_constant)) 543.70/241.89 down(g(a)) 543.70/241.89 down(g(f(x0))) 543.70/241.89 down(g(b)) 543.70/241.89 down(g(c)) 543.70/241.89 down(g(fresh_constant)) 543.70/241.89 down(f(f(a))) 543.70/241.89 down(f(f(b))) 543.70/241.89 down(f(f(g(x0)))) 543.70/241.89 down(f(f(c))) 543.70/241.89 down(f(f(fresh_constant))) 543.70/241.89 down(g(g(a))) 543.70/241.89 down(g(g(f(x0)))) 543.70/241.89 down(g(g(b))) 543.70/241.89 down(g(g(c))) 543.70/241.89 down(g(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) 543.70/241.89 down(f(f(f(g(x0))))) 543.70/241.89 down(f(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) 543.70/241.89 down(g(g(g(f(x0))))) 543.70/241.89 down(g(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(x0)))))) 543.70/241.89 down(f(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(x0)))))) 543.70/241.89 down(g(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(x0))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(x0))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 f_flat(up(x0)) 543.70/241.89 g_flat(up(x0)) 543.70/241.89 543.70/241.89 We have to consider all minimal (P,Q,R)-chains. 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (697) TransformationProof (EQUIVALENT) 543.70/241.89 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.89 543.70/241.89 (TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))),TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.70/241.89 543.70/241.89 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (698) 543.70/241.89 Obligation: 543.70/241.89 Q DP problem: 543.70/241.89 The TRS P consists of the following rules: 543.70/241.89 543.70/241.89 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.89 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.89 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.89 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.89 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.89 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.89 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.89 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.89 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.89 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.89 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.89 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.89 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.89 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.89 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.89 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.89 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.89 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.89 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.89 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.89 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.89 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.89 543.70/241.89 The TRS R consists of the following rules: 543.70/241.89 543.70/241.89 down(a) -> up(f(a)) 543.70/241.89 down(b) -> up(g(b)) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.89 down(f(a)) -> f_flat(down(a)) 543.70/241.89 down(f(b)) -> f_flat(down(b)) 543.70/241.89 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.89 down(f(c)) -> f_flat(down(c)) 543.70/241.89 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.89 down(g(a)) -> g_flat(down(a)) 543.70/241.89 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.89 down(g(b)) -> g_flat(down(b)) 543.70/241.89 down(g(c)) -> g_flat(down(c)) 543.70/241.89 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.89 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.89 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.89 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.89 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.89 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.89 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.89 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.89 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.89 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.89 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.89 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.89 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.89 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.89 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.89 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.89 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.89 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.89 543.70/241.89 The set Q consists of the following terms: 543.70/241.89 543.70/241.89 down(a) 543.70/241.89 down(b) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.89 down(f(a)) 543.70/241.89 down(f(b)) 543.70/241.89 down(f(g(x0))) 543.70/241.89 down(f(c)) 543.70/241.89 down(f(fresh_constant)) 543.70/241.89 down(g(a)) 543.70/241.89 down(g(f(x0))) 543.70/241.89 down(g(b)) 543.70/241.89 down(g(c)) 543.70/241.89 down(g(fresh_constant)) 543.70/241.89 down(f(f(a))) 543.70/241.89 down(f(f(b))) 543.70/241.89 down(f(f(g(x0)))) 543.70/241.89 down(f(f(c))) 543.70/241.89 down(f(f(fresh_constant))) 543.70/241.89 down(g(g(a))) 543.70/241.89 down(g(g(f(x0)))) 543.70/241.89 down(g(g(b))) 543.70/241.89 down(g(g(c))) 543.70/241.89 down(g(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) 543.70/241.89 down(f(f(f(g(x0))))) 543.70/241.89 down(f(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) 543.70/241.89 down(g(g(g(f(x0))))) 543.70/241.89 down(g(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(x0)))))) 543.70/241.89 down(f(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(x0)))))) 543.70/241.89 down(g(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(x0))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(x0))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 f_flat(up(x0)) 543.70/241.89 g_flat(up(x0)) 543.70/241.89 543.70/241.89 We have to consider all minimal (P,Q,R)-chains. 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (699) TransformationProof (EQUIVALENT) 543.70/241.89 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.89 543.70/241.89 (TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))),TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.70/241.89 543.70/241.89 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (700) 543.70/241.89 Obligation: 543.70/241.89 Q DP problem: 543.70/241.89 The TRS P consists of the following rules: 543.70/241.89 543.70/241.89 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.89 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.89 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.89 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.89 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.89 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.89 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.89 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.89 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.89 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.89 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.89 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.89 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.89 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.89 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.89 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.89 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.89 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.89 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.89 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.89 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.89 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.89 543.70/241.89 The TRS R consists of the following rules: 543.70/241.89 543.70/241.89 down(a) -> up(f(a)) 543.70/241.89 down(b) -> up(g(b)) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.89 down(f(a)) -> f_flat(down(a)) 543.70/241.89 down(f(b)) -> f_flat(down(b)) 543.70/241.89 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.89 down(f(c)) -> f_flat(down(c)) 543.70/241.89 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.89 down(g(a)) -> g_flat(down(a)) 543.70/241.89 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.89 down(g(b)) -> g_flat(down(b)) 543.70/241.89 down(g(c)) -> g_flat(down(c)) 543.70/241.89 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.89 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.89 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.89 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.89 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.89 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.89 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.89 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.89 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.89 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.89 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.89 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.89 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.89 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.89 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.89 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.89 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.89 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.89 543.70/241.89 The set Q consists of the following terms: 543.70/241.89 543.70/241.89 down(a) 543.70/241.89 down(b) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.89 down(f(a)) 543.70/241.89 down(f(b)) 543.70/241.89 down(f(g(x0))) 543.70/241.89 down(f(c)) 543.70/241.89 down(f(fresh_constant)) 543.70/241.89 down(g(a)) 543.70/241.89 down(g(f(x0))) 543.70/241.89 down(g(b)) 543.70/241.89 down(g(c)) 543.70/241.89 down(g(fresh_constant)) 543.70/241.89 down(f(f(a))) 543.70/241.89 down(f(f(b))) 543.70/241.89 down(f(f(g(x0)))) 543.70/241.89 down(f(f(c))) 543.70/241.89 down(f(f(fresh_constant))) 543.70/241.89 down(g(g(a))) 543.70/241.89 down(g(g(f(x0)))) 543.70/241.89 down(g(g(b))) 543.70/241.89 down(g(g(c))) 543.70/241.89 down(g(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) 543.70/241.89 down(f(f(f(g(x0))))) 543.70/241.89 down(f(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) 543.70/241.89 down(g(g(g(f(x0))))) 543.70/241.89 down(g(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(x0)))))) 543.70/241.89 down(f(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(x0)))))) 543.70/241.89 down(g(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(x0))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(x0))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 f_flat(up(x0)) 543.70/241.89 g_flat(up(x0)) 543.70/241.89 543.70/241.89 We have to consider all minimal (P,Q,R)-chains. 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (701) TransformationProof (EQUIVALENT) 543.70/241.89 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(a))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.89 543.70/241.89 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a)))))))))))) 543.70/241.89 543.70/241.89 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (702) 543.70/241.89 Obligation: 543.70/241.89 Q DP problem: 543.70/241.89 The TRS P consists of the following rules: 543.70/241.89 543.70/241.89 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.89 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.89 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.89 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.89 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.89 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.89 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.89 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.89 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.89 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.89 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.89 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.89 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.89 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.89 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.89 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.89 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.89 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.89 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.89 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.89 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.89 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.89 543.70/241.89 The TRS R consists of the following rules: 543.70/241.89 543.70/241.89 down(a) -> up(f(a)) 543.70/241.89 down(b) -> up(g(b)) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.89 down(f(a)) -> f_flat(down(a)) 543.70/241.89 down(f(b)) -> f_flat(down(b)) 543.70/241.89 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.89 down(f(c)) -> f_flat(down(c)) 543.70/241.89 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.89 down(g(a)) -> g_flat(down(a)) 543.70/241.89 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.89 down(g(b)) -> g_flat(down(b)) 543.70/241.89 down(g(c)) -> g_flat(down(c)) 543.70/241.89 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.89 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.89 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.89 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.89 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.89 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.89 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.89 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.89 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.89 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.89 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.89 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.89 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.89 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.89 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.89 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.89 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.89 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.89 543.70/241.89 The set Q consists of the following terms: 543.70/241.89 543.70/241.89 down(a) 543.70/241.89 down(b) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.89 down(f(a)) 543.70/241.89 down(f(b)) 543.70/241.89 down(f(g(x0))) 543.70/241.89 down(f(c)) 543.70/241.89 down(f(fresh_constant)) 543.70/241.89 down(g(a)) 543.70/241.89 down(g(f(x0))) 543.70/241.89 down(g(b)) 543.70/241.89 down(g(c)) 543.70/241.89 down(g(fresh_constant)) 543.70/241.89 down(f(f(a))) 543.70/241.89 down(f(f(b))) 543.70/241.89 down(f(f(g(x0)))) 543.70/241.89 down(f(f(c))) 543.70/241.89 down(f(f(fresh_constant))) 543.70/241.89 down(g(g(a))) 543.70/241.89 down(g(g(f(x0)))) 543.70/241.89 down(g(g(b))) 543.70/241.89 down(g(g(c))) 543.70/241.89 down(g(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) 543.70/241.89 down(f(f(f(g(x0))))) 543.70/241.89 down(f(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) 543.70/241.89 down(g(g(g(f(x0))))) 543.70/241.89 down(g(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(x0)))))) 543.70/241.89 down(f(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(x0)))))) 543.70/241.89 down(g(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(x0))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(x0))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 f_flat(up(x0)) 543.70/241.89 g_flat(up(x0)) 543.70/241.89 543.70/241.89 We have to consider all minimal (P,Q,R)-chains. 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (703) TransformationProof (EQUIVALENT) 543.70/241.89 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(f(x0)))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.89 543.70/241.89 (TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0))))))))))))) 543.70/241.89 543.70/241.89 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (704) 543.70/241.89 Obligation: 543.70/241.89 Q DP problem: 543.70/241.89 The TRS P consists of the following rules: 543.70/241.89 543.70/241.89 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.89 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.89 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.89 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.89 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.89 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.89 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.89 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.89 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.89 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.89 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.89 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.89 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.89 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.89 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.89 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.89 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.89 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.89 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.89 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.89 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.89 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.89 543.70/241.89 The TRS R consists of the following rules: 543.70/241.89 543.70/241.89 down(a) -> up(f(a)) 543.70/241.89 down(b) -> up(g(b)) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.89 down(f(a)) -> f_flat(down(a)) 543.70/241.89 down(f(b)) -> f_flat(down(b)) 543.70/241.89 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.89 down(f(c)) -> f_flat(down(c)) 543.70/241.89 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.89 down(g(a)) -> g_flat(down(a)) 543.70/241.89 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.89 down(g(b)) -> g_flat(down(b)) 543.70/241.89 down(g(c)) -> g_flat(down(c)) 543.70/241.89 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.89 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.89 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.89 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.89 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.89 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.89 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.89 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.89 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.89 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.89 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.89 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.89 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.89 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.89 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.89 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.89 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.89 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.89 543.70/241.89 The set Q consists of the following terms: 543.70/241.89 543.70/241.89 down(a) 543.70/241.89 down(b) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.89 down(f(a)) 543.70/241.89 down(f(b)) 543.70/241.89 down(f(g(x0))) 543.70/241.89 down(f(c)) 543.70/241.89 down(f(fresh_constant)) 543.70/241.89 down(g(a)) 543.70/241.89 down(g(f(x0))) 543.70/241.89 down(g(b)) 543.70/241.89 down(g(c)) 543.70/241.89 down(g(fresh_constant)) 543.70/241.89 down(f(f(a))) 543.70/241.89 down(f(f(b))) 543.70/241.89 down(f(f(g(x0)))) 543.70/241.89 down(f(f(c))) 543.70/241.89 down(f(f(fresh_constant))) 543.70/241.89 down(g(g(a))) 543.70/241.89 down(g(g(f(x0)))) 543.70/241.89 down(g(g(b))) 543.70/241.89 down(g(g(c))) 543.70/241.89 down(g(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) 543.70/241.89 down(f(f(f(g(x0))))) 543.70/241.89 down(f(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) 543.70/241.89 down(g(g(g(f(x0))))) 543.70/241.89 down(g(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(x0)))))) 543.70/241.89 down(f(f(f(f(c))))) 543.70/241.89 down(f(f(f(f(fresh_constant))))) 543.70/241.89 down(g(g(g(g(a))))) 543.70/241.89 down(g(g(g(g(f(x0)))))) 543.70/241.89 down(g(g(g(g(b))))) 543.70/241.89 down(g(g(g(g(c))))) 543.70/241.89 down(g(g(g(g(fresh_constant))))) 543.70/241.89 down(f(f(f(f(f(a)))))) 543.70/241.89 down(f(f(f(f(f(b)))))) 543.70/241.89 down(f(f(f(f(f(g(x0))))))) 543.70/241.89 down(f(f(f(f(f(c)))))) 543.70/241.89 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.89 down(g(g(g(g(g(a)))))) 543.70/241.89 down(g(g(g(g(g(f(x0))))))) 543.70/241.89 down(g(g(g(g(g(b)))))) 543.70/241.89 down(g(g(g(g(g(c)))))) 543.70/241.89 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.89 down(f(f(f(f(f(f(a))))))) 543.70/241.89 down(f(f(f(f(f(f(b))))))) 543.70/241.89 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.89 down(f(f(f(f(f(f(c))))))) 543.70/241.89 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.89 down(g(g(g(g(g(g(a))))))) 543.70/241.89 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.89 down(g(g(g(g(g(g(b))))))) 543.70/241.89 down(g(g(g(g(g(g(c))))))) 543.70/241.89 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.89 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.89 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.89 f_flat(up(x0)) 543.70/241.89 g_flat(up(x0)) 543.70/241.89 543.70/241.89 We have to consider all minimal (P,Q,R)-chains. 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (705) TransformationProof (EQUIVALENT) 543.70/241.89 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(c))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.89 543.70/241.89 (TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c)))))))))))) 543.70/241.89 543.70/241.89 543.70/241.89 ---------------------------------------- 543.70/241.89 543.70/241.89 (706) 543.70/241.89 Obligation: 543.70/241.89 Q DP problem: 543.70/241.89 The TRS P consists of the following rules: 543.70/241.89 543.70/241.89 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.89 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.89 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.89 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.89 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.89 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.89 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.89 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.89 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.89 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.89 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.89 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.89 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.89 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.89 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.89 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) 543.70/241.89 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.89 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.89 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.89 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.89 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.89 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.89 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.89 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.89 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.89 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.89 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.89 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.89 543.70/241.89 The TRS R consists of the following rules: 543.70/241.89 543.70/241.89 down(a) -> up(f(a)) 543.70/241.89 down(b) -> up(g(b)) 543.70/241.89 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.89 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.89 down(f(a)) -> f_flat(down(a)) 543.70/241.89 down(f(b)) -> f_flat(down(b)) 543.70/241.89 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.89 down(f(c)) -> f_flat(down(c)) 543.70/241.89 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.89 down(g(a)) -> g_flat(down(a)) 543.70/241.89 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.89 down(g(b)) -> g_flat(down(b)) 543.70/241.89 down(g(c)) -> g_flat(down(c)) 543.70/241.89 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.89 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.89 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.89 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.89 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.89 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.89 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.89 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.89 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.89 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.89 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.89 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.89 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.89 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.89 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.89 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.89 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.89 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.89 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.89 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.89 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.89 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.89 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.89 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.90 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.90 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.90 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.90 543.70/241.90 The set Q consists of the following terms: 543.70/241.90 543.70/241.90 down(a) 543.70/241.90 down(b) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.90 down(f(a)) 543.70/241.90 down(f(b)) 543.70/241.90 down(f(g(x0))) 543.70/241.90 down(f(c)) 543.70/241.90 down(f(fresh_constant)) 543.70/241.90 down(g(a)) 543.70/241.90 down(g(f(x0))) 543.70/241.90 down(g(b)) 543.70/241.90 down(g(c)) 543.70/241.90 down(g(fresh_constant)) 543.70/241.90 down(f(f(a))) 543.70/241.90 down(f(f(b))) 543.70/241.90 down(f(f(g(x0)))) 543.70/241.90 down(f(f(c))) 543.70/241.90 down(f(f(fresh_constant))) 543.70/241.90 down(g(g(a))) 543.70/241.90 down(g(g(f(x0)))) 543.70/241.90 down(g(g(b))) 543.70/241.90 down(g(g(c))) 543.70/241.90 down(g(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) 543.70/241.90 down(f(f(f(g(x0))))) 543.70/241.90 down(f(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) 543.70/241.90 down(g(g(g(f(x0))))) 543.70/241.90 down(g(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(x0)))))) 543.70/241.90 down(f(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(x0)))))) 543.70/241.90 down(g(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(x0))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(x0))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 f_flat(up(x0)) 543.70/241.90 g_flat(up(x0)) 543.70/241.90 543.70/241.90 We have to consider all minimal (P,Q,R)-chains. 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (707) TransformationProof (EQUIVALENT) 543.70/241.90 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(f(fresh_constant))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.90 543.70/241.90 (TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant)))))))))))) 543.70/241.90 543.70/241.90 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (708) 543.70/241.90 Obligation: 543.70/241.90 Q DP problem: 543.70/241.90 The TRS P consists of the following rules: 543.70/241.90 543.70/241.90 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.90 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.90 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.90 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.90 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.90 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.90 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.90 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.90 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.90 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.90 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.90 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.90 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.90 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.90 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.90 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.90 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.90 TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) 543.70/241.90 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.90 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.90 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.90 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.90 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.90 543.70/241.90 The TRS R consists of the following rules: 543.70/241.90 543.70/241.90 down(a) -> up(f(a)) 543.70/241.90 down(b) -> up(g(b)) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.90 down(f(a)) -> f_flat(down(a)) 543.70/241.90 down(f(b)) -> f_flat(down(b)) 543.70/241.90 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.90 down(f(c)) -> f_flat(down(c)) 543.70/241.90 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.90 down(g(a)) -> g_flat(down(a)) 543.70/241.90 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.90 down(g(b)) -> g_flat(down(b)) 543.70/241.90 down(g(c)) -> g_flat(down(c)) 543.70/241.90 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.90 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.90 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.90 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.90 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.90 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.90 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.90 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.90 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.90 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.90 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.90 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.90 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.90 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.90 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.90 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.90 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.90 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.90 543.70/241.90 The set Q consists of the following terms: 543.70/241.90 543.70/241.90 down(a) 543.70/241.90 down(b) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.90 down(f(a)) 543.70/241.90 down(f(b)) 543.70/241.90 down(f(g(x0))) 543.70/241.90 down(f(c)) 543.70/241.90 down(f(fresh_constant)) 543.70/241.90 down(g(a)) 543.70/241.90 down(g(f(x0))) 543.70/241.90 down(g(b)) 543.70/241.90 down(g(c)) 543.70/241.90 down(g(fresh_constant)) 543.70/241.90 down(f(f(a))) 543.70/241.90 down(f(f(b))) 543.70/241.90 down(f(f(g(x0)))) 543.70/241.90 down(f(f(c))) 543.70/241.90 down(f(f(fresh_constant))) 543.70/241.90 down(g(g(a))) 543.70/241.90 down(g(g(f(x0)))) 543.70/241.90 down(g(g(b))) 543.70/241.90 down(g(g(c))) 543.70/241.90 down(g(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) 543.70/241.90 down(f(f(f(g(x0))))) 543.70/241.90 down(f(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) 543.70/241.90 down(g(g(g(f(x0))))) 543.70/241.90 down(g(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(x0)))))) 543.70/241.90 down(f(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(x0)))))) 543.70/241.90 down(g(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(x0))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(x0))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 f_flat(up(x0)) 543.70/241.90 g_flat(up(x0)) 543.70/241.90 543.70/241.90 We have to consider all minimal (P,Q,R)-chains. 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (709) TransformationProof (EQUIVALENT) 543.70/241.90 By rewriting [LPAR04] the rule TOP(up(f(f(f(b))))) -> TOP(f_flat(f_flat(up(f(g(b)))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.70/241.90 543.70/241.90 (TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))),TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b))))))) 543.70/241.90 543.70/241.90 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (710) 543.70/241.90 Obligation: 543.70/241.90 Q DP problem: 543.70/241.90 The TRS P consists of the following rules: 543.70/241.90 543.70/241.90 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.90 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.90 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.90 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.90 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.90 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.90 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.90 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.90 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.90 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.90 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.90 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.90 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.90 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.90 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.90 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.90 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.90 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.90 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.90 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.90 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.90 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.90 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.90 543.70/241.90 The TRS R consists of the following rules: 543.70/241.90 543.70/241.90 down(a) -> up(f(a)) 543.70/241.90 down(b) -> up(g(b)) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.90 down(f(a)) -> f_flat(down(a)) 543.70/241.90 down(f(b)) -> f_flat(down(b)) 543.70/241.90 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.90 down(f(c)) -> f_flat(down(c)) 543.70/241.90 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.90 down(g(a)) -> g_flat(down(a)) 543.70/241.90 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.90 down(g(b)) -> g_flat(down(b)) 543.70/241.90 down(g(c)) -> g_flat(down(c)) 543.70/241.90 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.90 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.90 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.90 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.90 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.90 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.90 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.90 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.90 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.90 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.90 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.90 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.90 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.90 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.90 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.90 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.90 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.90 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.90 543.70/241.90 The set Q consists of the following terms: 543.70/241.90 543.70/241.90 down(a) 543.70/241.90 down(b) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.90 down(f(a)) 543.70/241.90 down(f(b)) 543.70/241.90 down(f(g(x0))) 543.70/241.90 down(f(c)) 543.70/241.90 down(f(fresh_constant)) 543.70/241.90 down(g(a)) 543.70/241.90 down(g(f(x0))) 543.70/241.90 down(g(b)) 543.70/241.90 down(g(c)) 543.70/241.90 down(g(fresh_constant)) 543.70/241.90 down(f(f(a))) 543.70/241.90 down(f(f(b))) 543.70/241.90 down(f(f(g(x0)))) 543.70/241.90 down(f(f(c))) 543.70/241.90 down(f(f(fresh_constant))) 543.70/241.90 down(g(g(a))) 543.70/241.90 down(g(g(f(x0)))) 543.70/241.90 down(g(g(b))) 543.70/241.90 down(g(g(c))) 543.70/241.90 down(g(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) 543.70/241.90 down(f(f(f(g(x0))))) 543.70/241.90 down(f(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) 543.70/241.90 down(g(g(g(f(x0))))) 543.70/241.90 down(g(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(x0)))))) 543.70/241.90 down(f(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(x0)))))) 543.70/241.90 down(g(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(x0))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(x0))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 f_flat(up(x0)) 543.70/241.90 g_flat(up(x0)) 543.70/241.90 543.70/241.90 We have to consider all minimal (P,Q,R)-chains. 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (711) TransformationProof (EQUIVALENT) 543.70/241.90 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(g(b))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.90 543.70/241.90 (TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))),TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.70/241.90 543.70/241.90 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (712) 543.70/241.90 Obligation: 543.70/241.90 Q DP problem: 543.70/241.90 The TRS P consists of the following rules: 543.70/241.90 543.70/241.90 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.90 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.90 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.90 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.90 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.90 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.90 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.90 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.90 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.90 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.90 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.90 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.90 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.90 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.90 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.90 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.90 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.90 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) 543.70/241.90 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.90 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.90 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.90 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.90 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.90 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.90 543.70/241.90 The TRS R consists of the following rules: 543.70/241.90 543.70/241.90 down(a) -> up(f(a)) 543.70/241.90 down(b) -> up(g(b)) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.90 down(f(a)) -> f_flat(down(a)) 543.70/241.90 down(f(b)) -> f_flat(down(b)) 543.70/241.90 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.90 down(f(c)) -> f_flat(down(c)) 543.70/241.90 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.90 down(g(a)) -> g_flat(down(a)) 543.70/241.90 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.90 down(g(b)) -> g_flat(down(b)) 543.70/241.90 down(g(c)) -> g_flat(down(c)) 543.70/241.90 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.90 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.90 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.90 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.90 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.90 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.90 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.90 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.90 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.90 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.90 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.90 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.90 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.90 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.90 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.90 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.90 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.90 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.90 543.70/241.90 The set Q consists of the following terms: 543.70/241.90 543.70/241.90 down(a) 543.70/241.90 down(b) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.90 down(f(a)) 543.70/241.90 down(f(b)) 543.70/241.90 down(f(g(x0))) 543.70/241.90 down(f(c)) 543.70/241.90 down(f(fresh_constant)) 543.70/241.90 down(g(a)) 543.70/241.90 down(g(f(x0))) 543.70/241.90 down(g(b)) 543.70/241.90 down(g(c)) 543.70/241.90 down(g(fresh_constant)) 543.70/241.90 down(f(f(a))) 543.70/241.90 down(f(f(b))) 543.70/241.90 down(f(f(g(x0)))) 543.70/241.90 down(f(f(c))) 543.70/241.90 down(f(f(fresh_constant))) 543.70/241.90 down(g(g(a))) 543.70/241.90 down(g(g(f(x0)))) 543.70/241.90 down(g(g(b))) 543.70/241.90 down(g(g(c))) 543.70/241.90 down(g(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) 543.70/241.90 down(f(f(f(g(x0))))) 543.70/241.90 down(f(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) 543.70/241.90 down(g(g(g(f(x0))))) 543.70/241.90 down(g(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(x0)))))) 543.70/241.90 down(f(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(x0)))))) 543.70/241.90 down(g(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(x0))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(x0))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 f_flat(up(x0)) 543.70/241.90 g_flat(up(x0)) 543.70/241.90 543.70/241.90 We have to consider all minimal (P,Q,R)-chains. 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (713) TransformationProof (EQUIVALENT) 543.70/241.90 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.90 543.70/241.90 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.70/241.90 543.70/241.90 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (714) 543.70/241.90 Obligation: 543.70/241.90 Q DP problem: 543.70/241.90 The TRS P consists of the following rules: 543.70/241.90 543.70/241.90 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.90 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.90 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.90 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.90 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.90 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.90 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.90 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.90 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.90 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.90 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.90 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.90 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.90 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.90 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.90 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.90 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.90 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.90 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.90 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.90 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.90 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.90 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.90 543.70/241.90 The TRS R consists of the following rules: 543.70/241.90 543.70/241.90 down(a) -> up(f(a)) 543.70/241.90 down(b) -> up(g(b)) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.90 down(f(a)) -> f_flat(down(a)) 543.70/241.90 down(f(b)) -> f_flat(down(b)) 543.70/241.90 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.90 down(f(c)) -> f_flat(down(c)) 543.70/241.90 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.90 down(g(a)) -> g_flat(down(a)) 543.70/241.90 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.90 down(g(b)) -> g_flat(down(b)) 543.70/241.90 down(g(c)) -> g_flat(down(c)) 543.70/241.90 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.90 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.90 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.90 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.90 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.90 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.90 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.90 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.90 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.90 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.90 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.90 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.90 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.90 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.90 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.90 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.90 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.90 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.90 543.70/241.90 The set Q consists of the following terms: 543.70/241.90 543.70/241.90 down(a) 543.70/241.90 down(b) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.90 down(f(a)) 543.70/241.90 down(f(b)) 543.70/241.90 down(f(g(x0))) 543.70/241.90 down(f(c)) 543.70/241.90 down(f(fresh_constant)) 543.70/241.90 down(g(a)) 543.70/241.90 down(g(f(x0))) 543.70/241.90 down(g(b)) 543.70/241.90 down(g(c)) 543.70/241.90 down(g(fresh_constant)) 543.70/241.90 down(f(f(a))) 543.70/241.90 down(f(f(b))) 543.70/241.90 down(f(f(g(x0)))) 543.70/241.90 down(f(f(c))) 543.70/241.90 down(f(f(fresh_constant))) 543.70/241.90 down(g(g(a))) 543.70/241.90 down(g(g(f(x0)))) 543.70/241.90 down(g(g(b))) 543.70/241.90 down(g(g(c))) 543.70/241.90 down(g(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) 543.70/241.90 down(f(f(f(g(x0))))) 543.70/241.90 down(f(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) 543.70/241.90 down(g(g(g(f(x0))))) 543.70/241.90 down(g(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(x0)))))) 543.70/241.90 down(f(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(x0)))))) 543.70/241.90 down(g(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(x0))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(x0))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 f_flat(up(x0)) 543.70/241.90 g_flat(up(x0)) 543.70/241.90 543.70/241.90 We have to consider all minimal (P,Q,R)-chains. 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (715) TransformationProof (EQUIVALENT) 543.70/241.90 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.90 543.70/241.90 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.70/241.90 543.70/241.90 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (716) 543.70/241.90 Obligation: 543.70/241.90 Q DP problem: 543.70/241.90 The TRS P consists of the following rules: 543.70/241.90 543.70/241.90 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.90 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.90 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.90 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.90 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.90 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.90 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.90 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.90 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.90 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.90 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.90 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.90 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.90 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.90 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.90 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.90 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.90 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.90 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.90 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.90 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.90 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.90 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.90 543.70/241.90 The TRS R consists of the following rules: 543.70/241.90 543.70/241.90 down(a) -> up(f(a)) 543.70/241.90 down(b) -> up(g(b)) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.90 down(f(a)) -> f_flat(down(a)) 543.70/241.90 down(f(b)) -> f_flat(down(b)) 543.70/241.90 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.90 down(f(c)) -> f_flat(down(c)) 543.70/241.90 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.90 down(g(a)) -> g_flat(down(a)) 543.70/241.90 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.90 down(g(b)) -> g_flat(down(b)) 543.70/241.90 down(g(c)) -> g_flat(down(c)) 543.70/241.90 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.90 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.90 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.90 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.90 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.90 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.90 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.90 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.90 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.90 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.90 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.90 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.90 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.90 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.90 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.90 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.90 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.90 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.90 543.70/241.90 The set Q consists of the following terms: 543.70/241.90 543.70/241.90 down(a) 543.70/241.90 down(b) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.90 down(f(a)) 543.70/241.90 down(f(b)) 543.70/241.90 down(f(g(x0))) 543.70/241.90 down(f(c)) 543.70/241.90 down(f(fresh_constant)) 543.70/241.90 down(g(a)) 543.70/241.90 down(g(f(x0))) 543.70/241.90 down(g(b)) 543.70/241.90 down(g(c)) 543.70/241.90 down(g(fresh_constant)) 543.70/241.90 down(f(f(a))) 543.70/241.90 down(f(f(b))) 543.70/241.90 down(f(f(g(x0)))) 543.70/241.90 down(f(f(c))) 543.70/241.90 down(f(f(fresh_constant))) 543.70/241.90 down(g(g(a))) 543.70/241.90 down(g(g(f(x0)))) 543.70/241.90 down(g(g(b))) 543.70/241.90 down(g(g(c))) 543.70/241.90 down(g(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) 543.70/241.90 down(f(f(f(g(x0))))) 543.70/241.90 down(f(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) 543.70/241.90 down(g(g(g(f(x0))))) 543.70/241.90 down(g(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(x0)))))) 543.70/241.90 down(f(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(x0)))))) 543.70/241.90 down(g(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(x0))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(x0))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 f_flat(up(x0)) 543.70/241.90 g_flat(up(x0)) 543.70/241.90 543.70/241.90 We have to consider all minimal (P,Q,R)-chains. 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (717) TransformationProof (EQUIVALENT) 543.70/241.90 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(b))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.90 543.70/241.90 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b)))))))))))) 543.70/241.90 543.70/241.90 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (718) 543.70/241.90 Obligation: 543.70/241.90 Q DP problem: 543.70/241.90 The TRS P consists of the following rules: 543.70/241.90 543.70/241.90 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.90 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.90 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.90 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.90 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.90 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.90 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.90 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.90 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.90 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.90 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.90 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.90 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.90 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.90 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.90 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.90 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.90 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.90 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.90 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.90 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.90 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.90 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.70/241.90 543.70/241.90 The TRS R consists of the following rules: 543.70/241.90 543.70/241.90 down(a) -> up(f(a)) 543.70/241.90 down(b) -> up(g(b)) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.90 down(f(a)) -> f_flat(down(a)) 543.70/241.90 down(f(b)) -> f_flat(down(b)) 543.70/241.90 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.90 down(f(c)) -> f_flat(down(c)) 543.70/241.90 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.90 down(g(a)) -> g_flat(down(a)) 543.70/241.90 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.90 down(g(b)) -> g_flat(down(b)) 543.70/241.90 down(g(c)) -> g_flat(down(c)) 543.70/241.90 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.90 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.90 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.90 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.90 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.90 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.90 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.90 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.90 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.90 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.90 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.90 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.90 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.90 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.90 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.90 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.90 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.90 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.90 543.70/241.90 The set Q consists of the following terms: 543.70/241.90 543.70/241.90 down(a) 543.70/241.90 down(b) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.90 down(f(a)) 543.70/241.90 down(f(b)) 543.70/241.90 down(f(g(x0))) 543.70/241.90 down(f(c)) 543.70/241.90 down(f(fresh_constant)) 543.70/241.90 down(g(a)) 543.70/241.90 down(g(f(x0))) 543.70/241.90 down(g(b)) 543.70/241.90 down(g(c)) 543.70/241.90 down(g(fresh_constant)) 543.70/241.90 down(f(f(a))) 543.70/241.90 down(f(f(b))) 543.70/241.90 down(f(f(g(x0)))) 543.70/241.90 down(f(f(c))) 543.70/241.90 down(f(f(fresh_constant))) 543.70/241.90 down(g(g(a))) 543.70/241.90 down(g(g(f(x0)))) 543.70/241.90 down(g(g(b))) 543.70/241.90 down(g(g(c))) 543.70/241.90 down(g(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) 543.70/241.90 down(f(f(f(g(x0))))) 543.70/241.90 down(f(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) 543.70/241.90 down(g(g(g(f(x0))))) 543.70/241.90 down(g(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(x0)))))) 543.70/241.90 down(f(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(x0)))))) 543.70/241.90 down(g(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(x0))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(x0))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.90 f_flat(up(x0)) 543.70/241.90 g_flat(up(x0)) 543.70/241.90 543.70/241.90 We have to consider all minimal (P,Q,R)-chains. 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (719) TransformationProof (EQUIVALENT) 543.70/241.90 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(c))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.90 543.70/241.90 (TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c)))))))))))) 543.70/241.90 543.70/241.90 543.70/241.90 ---------------------------------------- 543.70/241.90 543.70/241.90 (720) 543.70/241.90 Obligation: 543.70/241.90 Q DP problem: 543.70/241.90 The TRS P consists of the following rules: 543.70/241.90 543.70/241.90 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.90 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.90 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.90 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.90 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.90 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.90 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.90 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.90 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.90 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.90 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.90 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.90 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.90 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.90 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.90 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.90 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.90 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) 543.70/241.90 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.90 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.90 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.90 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.90 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.90 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.90 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.90 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.90 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.90 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.90 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.70/241.90 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.70/241.90 543.70/241.90 The TRS R consists of the following rules: 543.70/241.90 543.70/241.90 down(a) -> up(f(a)) 543.70/241.90 down(b) -> up(g(b)) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.90 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.90 down(f(a)) -> f_flat(down(a)) 543.70/241.90 down(f(b)) -> f_flat(down(b)) 543.70/241.90 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.90 down(f(c)) -> f_flat(down(c)) 543.70/241.90 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.90 down(g(a)) -> g_flat(down(a)) 543.70/241.90 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.90 down(g(b)) -> g_flat(down(b)) 543.70/241.90 down(g(c)) -> g_flat(down(c)) 543.70/241.90 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.90 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.90 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.90 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.90 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.90 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.90 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.90 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.90 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.90 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.90 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.90 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.90 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.90 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.90 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.90 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.90 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.90 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.90 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.90 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.90 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.90 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.90 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.90 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.90 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.90 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.90 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.90 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.90 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.90 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.90 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.90 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.90 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.90 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.90 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.90 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.90 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.90 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.90 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.90 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.90 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.90 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.90 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.90 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.90 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.90 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.90 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.90 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.90 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.90 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.90 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.90 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.90 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.90 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.90 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.91 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.91 543.70/241.91 The set Q consists of the following terms: 543.70/241.91 543.70/241.91 down(a) 543.70/241.91 down(b) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.91 down(f(a)) 543.70/241.91 down(f(b)) 543.70/241.91 down(f(g(x0))) 543.70/241.91 down(f(c)) 543.70/241.91 down(f(fresh_constant)) 543.70/241.91 down(g(a)) 543.70/241.91 down(g(f(x0))) 543.70/241.91 down(g(b)) 543.70/241.91 down(g(c)) 543.70/241.91 down(g(fresh_constant)) 543.70/241.91 down(f(f(a))) 543.70/241.91 down(f(f(b))) 543.70/241.91 down(f(f(g(x0)))) 543.70/241.91 down(f(f(c))) 543.70/241.91 down(f(f(fresh_constant))) 543.70/241.91 down(g(g(a))) 543.70/241.91 down(g(g(f(x0)))) 543.70/241.91 down(g(g(b))) 543.70/241.91 down(g(g(c))) 543.70/241.91 down(g(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) 543.70/241.91 down(f(f(f(g(x0))))) 543.70/241.91 down(f(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) 543.70/241.91 down(g(g(g(f(x0))))) 543.70/241.91 down(g(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(x0)))))) 543.70/241.91 down(f(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(x0)))))) 543.70/241.91 down(g(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(x0))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(x0))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 f_flat(up(x0)) 543.70/241.91 g_flat(up(x0)) 543.70/241.91 543.70/241.91 We have to consider all minimal (P,Q,R)-chains. 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (721) TransformationProof (EQUIVALENT) 543.70/241.91 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(g(fresh_constant))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.91 543.70/241.91 (TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant)))))))))))) 543.70/241.91 543.70/241.91 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (722) 543.70/241.91 Obligation: 543.70/241.91 Q DP problem: 543.70/241.91 The TRS P consists of the following rules: 543.70/241.91 543.70/241.91 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.91 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.91 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.91 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.91 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.91 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.91 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.91 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.91 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.91 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.91 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.91 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.91 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.91 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.91 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.91 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.91 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.91 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.91 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.91 TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) 543.70/241.91 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.91 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.91 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.91 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.91 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.91 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.70/241.91 543.70/241.91 The TRS R consists of the following rules: 543.70/241.91 543.70/241.91 down(a) -> up(f(a)) 543.70/241.91 down(b) -> up(g(b)) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.91 down(f(a)) -> f_flat(down(a)) 543.70/241.91 down(f(b)) -> f_flat(down(b)) 543.70/241.91 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.91 down(f(c)) -> f_flat(down(c)) 543.70/241.91 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.91 down(g(a)) -> g_flat(down(a)) 543.70/241.91 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.91 down(g(b)) -> g_flat(down(b)) 543.70/241.91 down(g(c)) -> g_flat(down(c)) 543.70/241.91 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.91 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.91 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.91 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.91 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.91 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.91 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.91 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.91 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.91 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.91 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.91 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.91 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.91 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.91 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.91 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.91 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.91 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.91 543.70/241.91 The set Q consists of the following terms: 543.70/241.91 543.70/241.91 down(a) 543.70/241.91 down(b) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.91 down(f(a)) 543.70/241.91 down(f(b)) 543.70/241.91 down(f(g(x0))) 543.70/241.91 down(f(c)) 543.70/241.91 down(f(fresh_constant)) 543.70/241.91 down(g(a)) 543.70/241.91 down(g(f(x0))) 543.70/241.91 down(g(b)) 543.70/241.91 down(g(c)) 543.70/241.91 down(g(fresh_constant)) 543.70/241.91 down(f(f(a))) 543.70/241.91 down(f(f(b))) 543.70/241.91 down(f(f(g(x0)))) 543.70/241.91 down(f(f(c))) 543.70/241.91 down(f(f(fresh_constant))) 543.70/241.91 down(g(g(a))) 543.70/241.91 down(g(g(f(x0)))) 543.70/241.91 down(g(g(b))) 543.70/241.91 down(g(g(c))) 543.70/241.91 down(g(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) 543.70/241.91 down(f(f(f(g(x0))))) 543.70/241.91 down(f(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) 543.70/241.91 down(g(g(g(f(x0))))) 543.70/241.91 down(g(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(x0)))))) 543.70/241.91 down(f(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(x0)))))) 543.70/241.91 down(g(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(x0))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(x0))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 f_flat(up(x0)) 543.70/241.91 g_flat(up(x0)) 543.70/241.91 543.70/241.91 We have to consider all minimal (P,Q,R)-chains. 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (723) TransformationProof (EQUIVALENT) 543.70/241.91 By rewriting [LPAR04] the rule TOP(up(g(g(g(a))))) -> TOP(g_flat(g_flat(up(g(f(a)))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.70/241.91 543.70/241.91 (TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))),TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a))))))) 543.70/241.91 543.70/241.91 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (724) 543.70/241.91 Obligation: 543.70/241.91 Q DP problem: 543.70/241.91 The TRS P consists of the following rules: 543.70/241.91 543.70/241.91 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.91 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.91 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.91 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.91 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.91 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.91 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.91 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.91 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.91 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.91 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.91 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.91 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.91 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.91 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.91 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.91 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.91 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.91 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.91 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.91 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.91 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.91 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.91 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.91 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.70/241.91 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.70/241.91 543.70/241.91 The TRS R consists of the following rules: 543.70/241.91 543.70/241.91 down(a) -> up(f(a)) 543.70/241.91 down(b) -> up(g(b)) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.91 down(f(a)) -> f_flat(down(a)) 543.70/241.91 down(f(b)) -> f_flat(down(b)) 543.70/241.91 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.91 down(f(c)) -> f_flat(down(c)) 543.70/241.91 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.91 down(g(a)) -> g_flat(down(a)) 543.70/241.91 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.91 down(g(b)) -> g_flat(down(b)) 543.70/241.91 down(g(c)) -> g_flat(down(c)) 543.70/241.91 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.91 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.91 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.91 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.91 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.91 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.91 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.91 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.91 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.91 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.91 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.91 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.91 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.91 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.91 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.91 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.91 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.91 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.91 543.70/241.91 The set Q consists of the following terms: 543.70/241.91 543.70/241.91 down(a) 543.70/241.91 down(b) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.91 down(f(a)) 543.70/241.91 down(f(b)) 543.70/241.91 down(f(g(x0))) 543.70/241.91 down(f(c)) 543.70/241.91 down(f(fresh_constant)) 543.70/241.91 down(g(a)) 543.70/241.91 down(g(f(x0))) 543.70/241.91 down(g(b)) 543.70/241.91 down(g(c)) 543.70/241.91 down(g(fresh_constant)) 543.70/241.91 down(f(f(a))) 543.70/241.91 down(f(f(b))) 543.70/241.91 down(f(f(g(x0)))) 543.70/241.91 down(f(f(c))) 543.70/241.91 down(f(f(fresh_constant))) 543.70/241.91 down(g(g(a))) 543.70/241.91 down(g(g(f(x0)))) 543.70/241.91 down(g(g(b))) 543.70/241.91 down(g(g(c))) 543.70/241.91 down(g(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) 543.70/241.91 down(f(f(f(g(x0))))) 543.70/241.91 down(f(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) 543.70/241.91 down(g(g(g(f(x0))))) 543.70/241.91 down(g(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(x0)))))) 543.70/241.91 down(f(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(x0)))))) 543.70/241.91 down(g(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(x0))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(x0))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 f_flat(up(x0)) 543.70/241.91 g_flat(up(x0)) 543.70/241.91 543.70/241.91 We have to consider all minimal (P,Q,R)-chains. 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (725) TransformationProof (EQUIVALENT) 543.70/241.91 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(f(a))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.91 543.70/241.91 (TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))),TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.70/241.91 543.70/241.91 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (726) 543.70/241.91 Obligation: 543.70/241.91 Q DP problem: 543.70/241.91 The TRS P consists of the following rules: 543.70/241.91 543.70/241.91 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.91 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.91 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.91 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.91 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.91 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.91 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.91 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.91 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.91 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.91 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.91 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.91 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.91 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.91 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.91 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.91 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.91 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.91 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.91 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) 543.70/241.91 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.91 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.91 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.91 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.91 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.70/241.91 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.70/241.91 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.70/241.91 543.70/241.91 The TRS R consists of the following rules: 543.70/241.91 543.70/241.91 down(a) -> up(f(a)) 543.70/241.91 down(b) -> up(g(b)) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.91 down(f(a)) -> f_flat(down(a)) 543.70/241.91 down(f(b)) -> f_flat(down(b)) 543.70/241.91 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.91 down(f(c)) -> f_flat(down(c)) 543.70/241.91 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.91 down(g(a)) -> g_flat(down(a)) 543.70/241.91 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.91 down(g(b)) -> g_flat(down(b)) 543.70/241.91 down(g(c)) -> g_flat(down(c)) 543.70/241.91 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.91 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.91 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.91 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.91 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.91 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.91 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.91 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.91 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.91 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.91 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.91 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.91 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.91 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.91 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.91 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.91 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.91 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.91 543.70/241.91 The set Q consists of the following terms: 543.70/241.91 543.70/241.91 down(a) 543.70/241.91 down(b) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.91 down(f(a)) 543.70/241.91 down(f(b)) 543.70/241.91 down(f(g(x0))) 543.70/241.91 down(f(c)) 543.70/241.91 down(f(fresh_constant)) 543.70/241.91 down(g(a)) 543.70/241.91 down(g(f(x0))) 543.70/241.91 down(g(b)) 543.70/241.91 down(g(c)) 543.70/241.91 down(g(fresh_constant)) 543.70/241.91 down(f(f(a))) 543.70/241.91 down(f(f(b))) 543.70/241.91 down(f(f(g(x0)))) 543.70/241.91 down(f(f(c))) 543.70/241.91 down(f(f(fresh_constant))) 543.70/241.91 down(g(g(a))) 543.70/241.91 down(g(g(f(x0)))) 543.70/241.91 down(g(g(b))) 543.70/241.91 down(g(g(c))) 543.70/241.91 down(g(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) 543.70/241.91 down(f(f(f(g(x0))))) 543.70/241.91 down(f(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) 543.70/241.91 down(g(g(g(f(x0))))) 543.70/241.91 down(g(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(x0)))))) 543.70/241.91 down(f(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(x0)))))) 543.70/241.91 down(g(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(x0))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(x0))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 f_flat(up(x0)) 543.70/241.91 g_flat(up(x0)) 543.70/241.91 543.70/241.91 We have to consider all minimal (P,Q,R)-chains. 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (727) TransformationProof (EQUIVALENT) 543.70/241.91 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.91 543.70/241.91 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.70/241.91 543.70/241.91 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (728) 543.70/241.91 Obligation: 543.70/241.91 Q DP problem: 543.70/241.91 The TRS P consists of the following rules: 543.70/241.91 543.70/241.91 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.91 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.91 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.91 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.91 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.91 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.91 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.91 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.91 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.91 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.91 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.91 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.91 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.91 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.91 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.91 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.91 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.91 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.91 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.91 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.91 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.91 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.91 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.91 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.70/241.91 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.70/241.91 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.70/241.91 543.70/241.91 The TRS R consists of the following rules: 543.70/241.91 543.70/241.91 down(a) -> up(f(a)) 543.70/241.91 down(b) -> up(g(b)) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.91 down(f(a)) -> f_flat(down(a)) 543.70/241.91 down(f(b)) -> f_flat(down(b)) 543.70/241.91 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.91 down(f(c)) -> f_flat(down(c)) 543.70/241.91 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.91 down(g(a)) -> g_flat(down(a)) 543.70/241.91 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.91 down(g(b)) -> g_flat(down(b)) 543.70/241.91 down(g(c)) -> g_flat(down(c)) 543.70/241.91 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.91 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.91 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.91 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.91 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.91 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.91 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.91 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.91 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.91 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.91 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.91 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.91 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.91 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.91 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.91 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.91 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.91 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.91 543.70/241.91 The set Q consists of the following terms: 543.70/241.91 543.70/241.91 down(a) 543.70/241.91 down(b) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.91 down(f(a)) 543.70/241.91 down(f(b)) 543.70/241.91 down(f(g(x0))) 543.70/241.91 down(f(c)) 543.70/241.91 down(f(fresh_constant)) 543.70/241.91 down(g(a)) 543.70/241.91 down(g(f(x0))) 543.70/241.91 down(g(b)) 543.70/241.91 down(g(c)) 543.70/241.91 down(g(fresh_constant)) 543.70/241.91 down(f(f(a))) 543.70/241.91 down(f(f(b))) 543.70/241.91 down(f(f(g(x0)))) 543.70/241.91 down(f(f(c))) 543.70/241.91 down(f(f(fresh_constant))) 543.70/241.91 down(g(g(a))) 543.70/241.91 down(g(g(f(x0)))) 543.70/241.91 down(g(g(b))) 543.70/241.91 down(g(g(c))) 543.70/241.91 down(g(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) 543.70/241.91 down(f(f(f(g(x0))))) 543.70/241.91 down(f(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) 543.70/241.91 down(g(g(g(f(x0))))) 543.70/241.91 down(g(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(x0)))))) 543.70/241.91 down(f(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(x0)))))) 543.70/241.91 down(g(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(x0))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(x0))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 f_flat(up(x0)) 543.70/241.91 g_flat(up(x0)) 543.70/241.91 543.70/241.91 We have to consider all minimal (P,Q,R)-chains. 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (729) TransformationProof (EQUIVALENT) 543.70/241.91 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.91 543.70/241.91 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.70/241.91 543.70/241.91 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (730) 543.70/241.91 Obligation: 543.70/241.91 Q DP problem: 543.70/241.91 The TRS P consists of the following rules: 543.70/241.91 543.70/241.91 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.91 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.91 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.91 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.91 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.91 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.91 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.91 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.91 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.91 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.91 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.91 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.91 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.91 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.91 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.91 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.91 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.91 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.91 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.91 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.91 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.91 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.91 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.91 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.70/241.91 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.70/241.91 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.70/241.91 543.70/241.91 The TRS R consists of the following rules: 543.70/241.91 543.70/241.91 down(a) -> up(f(a)) 543.70/241.91 down(b) -> up(g(b)) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.91 down(f(a)) -> f_flat(down(a)) 543.70/241.91 down(f(b)) -> f_flat(down(b)) 543.70/241.91 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.91 down(f(c)) -> f_flat(down(c)) 543.70/241.91 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.91 down(g(a)) -> g_flat(down(a)) 543.70/241.91 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.91 down(g(b)) -> g_flat(down(b)) 543.70/241.91 down(g(c)) -> g_flat(down(c)) 543.70/241.91 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.91 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.91 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.91 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.91 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.91 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.91 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.91 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.91 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.91 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.91 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.91 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.91 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.91 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.91 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.91 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.91 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.91 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.91 543.70/241.91 The set Q consists of the following terms: 543.70/241.91 543.70/241.91 down(a) 543.70/241.91 down(b) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.91 down(f(a)) 543.70/241.91 down(f(b)) 543.70/241.91 down(f(g(x0))) 543.70/241.91 down(f(c)) 543.70/241.91 down(f(fresh_constant)) 543.70/241.91 down(g(a)) 543.70/241.91 down(g(f(x0))) 543.70/241.91 down(g(b)) 543.70/241.91 down(g(c)) 543.70/241.91 down(g(fresh_constant)) 543.70/241.91 down(f(f(a))) 543.70/241.91 down(f(f(b))) 543.70/241.91 down(f(f(g(x0)))) 543.70/241.91 down(f(f(c))) 543.70/241.91 down(f(f(fresh_constant))) 543.70/241.91 down(g(g(a))) 543.70/241.91 down(g(g(f(x0)))) 543.70/241.91 down(g(g(b))) 543.70/241.91 down(g(g(c))) 543.70/241.91 down(g(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) 543.70/241.91 down(f(f(f(g(x0))))) 543.70/241.91 down(f(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) 543.70/241.91 down(g(g(g(f(x0))))) 543.70/241.91 down(g(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(x0)))))) 543.70/241.91 down(f(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(x0)))))) 543.70/241.91 down(g(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(x0))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(x0))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 f_flat(up(x0)) 543.70/241.91 g_flat(up(x0)) 543.70/241.91 543.70/241.91 We have to consider all minimal (P,Q,R)-chains. 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (731) TransformationProof (EQUIVALENT) 543.70/241.91 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.91 543.70/241.91 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.70/241.91 543.70/241.91 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (732) 543.70/241.91 Obligation: 543.70/241.91 Q DP problem: 543.70/241.91 The TRS P consists of the following rules: 543.70/241.91 543.70/241.91 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.91 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.91 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.91 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.91 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.91 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.91 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.91 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.91 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.91 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.91 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.91 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.91 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.91 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.91 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.91 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.91 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.91 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.91 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.91 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.91 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.91 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.91 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.91 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.70/241.91 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.70/241.91 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.70/241.91 543.70/241.91 The TRS R consists of the following rules: 543.70/241.91 543.70/241.91 down(a) -> up(f(a)) 543.70/241.91 down(b) -> up(g(b)) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.91 down(f(a)) -> f_flat(down(a)) 543.70/241.91 down(f(b)) -> f_flat(down(b)) 543.70/241.91 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.91 down(f(c)) -> f_flat(down(c)) 543.70/241.91 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.91 down(g(a)) -> g_flat(down(a)) 543.70/241.91 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.91 down(g(b)) -> g_flat(down(b)) 543.70/241.91 down(g(c)) -> g_flat(down(c)) 543.70/241.91 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.91 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.91 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.91 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.91 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.91 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.91 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.91 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.91 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.91 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.91 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.91 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.91 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.91 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.91 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.91 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.91 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.91 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.91 543.70/241.91 The set Q consists of the following terms: 543.70/241.91 543.70/241.91 down(a) 543.70/241.91 down(b) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.91 down(f(a)) 543.70/241.91 down(f(b)) 543.70/241.91 down(f(g(x0))) 543.70/241.91 down(f(c)) 543.70/241.91 down(f(fresh_constant)) 543.70/241.91 down(g(a)) 543.70/241.91 down(g(f(x0))) 543.70/241.91 down(g(b)) 543.70/241.91 down(g(c)) 543.70/241.91 down(g(fresh_constant)) 543.70/241.91 down(f(f(a))) 543.70/241.91 down(f(f(b))) 543.70/241.91 down(f(f(g(x0)))) 543.70/241.91 down(f(f(c))) 543.70/241.91 down(f(f(fresh_constant))) 543.70/241.91 down(g(g(a))) 543.70/241.91 down(g(g(f(x0)))) 543.70/241.91 down(g(g(b))) 543.70/241.91 down(g(g(c))) 543.70/241.91 down(g(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) 543.70/241.91 down(f(f(f(g(x0))))) 543.70/241.91 down(f(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) 543.70/241.91 down(g(g(g(f(x0))))) 543.70/241.91 down(g(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(x0)))))) 543.70/241.91 down(f(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(x0)))))) 543.70/241.91 down(g(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(x0))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(x0))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 f_flat(up(x0)) 543.70/241.91 g_flat(up(x0)) 543.70/241.91 543.70/241.91 We have to consider all minimal (P,Q,R)-chains. 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (733) TransformationProof (EQUIVALENT) 543.70/241.91 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.91 543.70/241.91 (TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))),TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.70/241.91 543.70/241.91 543.70/241.91 ---------------------------------------- 543.70/241.91 543.70/241.91 (734) 543.70/241.91 Obligation: 543.70/241.91 Q DP problem: 543.70/241.91 The TRS P consists of the following rules: 543.70/241.91 543.70/241.91 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.91 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.91 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.91 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.91 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.91 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.70/241.91 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.70/241.91 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.70/241.91 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.70/241.91 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.70/241.91 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.70/241.91 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.70/241.91 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.70/241.91 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.70/241.91 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.70/241.91 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.70/241.91 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.70/241.91 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.70/241.91 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.70/241.91 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) 543.70/241.91 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.70/241.91 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.70/241.91 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.70/241.91 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.70/241.91 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.70/241.91 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.70/241.91 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.70/241.91 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.70/241.91 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.70/241.91 543.70/241.91 The TRS R consists of the following rules: 543.70/241.91 543.70/241.91 down(a) -> up(f(a)) 543.70/241.91 down(b) -> up(g(b)) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.70/241.91 down(f(a)) -> f_flat(down(a)) 543.70/241.91 down(f(b)) -> f_flat(down(b)) 543.70/241.91 down(f(g(y4))) -> f_flat(down(g(y4))) 543.70/241.91 down(f(c)) -> f_flat(down(c)) 543.70/241.91 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.70/241.91 down(g(a)) -> g_flat(down(a)) 543.70/241.91 down(g(f(y6))) -> g_flat(down(f(y6))) 543.70/241.91 down(g(b)) -> g_flat(down(b)) 543.70/241.91 down(g(c)) -> g_flat(down(c)) 543.70/241.91 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.70/241.91 down(f(f(a))) -> f_flat(down(f(a))) 543.70/241.91 down(f(f(b))) -> f_flat(down(f(b))) 543.70/241.91 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.70/241.91 down(f(f(c))) -> f_flat(down(f(c))) 543.70/241.91 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.70/241.91 down(g(g(a))) -> g_flat(down(g(a))) 543.70/241.91 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.70/241.91 down(g(g(b))) -> g_flat(down(g(b))) 543.70/241.91 down(g(g(c))) -> g_flat(down(g(c))) 543.70/241.91 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.70/241.91 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.70/241.91 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.70/241.91 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.70/241.91 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.70/241.91 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.70/241.91 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.70/241.91 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.91 g_flat(up(x_1)) -> up(g(x_1)) 543.70/241.91 f_flat(up(x_1)) -> up(f(x_1)) 543.70/241.91 543.70/241.91 The set Q consists of the following terms: 543.70/241.91 543.70/241.91 down(a) 543.70/241.91 down(b) 543.70/241.91 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.70/241.91 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.70/241.91 down(f(a)) 543.70/241.91 down(f(b)) 543.70/241.91 down(f(g(x0))) 543.70/241.91 down(f(c)) 543.70/241.91 down(f(fresh_constant)) 543.70/241.91 down(g(a)) 543.70/241.91 down(g(f(x0))) 543.70/241.91 down(g(b)) 543.70/241.91 down(g(c)) 543.70/241.91 down(g(fresh_constant)) 543.70/241.91 down(f(f(a))) 543.70/241.91 down(f(f(b))) 543.70/241.91 down(f(f(g(x0)))) 543.70/241.91 down(f(f(c))) 543.70/241.91 down(f(f(fresh_constant))) 543.70/241.91 down(g(g(a))) 543.70/241.91 down(g(g(f(x0)))) 543.70/241.91 down(g(g(b))) 543.70/241.91 down(g(g(c))) 543.70/241.91 down(g(g(fresh_constant))) 543.70/241.91 down(f(f(f(a)))) 543.70/241.91 down(f(f(f(b)))) 543.70/241.91 down(f(f(f(g(x0))))) 543.70/241.91 down(f(f(f(c)))) 543.70/241.91 down(f(f(f(fresh_constant)))) 543.70/241.91 down(g(g(g(a)))) 543.70/241.91 down(g(g(g(f(x0))))) 543.70/241.91 down(g(g(g(b)))) 543.70/241.91 down(g(g(g(c)))) 543.70/241.91 down(g(g(g(fresh_constant)))) 543.70/241.91 down(f(f(f(f(a))))) 543.70/241.91 down(f(f(f(f(b))))) 543.70/241.91 down(f(f(f(f(g(x0)))))) 543.70/241.91 down(f(f(f(f(c))))) 543.70/241.91 down(f(f(f(f(fresh_constant))))) 543.70/241.91 down(g(g(g(g(a))))) 543.70/241.91 down(g(g(g(g(f(x0)))))) 543.70/241.91 down(g(g(g(g(b))))) 543.70/241.91 down(g(g(g(g(c))))) 543.70/241.91 down(g(g(g(g(fresh_constant))))) 543.70/241.91 down(f(f(f(f(f(a)))))) 543.70/241.91 down(f(f(f(f(f(b)))))) 543.70/241.91 down(f(f(f(f(f(g(x0))))))) 543.70/241.91 down(f(f(f(f(f(c)))))) 543.70/241.91 down(f(f(f(f(f(fresh_constant)))))) 543.70/241.91 down(g(g(g(g(g(a)))))) 543.70/241.91 down(g(g(g(g(g(f(x0))))))) 543.70/241.91 down(g(g(g(g(g(b)))))) 543.70/241.91 down(g(g(g(g(g(c)))))) 543.70/241.91 down(g(g(g(g(g(fresh_constant)))))) 543.70/241.91 down(f(f(f(f(f(f(a))))))) 543.70/241.91 down(f(f(f(f(f(f(b))))))) 543.70/241.91 down(f(f(f(f(f(f(g(x0)))))))) 543.70/241.91 down(f(f(f(f(f(f(c))))))) 543.70/241.91 down(f(f(f(f(f(f(fresh_constant))))))) 543.70/241.91 down(g(g(g(g(g(g(a))))))) 543.70/241.91 down(g(g(g(g(g(g(f(x0)))))))) 543.70/241.91 down(g(g(g(g(g(g(b))))))) 543.70/241.91 down(g(g(g(g(g(g(c))))))) 543.70/241.91 down(g(g(g(g(g(g(fresh_constant))))))) 543.70/241.91 down(f(f(f(f(f(f(f(a)))))))) 543.70/241.92 down(f(f(f(f(f(f(f(b)))))))) 543.70/241.92 down(f(f(f(f(f(f(f(g(x0))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(c)))))))) 543.70/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.70/241.92 down(g(g(g(g(g(g(g(a)))))))) 543.70/241.92 down(g(g(g(g(g(g(g(f(x0))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(b)))))))) 543.70/241.92 down(g(g(g(g(g(g(g(c)))))))) 543.70/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(a))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(b))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(c))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(a))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(b))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(c))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.70/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.70/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.70/241.92 f_flat(up(x0)) 543.70/241.92 g_flat(up(x0)) 543.70/241.92 543.70/241.92 We have to consider all minimal (P,Q,R)-chains. 543.70/241.92 ---------------------------------------- 543.70/241.92 543.70/241.92 (735) TransformationProof (EQUIVALENT) 543.70/241.92 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.70/241.92 543.70/241.92 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) 543.70/241.92 543.70/241.92 543.70/241.92 ---------------------------------------- 543.70/241.92 543.70/241.92 (736) 543.70/241.92 Obligation: 543.70/241.92 Q DP problem: 543.70/241.92 The TRS P consists of the following rules: 543.70/241.92 543.70/241.92 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.70/241.92 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.70/241.92 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.70/241.92 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.70/241.92 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.70/241.92 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.92 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.92 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.92 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.92 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.92 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.92 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.92 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.92 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.92 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.92 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.92 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.92 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.92 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.92 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.92 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.92 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.92 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.92 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.92 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.92 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))) 543.78/241.92 543.78/241.92 The TRS R consists of the following rules: 543.78/241.92 543.78/241.92 down(a) -> up(f(a)) 543.78/241.92 down(b) -> up(g(b)) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.92 down(f(a)) -> f_flat(down(a)) 543.78/241.92 down(f(b)) -> f_flat(down(b)) 543.78/241.92 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.92 down(f(c)) -> f_flat(down(c)) 543.78/241.92 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.92 down(g(a)) -> g_flat(down(a)) 543.78/241.92 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.92 down(g(b)) -> g_flat(down(b)) 543.78/241.92 down(g(c)) -> g_flat(down(c)) 543.78/241.92 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.92 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.92 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.92 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.92 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.92 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.92 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.92 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.92 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.92 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.92 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.92 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.92 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.92 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.92 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.92 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.92 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.92 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.92 543.78/241.92 The set Q consists of the following terms: 543.78/241.92 543.78/241.92 down(a) 543.78/241.92 down(b) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.92 down(f(a)) 543.78/241.92 down(f(b)) 543.78/241.92 down(f(g(x0))) 543.78/241.92 down(f(c)) 543.78/241.92 down(f(fresh_constant)) 543.78/241.92 down(g(a)) 543.78/241.92 down(g(f(x0))) 543.78/241.92 down(g(b)) 543.78/241.92 down(g(c)) 543.78/241.92 down(g(fresh_constant)) 543.78/241.92 down(f(f(a))) 543.78/241.92 down(f(f(b))) 543.78/241.92 down(f(f(g(x0)))) 543.78/241.92 down(f(f(c))) 543.78/241.92 down(f(f(fresh_constant))) 543.78/241.92 down(g(g(a))) 543.78/241.92 down(g(g(f(x0)))) 543.78/241.92 down(g(g(b))) 543.78/241.92 down(g(g(c))) 543.78/241.92 down(g(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) 543.78/241.92 down(f(f(f(g(x0))))) 543.78/241.92 down(f(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) 543.78/241.92 down(g(g(g(f(x0))))) 543.78/241.92 down(g(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(x0)))))) 543.78/241.92 down(f(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(x0)))))) 543.78/241.92 down(g(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(x0))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(x0))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 f_flat(up(x0)) 543.78/241.92 g_flat(up(x0)) 543.78/241.92 543.78/241.92 We have to consider all minimal (P,Q,R)-chains. 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (737) TransformationProof (EQUIVALENT) 543.78/241.92 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.92 543.78/241.92 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.78/241.92 543.78/241.92 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (738) 543.78/241.92 Obligation: 543.78/241.92 Q DP problem: 543.78/241.92 The TRS P consists of the following rules: 543.78/241.92 543.78/241.92 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.92 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.92 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.92 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.92 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.92 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.92 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.92 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.92 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.92 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.92 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.92 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.92 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.92 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.92 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.92 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.92 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.92 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.92 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.92 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.92 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.92 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.92 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.92 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.92 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.92 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.92 543.78/241.92 The TRS R consists of the following rules: 543.78/241.92 543.78/241.92 down(a) -> up(f(a)) 543.78/241.92 down(b) -> up(g(b)) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.92 down(f(a)) -> f_flat(down(a)) 543.78/241.92 down(f(b)) -> f_flat(down(b)) 543.78/241.92 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.92 down(f(c)) -> f_flat(down(c)) 543.78/241.92 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.92 down(g(a)) -> g_flat(down(a)) 543.78/241.92 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.92 down(g(b)) -> g_flat(down(b)) 543.78/241.92 down(g(c)) -> g_flat(down(c)) 543.78/241.92 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.92 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.92 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.92 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.92 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.92 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.92 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.92 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.92 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.92 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.92 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.92 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.92 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.92 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.92 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.92 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.92 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.92 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.92 543.78/241.92 The set Q consists of the following terms: 543.78/241.92 543.78/241.92 down(a) 543.78/241.92 down(b) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.92 down(f(a)) 543.78/241.92 down(f(b)) 543.78/241.92 down(f(g(x0))) 543.78/241.92 down(f(c)) 543.78/241.92 down(f(fresh_constant)) 543.78/241.92 down(g(a)) 543.78/241.92 down(g(f(x0))) 543.78/241.92 down(g(b)) 543.78/241.92 down(g(c)) 543.78/241.92 down(g(fresh_constant)) 543.78/241.92 down(f(f(a))) 543.78/241.92 down(f(f(b))) 543.78/241.92 down(f(f(g(x0)))) 543.78/241.92 down(f(f(c))) 543.78/241.92 down(f(f(fresh_constant))) 543.78/241.92 down(g(g(a))) 543.78/241.92 down(g(g(f(x0)))) 543.78/241.92 down(g(g(b))) 543.78/241.92 down(g(g(c))) 543.78/241.92 down(g(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) 543.78/241.92 down(f(f(f(g(x0))))) 543.78/241.92 down(f(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) 543.78/241.92 down(g(g(g(f(x0))))) 543.78/241.92 down(g(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(x0)))))) 543.78/241.92 down(f(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(x0)))))) 543.78/241.92 down(g(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(x0))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(x0))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 f_flat(up(x0)) 543.78/241.92 g_flat(up(x0)) 543.78/241.92 543.78/241.92 We have to consider all minimal (P,Q,R)-chains. 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (739) TransformationProof (EQUIVALENT) 543.78/241.92 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.92 543.78/241.92 (TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))),TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.78/241.92 543.78/241.92 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (740) 543.78/241.92 Obligation: 543.78/241.92 Q DP problem: 543.78/241.92 The TRS P consists of the following rules: 543.78/241.92 543.78/241.92 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.92 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.92 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.92 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.92 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.92 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.92 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.92 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.92 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.92 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.92 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.92 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.92 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.92 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.92 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.92 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.92 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.92 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.92 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.92 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.92 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.92 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.92 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.92 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.92 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.92 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.92 543.78/241.92 The TRS R consists of the following rules: 543.78/241.92 543.78/241.92 down(a) -> up(f(a)) 543.78/241.92 down(b) -> up(g(b)) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.92 down(f(a)) -> f_flat(down(a)) 543.78/241.92 down(f(b)) -> f_flat(down(b)) 543.78/241.92 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.92 down(f(c)) -> f_flat(down(c)) 543.78/241.92 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.92 down(g(a)) -> g_flat(down(a)) 543.78/241.92 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.92 down(g(b)) -> g_flat(down(b)) 543.78/241.92 down(g(c)) -> g_flat(down(c)) 543.78/241.92 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.92 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.92 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.92 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.92 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.92 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.92 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.92 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.92 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.92 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.92 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.92 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.92 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.92 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.92 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.92 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.92 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.92 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.92 543.78/241.92 The set Q consists of the following terms: 543.78/241.92 543.78/241.92 down(a) 543.78/241.92 down(b) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.92 down(f(a)) 543.78/241.92 down(f(b)) 543.78/241.92 down(f(g(x0))) 543.78/241.92 down(f(c)) 543.78/241.92 down(f(fresh_constant)) 543.78/241.92 down(g(a)) 543.78/241.92 down(g(f(x0))) 543.78/241.92 down(g(b)) 543.78/241.92 down(g(c)) 543.78/241.92 down(g(fresh_constant)) 543.78/241.92 down(f(f(a))) 543.78/241.92 down(f(f(b))) 543.78/241.92 down(f(f(g(x0)))) 543.78/241.92 down(f(f(c))) 543.78/241.92 down(f(f(fresh_constant))) 543.78/241.92 down(g(g(a))) 543.78/241.92 down(g(g(f(x0)))) 543.78/241.92 down(g(g(b))) 543.78/241.92 down(g(g(c))) 543.78/241.92 down(g(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) 543.78/241.92 down(f(f(f(g(x0))))) 543.78/241.92 down(f(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) 543.78/241.92 down(g(g(g(f(x0))))) 543.78/241.92 down(g(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(x0)))))) 543.78/241.92 down(f(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(x0)))))) 543.78/241.92 down(g(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(x0))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(x0))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 f_flat(up(x0)) 543.78/241.92 g_flat(up(x0)) 543.78/241.92 543.78/241.92 We have to consider all minimal (P,Q,R)-chains. 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (741) TransformationProof (EQUIVALENT) 543.78/241.92 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.92 543.78/241.92 (TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c)))))))),TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c))))))))) 543.78/241.92 543.78/241.92 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (742) 543.78/241.92 Obligation: 543.78/241.92 Q DP problem: 543.78/241.92 The TRS P consists of the following rules: 543.78/241.92 543.78/241.92 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.92 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.92 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.92 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.92 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.92 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.92 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.92 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.92 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.92 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.92 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.92 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.92 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.92 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.92 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.92 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.92 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.92 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.92 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.92 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.92 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.92 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.92 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.92 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.92 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.92 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(c)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c)))))))) 543.78/241.92 543.78/241.92 The TRS R consists of the following rules: 543.78/241.92 543.78/241.92 down(a) -> up(f(a)) 543.78/241.92 down(b) -> up(g(b)) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.92 down(f(a)) -> f_flat(down(a)) 543.78/241.92 down(f(b)) -> f_flat(down(b)) 543.78/241.92 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.92 down(f(c)) -> f_flat(down(c)) 543.78/241.92 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.92 down(g(a)) -> g_flat(down(a)) 543.78/241.92 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.92 down(g(b)) -> g_flat(down(b)) 543.78/241.92 down(g(c)) -> g_flat(down(c)) 543.78/241.92 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.92 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.92 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.92 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.92 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.92 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.92 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.92 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.92 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.92 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.92 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.92 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.92 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.92 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.92 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.92 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.92 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.92 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.92 543.78/241.92 The set Q consists of the following terms: 543.78/241.92 543.78/241.92 down(a) 543.78/241.92 down(b) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.92 down(f(a)) 543.78/241.92 down(f(b)) 543.78/241.92 down(f(g(x0))) 543.78/241.92 down(f(c)) 543.78/241.92 down(f(fresh_constant)) 543.78/241.92 down(g(a)) 543.78/241.92 down(g(f(x0))) 543.78/241.92 down(g(b)) 543.78/241.92 down(g(c)) 543.78/241.92 down(g(fresh_constant)) 543.78/241.92 down(f(f(a))) 543.78/241.92 down(f(f(b))) 543.78/241.92 down(f(f(g(x0)))) 543.78/241.92 down(f(f(c))) 543.78/241.92 down(f(f(fresh_constant))) 543.78/241.92 down(g(g(a))) 543.78/241.92 down(g(g(f(x0)))) 543.78/241.92 down(g(g(b))) 543.78/241.92 down(g(g(c))) 543.78/241.92 down(g(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) 543.78/241.92 down(f(f(f(g(x0))))) 543.78/241.92 down(f(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) 543.78/241.92 down(g(g(g(f(x0))))) 543.78/241.92 down(g(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(x0)))))) 543.78/241.92 down(f(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(x0)))))) 543.78/241.92 down(g(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(x0))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(x0))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 f_flat(up(x0)) 543.78/241.92 g_flat(up(x0)) 543.78/241.92 543.78/241.92 We have to consider all minimal (P,Q,R)-chains. 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (743) DependencyGraphProof (EQUIVALENT) 543.78/241.92 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (744) 543.78/241.92 Obligation: 543.78/241.92 Q DP problem: 543.78/241.92 The TRS P consists of the following rules: 543.78/241.92 543.78/241.92 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.92 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.92 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.92 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.92 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.92 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.92 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.92 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.92 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) 543.78/241.92 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.92 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.92 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.92 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.92 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.92 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.92 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))) 543.78/241.92 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.92 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.92 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.92 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.92 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.92 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.92 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.92 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.92 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.92 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.92 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.92 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.92 543.78/241.92 The TRS R consists of the following rules: 543.78/241.92 543.78/241.92 down(a) -> up(f(a)) 543.78/241.92 down(b) -> up(g(b)) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.92 down(f(a)) -> f_flat(down(a)) 543.78/241.92 down(f(b)) -> f_flat(down(b)) 543.78/241.92 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.92 down(f(c)) -> f_flat(down(c)) 543.78/241.92 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.92 down(g(a)) -> g_flat(down(a)) 543.78/241.92 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.92 down(g(b)) -> g_flat(down(b)) 543.78/241.92 down(g(c)) -> g_flat(down(c)) 543.78/241.92 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.92 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.92 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.92 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.92 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.92 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.92 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.92 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.92 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.92 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.92 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.92 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.92 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.92 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.92 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.92 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.92 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.92 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.92 543.78/241.92 The set Q consists of the following terms: 543.78/241.92 543.78/241.92 down(a) 543.78/241.92 down(b) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.92 down(f(a)) 543.78/241.92 down(f(b)) 543.78/241.92 down(f(g(x0))) 543.78/241.92 down(f(c)) 543.78/241.92 down(f(fresh_constant)) 543.78/241.92 down(g(a)) 543.78/241.92 down(g(f(x0))) 543.78/241.92 down(g(b)) 543.78/241.92 down(g(c)) 543.78/241.92 down(g(fresh_constant)) 543.78/241.92 down(f(f(a))) 543.78/241.92 down(f(f(b))) 543.78/241.92 down(f(f(g(x0)))) 543.78/241.92 down(f(f(c))) 543.78/241.92 down(f(f(fresh_constant))) 543.78/241.92 down(g(g(a))) 543.78/241.92 down(g(g(f(x0)))) 543.78/241.92 down(g(g(b))) 543.78/241.92 down(g(g(c))) 543.78/241.92 down(g(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) 543.78/241.92 down(f(f(f(g(x0))))) 543.78/241.92 down(f(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) 543.78/241.92 down(g(g(g(f(x0))))) 543.78/241.92 down(g(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(x0)))))) 543.78/241.92 down(f(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(x0)))))) 543.78/241.92 down(g(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(x0))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(x0))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 f_flat(up(x0)) 543.78/241.92 g_flat(up(x0)) 543.78/241.92 543.78/241.92 We have to consider all minimal (P,Q,R)-chains. 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (745) TransformationProof (EQUIVALENT) 543.78/241.92 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.92 543.78/241.92 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))) 543.78/241.92 543.78/241.92 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (746) 543.78/241.92 Obligation: 543.78/241.92 Q DP problem: 543.78/241.92 The TRS P consists of the following rules: 543.78/241.92 543.78/241.92 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.92 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.92 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.92 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.92 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.92 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.92 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.92 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.92 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.92 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.92 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.92 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.92 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.92 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.92 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))) 543.78/241.92 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.92 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.92 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.92 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.92 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.92 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.92 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.92 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.92 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.92 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.92 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.92 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))) 543.78/241.92 543.78/241.92 The TRS R consists of the following rules: 543.78/241.92 543.78/241.92 down(a) -> up(f(a)) 543.78/241.92 down(b) -> up(g(b)) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.92 down(f(a)) -> f_flat(down(a)) 543.78/241.92 down(f(b)) -> f_flat(down(b)) 543.78/241.92 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.92 down(f(c)) -> f_flat(down(c)) 543.78/241.92 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.92 down(g(a)) -> g_flat(down(a)) 543.78/241.92 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.92 down(g(b)) -> g_flat(down(b)) 543.78/241.92 down(g(c)) -> g_flat(down(c)) 543.78/241.92 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.92 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.92 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.92 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.92 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.92 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.92 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.92 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.92 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.92 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.92 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.92 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.92 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.92 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.92 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.92 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.92 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.92 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.92 543.78/241.92 The set Q consists of the following terms: 543.78/241.92 543.78/241.92 down(a) 543.78/241.92 down(b) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.92 down(f(a)) 543.78/241.92 down(f(b)) 543.78/241.92 down(f(g(x0))) 543.78/241.92 down(f(c)) 543.78/241.92 down(f(fresh_constant)) 543.78/241.92 down(g(a)) 543.78/241.92 down(g(f(x0))) 543.78/241.92 down(g(b)) 543.78/241.92 down(g(c)) 543.78/241.92 down(g(fresh_constant)) 543.78/241.92 down(f(f(a))) 543.78/241.92 down(f(f(b))) 543.78/241.92 down(f(f(g(x0)))) 543.78/241.92 down(f(f(c))) 543.78/241.92 down(f(f(fresh_constant))) 543.78/241.92 down(g(g(a))) 543.78/241.92 down(g(g(f(x0)))) 543.78/241.92 down(g(g(b))) 543.78/241.92 down(g(g(c))) 543.78/241.92 down(g(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) 543.78/241.92 down(f(f(f(g(x0))))) 543.78/241.92 down(f(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) 543.78/241.92 down(g(g(g(f(x0))))) 543.78/241.92 down(g(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(x0)))))) 543.78/241.92 down(f(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(x0)))))) 543.78/241.92 down(g(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(x0))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(x0))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 f_flat(up(x0)) 543.78/241.92 g_flat(up(x0)) 543.78/241.92 543.78/241.92 We have to consider all minimal (P,Q,R)-chains. 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (747) TransformationProof (EQUIVALENT) 543.78/241.92 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.92 543.78/241.92 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))) 543.78/241.92 543.78/241.92 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (748) 543.78/241.92 Obligation: 543.78/241.92 Q DP problem: 543.78/241.92 The TRS P consists of the following rules: 543.78/241.92 543.78/241.92 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.92 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.92 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.92 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.92 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.92 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.92 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.92 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.92 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.92 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.92 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.92 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.92 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.92 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.92 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.92 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.92 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.92 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.92 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.92 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.92 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.92 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.92 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.92 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.92 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.92 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.92 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.92 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.92 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))) 543.78/241.92 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))) 543.78/241.92 543.78/241.92 The TRS R consists of the following rules: 543.78/241.92 543.78/241.92 down(a) -> up(f(a)) 543.78/241.92 down(b) -> up(g(b)) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.92 down(f(a)) -> f_flat(down(a)) 543.78/241.92 down(f(b)) -> f_flat(down(b)) 543.78/241.92 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.92 down(f(c)) -> f_flat(down(c)) 543.78/241.92 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.92 down(g(a)) -> g_flat(down(a)) 543.78/241.92 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.92 down(g(b)) -> g_flat(down(b)) 543.78/241.92 down(g(c)) -> g_flat(down(c)) 543.78/241.92 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.92 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.92 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.92 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.92 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.92 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.92 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.92 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.92 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.92 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.92 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.92 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.92 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.92 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.92 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.92 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.92 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.92 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.92 543.78/241.92 The set Q consists of the following terms: 543.78/241.92 543.78/241.92 down(a) 543.78/241.92 down(b) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.92 down(f(a)) 543.78/241.92 down(f(b)) 543.78/241.92 down(f(g(x0))) 543.78/241.92 down(f(c)) 543.78/241.92 down(f(fresh_constant)) 543.78/241.92 down(g(a)) 543.78/241.92 down(g(f(x0))) 543.78/241.92 down(g(b)) 543.78/241.92 down(g(c)) 543.78/241.92 down(g(fresh_constant)) 543.78/241.92 down(f(f(a))) 543.78/241.92 down(f(f(b))) 543.78/241.92 down(f(f(g(x0)))) 543.78/241.92 down(f(f(c))) 543.78/241.92 down(f(f(fresh_constant))) 543.78/241.92 down(g(g(a))) 543.78/241.92 down(g(g(f(x0)))) 543.78/241.92 down(g(g(b))) 543.78/241.92 down(g(g(c))) 543.78/241.92 down(g(g(fresh_constant))) 543.78/241.92 down(f(f(f(a)))) 543.78/241.92 down(f(f(f(b)))) 543.78/241.92 down(f(f(f(g(x0))))) 543.78/241.92 down(f(f(f(c)))) 543.78/241.92 down(f(f(f(fresh_constant)))) 543.78/241.92 down(g(g(g(a)))) 543.78/241.92 down(g(g(g(f(x0))))) 543.78/241.92 down(g(g(g(b)))) 543.78/241.92 down(g(g(g(c)))) 543.78/241.92 down(g(g(g(fresh_constant)))) 543.78/241.92 down(f(f(f(f(a))))) 543.78/241.92 down(f(f(f(f(b))))) 543.78/241.92 down(f(f(f(f(g(x0)))))) 543.78/241.92 down(f(f(f(f(c))))) 543.78/241.92 down(f(f(f(f(fresh_constant))))) 543.78/241.92 down(g(g(g(g(a))))) 543.78/241.92 down(g(g(g(g(f(x0)))))) 543.78/241.92 down(g(g(g(g(b))))) 543.78/241.92 down(g(g(g(g(c))))) 543.78/241.92 down(g(g(g(g(fresh_constant))))) 543.78/241.92 down(f(f(f(f(f(a)))))) 543.78/241.92 down(f(f(f(f(f(b)))))) 543.78/241.92 down(f(f(f(f(f(g(x0))))))) 543.78/241.92 down(f(f(f(f(f(c)))))) 543.78/241.92 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.92 down(g(g(g(g(g(a)))))) 543.78/241.92 down(g(g(g(g(g(f(x0))))))) 543.78/241.92 down(g(g(g(g(g(b)))))) 543.78/241.92 down(g(g(g(g(g(c)))))) 543.78/241.92 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.92 down(f(f(f(f(f(f(a))))))) 543.78/241.92 down(f(f(f(f(f(f(b))))))) 543.78/241.92 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.92 down(f(f(f(f(f(f(c))))))) 543.78/241.92 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.92 down(g(g(g(g(g(g(a))))))) 543.78/241.92 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.92 down(g(g(g(g(g(g(b))))))) 543.78/241.92 down(g(g(g(g(g(g(c))))))) 543.78/241.92 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.92 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.92 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.92 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.92 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.92 f_flat(up(x0)) 543.78/241.92 g_flat(up(x0)) 543.78/241.92 543.78/241.92 We have to consider all minimal (P,Q,R)-chains. 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (749) TransformationProof (EQUIVALENT) 543.78/241.92 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.92 543.78/241.92 (TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant)))))))),TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant))))))))) 543.78/241.92 543.78/241.92 543.78/241.92 ---------------------------------------- 543.78/241.92 543.78/241.92 (750) 543.78/241.92 Obligation: 543.78/241.92 Q DP problem: 543.78/241.92 The TRS P consists of the following rules: 543.78/241.92 543.78/241.92 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.93 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.93 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.93 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.93 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.93 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.93 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.93 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.93 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.93 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.93 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.93 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.93 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.93 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.93 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.93 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.93 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.93 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.93 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.93 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.93 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.93 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.93 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.93 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.93 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.93 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.93 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(fresh_constant)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant)))))))) 543.78/241.93 543.78/241.93 The TRS R consists of the following rules: 543.78/241.93 543.78/241.93 down(a) -> up(f(a)) 543.78/241.93 down(b) -> up(g(b)) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.93 down(f(a)) -> f_flat(down(a)) 543.78/241.93 down(f(b)) -> f_flat(down(b)) 543.78/241.93 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.93 down(f(c)) -> f_flat(down(c)) 543.78/241.93 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.93 down(g(a)) -> g_flat(down(a)) 543.78/241.93 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.93 down(g(b)) -> g_flat(down(b)) 543.78/241.93 down(g(c)) -> g_flat(down(c)) 543.78/241.93 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.93 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.93 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.93 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.93 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.93 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.93 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.93 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.93 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.93 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.93 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.93 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.93 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.93 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.93 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.93 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.93 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.93 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.93 543.78/241.93 The set Q consists of the following terms: 543.78/241.93 543.78/241.93 down(a) 543.78/241.93 down(b) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.93 down(f(a)) 543.78/241.93 down(f(b)) 543.78/241.93 down(f(g(x0))) 543.78/241.93 down(f(c)) 543.78/241.93 down(f(fresh_constant)) 543.78/241.93 down(g(a)) 543.78/241.93 down(g(f(x0))) 543.78/241.93 down(g(b)) 543.78/241.93 down(g(c)) 543.78/241.93 down(g(fresh_constant)) 543.78/241.93 down(f(f(a))) 543.78/241.93 down(f(f(b))) 543.78/241.93 down(f(f(g(x0)))) 543.78/241.93 down(f(f(c))) 543.78/241.93 down(f(f(fresh_constant))) 543.78/241.93 down(g(g(a))) 543.78/241.93 down(g(g(f(x0)))) 543.78/241.93 down(g(g(b))) 543.78/241.93 down(g(g(c))) 543.78/241.93 down(g(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) 543.78/241.93 down(f(f(f(g(x0))))) 543.78/241.93 down(f(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) 543.78/241.93 down(g(g(g(f(x0))))) 543.78/241.93 down(g(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(x0)))))) 543.78/241.93 down(f(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(x0)))))) 543.78/241.93 down(g(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(x0))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(x0))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 f_flat(up(x0)) 543.78/241.93 g_flat(up(x0)) 543.78/241.93 543.78/241.93 We have to consider all minimal (P,Q,R)-chains. 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (751) DependencyGraphProof (EQUIVALENT) 543.78/241.93 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (752) 543.78/241.93 Obligation: 543.78/241.93 Q DP problem: 543.78/241.93 The TRS P consists of the following rules: 543.78/241.93 543.78/241.93 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.93 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.93 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.93 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.93 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.93 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.93 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.93 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.93 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))) 543.78/241.93 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.93 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.93 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.93 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.93 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.93 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.93 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))) 543.78/241.93 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.93 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.93 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.93 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.93 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.93 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.93 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.93 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.93 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.93 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.93 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.93 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.93 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.93 543.78/241.93 The TRS R consists of the following rules: 543.78/241.93 543.78/241.93 down(a) -> up(f(a)) 543.78/241.93 down(b) -> up(g(b)) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.93 down(f(a)) -> f_flat(down(a)) 543.78/241.93 down(f(b)) -> f_flat(down(b)) 543.78/241.93 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.93 down(f(c)) -> f_flat(down(c)) 543.78/241.93 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.93 down(g(a)) -> g_flat(down(a)) 543.78/241.93 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.93 down(g(b)) -> g_flat(down(b)) 543.78/241.93 down(g(c)) -> g_flat(down(c)) 543.78/241.93 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.93 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.93 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.93 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.93 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.93 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.93 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.93 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.93 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.93 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.93 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.93 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.93 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.93 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.93 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.93 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.93 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.93 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.93 543.78/241.93 The set Q consists of the following terms: 543.78/241.93 543.78/241.93 down(a) 543.78/241.93 down(b) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.93 down(f(a)) 543.78/241.93 down(f(b)) 543.78/241.93 down(f(g(x0))) 543.78/241.93 down(f(c)) 543.78/241.93 down(f(fresh_constant)) 543.78/241.93 down(g(a)) 543.78/241.93 down(g(f(x0))) 543.78/241.93 down(g(b)) 543.78/241.93 down(g(c)) 543.78/241.93 down(g(fresh_constant)) 543.78/241.93 down(f(f(a))) 543.78/241.93 down(f(f(b))) 543.78/241.93 down(f(f(g(x0)))) 543.78/241.93 down(f(f(c))) 543.78/241.93 down(f(f(fresh_constant))) 543.78/241.93 down(g(g(a))) 543.78/241.93 down(g(g(f(x0)))) 543.78/241.93 down(g(g(b))) 543.78/241.93 down(g(g(c))) 543.78/241.93 down(g(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) 543.78/241.93 down(f(f(f(g(x0))))) 543.78/241.93 down(f(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) 543.78/241.93 down(g(g(g(f(x0))))) 543.78/241.93 down(g(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(x0)))))) 543.78/241.93 down(f(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(x0)))))) 543.78/241.93 down(g(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(x0))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(x0))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 f_flat(up(x0)) 543.78/241.93 g_flat(up(x0)) 543.78/241.93 543.78/241.93 We have to consider all minimal (P,Q,R)-chains. 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (753) TransformationProof (EQUIVALENT) 543.78/241.93 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.93 543.78/241.93 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) 543.78/241.93 543.78/241.93 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (754) 543.78/241.93 Obligation: 543.78/241.93 Q DP problem: 543.78/241.93 The TRS P consists of the following rules: 543.78/241.93 543.78/241.93 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.93 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.93 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.93 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.93 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.93 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.93 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.93 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.93 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.93 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.93 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.93 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.93 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.93 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.93 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))) 543.78/241.93 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.93 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.93 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.93 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.93 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.93 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.93 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.93 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.93 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.93 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.93 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.93 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.93 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))) 543.78/241.93 543.78/241.93 The TRS R consists of the following rules: 543.78/241.93 543.78/241.93 down(a) -> up(f(a)) 543.78/241.93 down(b) -> up(g(b)) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.93 down(f(a)) -> f_flat(down(a)) 543.78/241.93 down(f(b)) -> f_flat(down(b)) 543.78/241.93 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.93 down(f(c)) -> f_flat(down(c)) 543.78/241.93 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.93 down(g(a)) -> g_flat(down(a)) 543.78/241.93 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.93 down(g(b)) -> g_flat(down(b)) 543.78/241.93 down(g(c)) -> g_flat(down(c)) 543.78/241.93 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.93 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.93 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.93 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.93 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.93 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.93 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.93 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.93 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.93 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.93 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.93 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.93 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.93 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.93 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.93 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.93 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.93 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.93 543.78/241.93 The set Q consists of the following terms: 543.78/241.93 543.78/241.93 down(a) 543.78/241.93 down(b) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.93 down(f(a)) 543.78/241.93 down(f(b)) 543.78/241.93 down(f(g(x0))) 543.78/241.93 down(f(c)) 543.78/241.93 down(f(fresh_constant)) 543.78/241.93 down(g(a)) 543.78/241.93 down(g(f(x0))) 543.78/241.93 down(g(b)) 543.78/241.93 down(g(c)) 543.78/241.93 down(g(fresh_constant)) 543.78/241.93 down(f(f(a))) 543.78/241.93 down(f(f(b))) 543.78/241.93 down(f(f(g(x0)))) 543.78/241.93 down(f(f(c))) 543.78/241.93 down(f(f(fresh_constant))) 543.78/241.93 down(g(g(a))) 543.78/241.93 down(g(g(f(x0)))) 543.78/241.93 down(g(g(b))) 543.78/241.93 down(g(g(c))) 543.78/241.93 down(g(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) 543.78/241.93 down(f(f(f(g(x0))))) 543.78/241.93 down(f(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) 543.78/241.93 down(g(g(g(f(x0))))) 543.78/241.93 down(g(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(x0)))))) 543.78/241.93 down(f(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(x0)))))) 543.78/241.93 down(g(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(x0))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(x0))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 f_flat(up(x0)) 543.78/241.93 g_flat(up(x0)) 543.78/241.93 543.78/241.93 We have to consider all minimal (P,Q,R)-chains. 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (755) TransformationProof (EQUIVALENT) 543.78/241.93 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.93 543.78/241.93 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) 543.78/241.93 543.78/241.93 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (756) 543.78/241.93 Obligation: 543.78/241.93 Q DP problem: 543.78/241.93 The TRS P consists of the following rules: 543.78/241.93 543.78/241.93 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.93 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.93 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.93 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.93 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.93 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.93 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.93 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.93 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.93 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.93 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.93 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.93 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.93 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.93 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.93 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.93 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.93 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.93 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.93 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.93 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.93 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.93 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.93 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.93 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.93 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.93 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))) 543.78/241.93 543.78/241.93 The TRS R consists of the following rules: 543.78/241.93 543.78/241.93 down(a) -> up(f(a)) 543.78/241.93 down(b) -> up(g(b)) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.93 down(f(a)) -> f_flat(down(a)) 543.78/241.93 down(f(b)) -> f_flat(down(b)) 543.78/241.93 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.93 down(f(c)) -> f_flat(down(c)) 543.78/241.93 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.93 down(g(a)) -> g_flat(down(a)) 543.78/241.93 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.93 down(g(b)) -> g_flat(down(b)) 543.78/241.93 down(g(c)) -> g_flat(down(c)) 543.78/241.93 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.93 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.93 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.93 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.93 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.93 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.93 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.93 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.93 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.93 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.93 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.93 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.93 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.93 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.93 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.93 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.93 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.93 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.93 543.78/241.93 The set Q consists of the following terms: 543.78/241.93 543.78/241.93 down(a) 543.78/241.93 down(b) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.93 down(f(a)) 543.78/241.93 down(f(b)) 543.78/241.93 down(f(g(x0))) 543.78/241.93 down(f(c)) 543.78/241.93 down(f(fresh_constant)) 543.78/241.93 down(g(a)) 543.78/241.93 down(g(f(x0))) 543.78/241.93 down(g(b)) 543.78/241.93 down(g(c)) 543.78/241.93 down(g(fresh_constant)) 543.78/241.93 down(f(f(a))) 543.78/241.93 down(f(f(b))) 543.78/241.93 down(f(f(g(x0)))) 543.78/241.93 down(f(f(c))) 543.78/241.93 down(f(f(fresh_constant))) 543.78/241.93 down(g(g(a))) 543.78/241.93 down(g(g(f(x0)))) 543.78/241.93 down(g(g(b))) 543.78/241.93 down(g(g(c))) 543.78/241.93 down(g(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) 543.78/241.93 down(f(f(f(g(x0))))) 543.78/241.93 down(f(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) 543.78/241.93 down(g(g(g(f(x0))))) 543.78/241.93 down(g(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(x0)))))) 543.78/241.93 down(f(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(x0)))))) 543.78/241.93 down(g(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(x0))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(x0))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 f_flat(up(x0)) 543.78/241.93 g_flat(up(x0)) 543.78/241.93 543.78/241.93 We have to consider all minimal (P,Q,R)-chains. 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (757) TransformationProof (EQUIVALENT) 543.78/241.93 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.93 543.78/241.93 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.78/241.93 543.78/241.93 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (758) 543.78/241.93 Obligation: 543.78/241.93 Q DP problem: 543.78/241.93 The TRS P consists of the following rules: 543.78/241.93 543.78/241.93 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.93 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.93 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.93 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.93 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.93 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.93 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.93 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.93 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.93 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.93 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.93 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.93 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.93 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.93 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.93 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.93 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.93 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.93 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.93 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.93 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.93 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.93 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.93 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.93 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.93 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.93 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.93 543.78/241.93 The TRS R consists of the following rules: 543.78/241.93 543.78/241.93 down(a) -> up(f(a)) 543.78/241.93 down(b) -> up(g(b)) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.93 down(f(a)) -> f_flat(down(a)) 543.78/241.93 down(f(b)) -> f_flat(down(b)) 543.78/241.93 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.93 down(f(c)) -> f_flat(down(c)) 543.78/241.93 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.93 down(g(a)) -> g_flat(down(a)) 543.78/241.93 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.93 down(g(b)) -> g_flat(down(b)) 543.78/241.93 down(g(c)) -> g_flat(down(c)) 543.78/241.93 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.93 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.93 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.93 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.93 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.93 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.93 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.93 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.93 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.93 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.93 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.93 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.93 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.93 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.93 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.93 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.93 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.93 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.93 543.78/241.93 The set Q consists of the following terms: 543.78/241.93 543.78/241.93 down(a) 543.78/241.93 down(b) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.93 down(f(a)) 543.78/241.93 down(f(b)) 543.78/241.93 down(f(g(x0))) 543.78/241.93 down(f(c)) 543.78/241.93 down(f(fresh_constant)) 543.78/241.93 down(g(a)) 543.78/241.93 down(g(f(x0))) 543.78/241.93 down(g(b)) 543.78/241.93 down(g(c)) 543.78/241.93 down(g(fresh_constant)) 543.78/241.93 down(f(f(a))) 543.78/241.93 down(f(f(b))) 543.78/241.93 down(f(f(g(x0)))) 543.78/241.93 down(f(f(c))) 543.78/241.93 down(f(f(fresh_constant))) 543.78/241.93 down(g(g(a))) 543.78/241.93 down(g(g(f(x0)))) 543.78/241.93 down(g(g(b))) 543.78/241.93 down(g(g(c))) 543.78/241.93 down(g(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) 543.78/241.93 down(f(f(f(g(x0))))) 543.78/241.93 down(f(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) 543.78/241.93 down(g(g(g(f(x0))))) 543.78/241.93 down(g(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(x0)))))) 543.78/241.93 down(f(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(x0)))))) 543.78/241.93 down(g(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(x0))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(x0))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 f_flat(up(x0)) 543.78/241.93 g_flat(up(x0)) 543.78/241.93 543.78/241.93 We have to consider all minimal (P,Q,R)-chains. 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (759) TransformationProof (EQUIVALENT) 543.78/241.93 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.93 543.78/241.93 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.78/241.93 543.78/241.93 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (760) 543.78/241.93 Obligation: 543.78/241.93 Q DP problem: 543.78/241.93 The TRS P consists of the following rules: 543.78/241.93 543.78/241.93 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.93 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.93 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.93 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.93 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.93 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.93 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.93 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.93 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.93 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.93 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.93 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.93 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.93 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.93 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.93 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.93 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.93 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.93 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.93 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.93 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.93 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.93 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.93 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.93 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.93 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.93 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.93 543.78/241.93 The TRS R consists of the following rules: 543.78/241.93 543.78/241.93 down(a) -> up(f(a)) 543.78/241.93 down(b) -> up(g(b)) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.93 down(f(a)) -> f_flat(down(a)) 543.78/241.93 down(f(b)) -> f_flat(down(b)) 543.78/241.93 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.93 down(f(c)) -> f_flat(down(c)) 543.78/241.93 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.93 down(g(a)) -> g_flat(down(a)) 543.78/241.93 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.93 down(g(b)) -> g_flat(down(b)) 543.78/241.93 down(g(c)) -> g_flat(down(c)) 543.78/241.93 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.93 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.93 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.93 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.93 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.93 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.93 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.93 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.93 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.93 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.93 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.93 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.93 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.93 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.93 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.93 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.93 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.93 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.93 543.78/241.93 The set Q consists of the following terms: 543.78/241.93 543.78/241.93 down(a) 543.78/241.93 down(b) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.93 down(f(a)) 543.78/241.93 down(f(b)) 543.78/241.93 down(f(g(x0))) 543.78/241.93 down(f(c)) 543.78/241.93 down(f(fresh_constant)) 543.78/241.93 down(g(a)) 543.78/241.93 down(g(f(x0))) 543.78/241.93 down(g(b)) 543.78/241.93 down(g(c)) 543.78/241.93 down(g(fresh_constant)) 543.78/241.93 down(f(f(a))) 543.78/241.93 down(f(f(b))) 543.78/241.93 down(f(f(g(x0)))) 543.78/241.93 down(f(f(c))) 543.78/241.93 down(f(f(fresh_constant))) 543.78/241.93 down(g(g(a))) 543.78/241.93 down(g(g(f(x0)))) 543.78/241.93 down(g(g(b))) 543.78/241.93 down(g(g(c))) 543.78/241.93 down(g(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) 543.78/241.93 down(f(f(f(g(x0))))) 543.78/241.93 down(f(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) 543.78/241.93 down(g(g(g(f(x0))))) 543.78/241.93 down(g(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(x0)))))) 543.78/241.93 down(f(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(x0)))))) 543.78/241.93 down(g(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(x0))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(x0))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 f_flat(up(x0)) 543.78/241.93 g_flat(up(x0)) 543.78/241.93 543.78/241.93 We have to consider all minimal (P,Q,R)-chains. 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (761) TransformationProof (EQUIVALENT) 543.78/241.93 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.93 543.78/241.93 (TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))),TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.78/241.93 543.78/241.93 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (762) 543.78/241.93 Obligation: 543.78/241.93 Q DP problem: 543.78/241.93 The TRS P consists of the following rules: 543.78/241.93 543.78/241.93 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.93 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.93 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.93 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.93 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.93 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.93 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.93 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.93 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.93 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.93 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.93 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.93 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.93 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.93 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.93 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.93 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.93 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.93 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.93 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.93 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.93 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.93 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.93 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.93 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.93 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.93 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.93 543.78/241.93 The TRS R consists of the following rules: 543.78/241.93 543.78/241.93 down(a) -> up(f(a)) 543.78/241.93 down(b) -> up(g(b)) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.93 down(f(a)) -> f_flat(down(a)) 543.78/241.93 down(f(b)) -> f_flat(down(b)) 543.78/241.93 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.93 down(f(c)) -> f_flat(down(c)) 543.78/241.93 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.93 down(g(a)) -> g_flat(down(a)) 543.78/241.93 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.93 down(g(b)) -> g_flat(down(b)) 543.78/241.93 down(g(c)) -> g_flat(down(c)) 543.78/241.93 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.93 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.93 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.93 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.93 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.93 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.93 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.93 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.93 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.93 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.93 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.93 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.93 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.93 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.93 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.93 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.93 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.93 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.93 543.78/241.93 The set Q consists of the following terms: 543.78/241.93 543.78/241.93 down(a) 543.78/241.93 down(b) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.93 down(f(a)) 543.78/241.93 down(f(b)) 543.78/241.93 down(f(g(x0))) 543.78/241.93 down(f(c)) 543.78/241.93 down(f(fresh_constant)) 543.78/241.93 down(g(a)) 543.78/241.93 down(g(f(x0))) 543.78/241.93 down(g(b)) 543.78/241.93 down(g(c)) 543.78/241.93 down(g(fresh_constant)) 543.78/241.93 down(f(f(a))) 543.78/241.93 down(f(f(b))) 543.78/241.93 down(f(f(g(x0)))) 543.78/241.93 down(f(f(c))) 543.78/241.93 down(f(f(fresh_constant))) 543.78/241.93 down(g(g(a))) 543.78/241.93 down(g(g(f(x0)))) 543.78/241.93 down(g(g(b))) 543.78/241.93 down(g(g(c))) 543.78/241.93 down(g(g(fresh_constant))) 543.78/241.93 down(f(f(f(a)))) 543.78/241.93 down(f(f(f(b)))) 543.78/241.93 down(f(f(f(g(x0))))) 543.78/241.93 down(f(f(f(c)))) 543.78/241.93 down(f(f(f(fresh_constant)))) 543.78/241.93 down(g(g(g(a)))) 543.78/241.93 down(g(g(g(f(x0))))) 543.78/241.93 down(g(g(g(b)))) 543.78/241.93 down(g(g(g(c)))) 543.78/241.93 down(g(g(g(fresh_constant)))) 543.78/241.93 down(f(f(f(f(a))))) 543.78/241.93 down(f(f(f(f(b))))) 543.78/241.93 down(f(f(f(f(g(x0)))))) 543.78/241.93 down(f(f(f(f(c))))) 543.78/241.93 down(f(f(f(f(fresh_constant))))) 543.78/241.93 down(g(g(g(g(a))))) 543.78/241.93 down(g(g(g(g(f(x0)))))) 543.78/241.93 down(g(g(g(g(b))))) 543.78/241.93 down(g(g(g(g(c))))) 543.78/241.93 down(g(g(g(g(fresh_constant))))) 543.78/241.93 down(f(f(f(f(f(a)))))) 543.78/241.93 down(f(f(f(f(f(b)))))) 543.78/241.93 down(f(f(f(f(f(g(x0))))))) 543.78/241.93 down(f(f(f(f(f(c)))))) 543.78/241.93 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.93 down(g(g(g(g(g(a)))))) 543.78/241.93 down(g(g(g(g(g(f(x0))))))) 543.78/241.93 down(g(g(g(g(g(b)))))) 543.78/241.93 down(g(g(g(g(g(c)))))) 543.78/241.93 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.93 down(f(f(f(f(f(f(a))))))) 543.78/241.93 down(f(f(f(f(f(f(b))))))) 543.78/241.93 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.93 down(f(f(f(f(f(f(c))))))) 543.78/241.93 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.93 down(g(g(g(g(g(g(a))))))) 543.78/241.93 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.93 down(g(g(g(g(g(g(b))))))) 543.78/241.93 down(g(g(g(g(g(g(c))))))) 543.78/241.93 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.93 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.93 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.93 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.93 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.93 f_flat(up(x0)) 543.78/241.93 g_flat(up(x0)) 543.78/241.93 543.78/241.93 We have to consider all minimal (P,Q,R)-chains. 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (763) TransformationProof (EQUIVALENT) 543.78/241.93 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.93 543.78/241.93 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.78/241.93 543.78/241.93 543.78/241.93 ---------------------------------------- 543.78/241.93 543.78/241.93 (764) 543.78/241.93 Obligation: 543.78/241.93 Q DP problem: 543.78/241.93 The TRS P consists of the following rules: 543.78/241.93 543.78/241.93 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.93 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.93 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.93 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.93 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.93 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.93 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.93 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.93 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.93 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.93 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.93 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.93 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.93 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.93 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.93 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.93 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.93 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.93 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.93 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.93 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.93 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.93 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.93 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.93 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.93 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.93 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.93 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.94 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.94 543.78/241.94 The TRS R consists of the following rules: 543.78/241.94 543.78/241.94 down(a) -> up(f(a)) 543.78/241.94 down(b) -> up(g(b)) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.94 down(f(a)) -> f_flat(down(a)) 543.78/241.94 down(f(b)) -> f_flat(down(b)) 543.78/241.94 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.94 down(f(c)) -> f_flat(down(c)) 543.78/241.94 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.94 down(g(a)) -> g_flat(down(a)) 543.78/241.94 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.94 down(g(b)) -> g_flat(down(b)) 543.78/241.94 down(g(c)) -> g_flat(down(c)) 543.78/241.94 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.94 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.94 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.94 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.94 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.94 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.94 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.94 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.94 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.94 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.94 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.94 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.94 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.94 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.94 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.94 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.94 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.94 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.94 543.78/241.94 The set Q consists of the following terms: 543.78/241.94 543.78/241.94 down(a) 543.78/241.94 down(b) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.94 down(f(a)) 543.78/241.94 down(f(b)) 543.78/241.94 down(f(g(x0))) 543.78/241.94 down(f(c)) 543.78/241.94 down(f(fresh_constant)) 543.78/241.94 down(g(a)) 543.78/241.94 down(g(f(x0))) 543.78/241.94 down(g(b)) 543.78/241.94 down(g(c)) 543.78/241.94 down(g(fresh_constant)) 543.78/241.94 down(f(f(a))) 543.78/241.94 down(f(f(b))) 543.78/241.94 down(f(f(g(x0)))) 543.78/241.94 down(f(f(c))) 543.78/241.94 down(f(f(fresh_constant))) 543.78/241.94 down(g(g(a))) 543.78/241.94 down(g(g(f(x0)))) 543.78/241.94 down(g(g(b))) 543.78/241.94 down(g(g(c))) 543.78/241.94 down(g(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) 543.78/241.94 down(f(f(f(g(x0))))) 543.78/241.94 down(f(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) 543.78/241.94 down(g(g(g(f(x0))))) 543.78/241.94 down(g(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(x0)))))) 543.78/241.94 down(f(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(x0)))))) 543.78/241.94 down(g(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(x0))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(x0))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 f_flat(up(x0)) 543.78/241.94 g_flat(up(x0)) 543.78/241.94 543.78/241.94 We have to consider all minimal (P,Q,R)-chains. 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (765) TransformationProof (EQUIVALENT) 543.78/241.94 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.94 543.78/241.94 (TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c)))))))),TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c))))))))) 543.78/241.94 543.78/241.94 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (766) 543.78/241.94 Obligation: 543.78/241.94 Q DP problem: 543.78/241.94 The TRS P consists of the following rules: 543.78/241.94 543.78/241.94 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.94 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.94 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.94 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.94 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.94 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.94 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.94 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.94 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.94 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.94 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.94 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.94 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.94 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.94 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.94 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.94 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.94 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.94 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.94 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.94 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.94 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.94 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.94 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.94 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.94 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.94 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(c)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c)))))))) 543.78/241.94 543.78/241.94 The TRS R consists of the following rules: 543.78/241.94 543.78/241.94 down(a) -> up(f(a)) 543.78/241.94 down(b) -> up(g(b)) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.94 down(f(a)) -> f_flat(down(a)) 543.78/241.94 down(f(b)) -> f_flat(down(b)) 543.78/241.94 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.94 down(f(c)) -> f_flat(down(c)) 543.78/241.94 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.94 down(g(a)) -> g_flat(down(a)) 543.78/241.94 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.94 down(g(b)) -> g_flat(down(b)) 543.78/241.94 down(g(c)) -> g_flat(down(c)) 543.78/241.94 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.94 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.94 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.94 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.94 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.94 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.94 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.94 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.94 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.94 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.94 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.94 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.94 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.94 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.94 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.94 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.94 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.94 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.94 543.78/241.94 The set Q consists of the following terms: 543.78/241.94 543.78/241.94 down(a) 543.78/241.94 down(b) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.94 down(f(a)) 543.78/241.94 down(f(b)) 543.78/241.94 down(f(g(x0))) 543.78/241.94 down(f(c)) 543.78/241.94 down(f(fresh_constant)) 543.78/241.94 down(g(a)) 543.78/241.94 down(g(f(x0))) 543.78/241.94 down(g(b)) 543.78/241.94 down(g(c)) 543.78/241.94 down(g(fresh_constant)) 543.78/241.94 down(f(f(a))) 543.78/241.94 down(f(f(b))) 543.78/241.94 down(f(f(g(x0)))) 543.78/241.94 down(f(f(c))) 543.78/241.94 down(f(f(fresh_constant))) 543.78/241.94 down(g(g(a))) 543.78/241.94 down(g(g(f(x0)))) 543.78/241.94 down(g(g(b))) 543.78/241.94 down(g(g(c))) 543.78/241.94 down(g(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) 543.78/241.94 down(f(f(f(g(x0))))) 543.78/241.94 down(f(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) 543.78/241.94 down(g(g(g(f(x0))))) 543.78/241.94 down(g(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(x0)))))) 543.78/241.94 down(f(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(x0)))))) 543.78/241.94 down(g(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(x0))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(x0))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 f_flat(up(x0)) 543.78/241.94 g_flat(up(x0)) 543.78/241.94 543.78/241.94 We have to consider all minimal (P,Q,R)-chains. 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (767) DependencyGraphProof (EQUIVALENT) 543.78/241.94 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (768) 543.78/241.94 Obligation: 543.78/241.94 Q DP problem: 543.78/241.94 The TRS P consists of the following rules: 543.78/241.94 543.78/241.94 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.94 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.94 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.94 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.94 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.94 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.94 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.94 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.94 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))) 543.78/241.94 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.94 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.94 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.94 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.94 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.94 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.94 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))) 543.78/241.94 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.94 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.94 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.94 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.94 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.94 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.94 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.94 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.94 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.94 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.94 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.94 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.94 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.94 543.78/241.94 The TRS R consists of the following rules: 543.78/241.94 543.78/241.94 down(a) -> up(f(a)) 543.78/241.94 down(b) -> up(g(b)) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.94 down(f(a)) -> f_flat(down(a)) 543.78/241.94 down(f(b)) -> f_flat(down(b)) 543.78/241.94 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.94 down(f(c)) -> f_flat(down(c)) 543.78/241.94 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.94 down(g(a)) -> g_flat(down(a)) 543.78/241.94 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.94 down(g(b)) -> g_flat(down(b)) 543.78/241.94 down(g(c)) -> g_flat(down(c)) 543.78/241.94 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.94 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.94 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.94 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.94 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.94 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.94 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.94 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.94 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.94 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.94 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.94 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.94 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.94 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.94 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.94 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.94 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.94 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.94 543.78/241.94 The set Q consists of the following terms: 543.78/241.94 543.78/241.94 down(a) 543.78/241.94 down(b) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.94 down(f(a)) 543.78/241.94 down(f(b)) 543.78/241.94 down(f(g(x0))) 543.78/241.94 down(f(c)) 543.78/241.94 down(f(fresh_constant)) 543.78/241.94 down(g(a)) 543.78/241.94 down(g(f(x0))) 543.78/241.94 down(g(b)) 543.78/241.94 down(g(c)) 543.78/241.94 down(g(fresh_constant)) 543.78/241.94 down(f(f(a))) 543.78/241.94 down(f(f(b))) 543.78/241.94 down(f(f(g(x0)))) 543.78/241.94 down(f(f(c))) 543.78/241.94 down(f(f(fresh_constant))) 543.78/241.94 down(g(g(a))) 543.78/241.94 down(g(g(f(x0)))) 543.78/241.94 down(g(g(b))) 543.78/241.94 down(g(g(c))) 543.78/241.94 down(g(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) 543.78/241.94 down(f(f(f(g(x0))))) 543.78/241.94 down(f(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) 543.78/241.94 down(g(g(g(f(x0))))) 543.78/241.94 down(g(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(x0)))))) 543.78/241.94 down(f(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(x0)))))) 543.78/241.94 down(g(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(x0))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(x0))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 f_flat(up(x0)) 543.78/241.94 g_flat(up(x0)) 543.78/241.94 543.78/241.94 We have to consider all minimal (P,Q,R)-chains. 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (769) TransformationProof (EQUIVALENT) 543.78/241.94 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(a)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.94 543.78/241.94 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(a)))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(a))))))))) 543.78/241.94 543.78/241.94 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (770) 543.78/241.94 Obligation: 543.78/241.94 Q DP problem: 543.78/241.94 The TRS P consists of the following rules: 543.78/241.94 543.78/241.94 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.94 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.94 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.94 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.94 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.94 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.94 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.94 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.94 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.94 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.94 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.94 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.94 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.94 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.94 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))) 543.78/241.94 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.94 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.94 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.94 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.94 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.94 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.94 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.94 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.94 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.94 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.94 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.94 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.94 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(a)))))))) 543.78/241.94 543.78/241.94 The TRS R consists of the following rules: 543.78/241.94 543.78/241.94 down(a) -> up(f(a)) 543.78/241.94 down(b) -> up(g(b)) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.94 down(f(a)) -> f_flat(down(a)) 543.78/241.94 down(f(b)) -> f_flat(down(b)) 543.78/241.94 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.94 down(f(c)) -> f_flat(down(c)) 543.78/241.94 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.94 down(g(a)) -> g_flat(down(a)) 543.78/241.94 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.94 down(g(b)) -> g_flat(down(b)) 543.78/241.94 down(g(c)) -> g_flat(down(c)) 543.78/241.94 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.94 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.94 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.94 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.94 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.94 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.94 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.94 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.94 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.94 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.94 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.94 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.94 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.94 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.94 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.94 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.94 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.94 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.94 543.78/241.94 The set Q consists of the following terms: 543.78/241.94 543.78/241.94 down(a) 543.78/241.94 down(b) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.94 down(f(a)) 543.78/241.94 down(f(b)) 543.78/241.94 down(f(g(x0))) 543.78/241.94 down(f(c)) 543.78/241.94 down(f(fresh_constant)) 543.78/241.94 down(g(a)) 543.78/241.94 down(g(f(x0))) 543.78/241.94 down(g(b)) 543.78/241.94 down(g(c)) 543.78/241.94 down(g(fresh_constant)) 543.78/241.94 down(f(f(a))) 543.78/241.94 down(f(f(b))) 543.78/241.94 down(f(f(g(x0)))) 543.78/241.94 down(f(f(c))) 543.78/241.94 down(f(f(fresh_constant))) 543.78/241.94 down(g(g(a))) 543.78/241.94 down(g(g(f(x0)))) 543.78/241.94 down(g(g(b))) 543.78/241.94 down(g(g(c))) 543.78/241.94 down(g(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) 543.78/241.94 down(f(f(f(g(x0))))) 543.78/241.94 down(f(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) 543.78/241.94 down(g(g(g(f(x0))))) 543.78/241.94 down(g(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(x0)))))) 543.78/241.94 down(f(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(x0)))))) 543.78/241.94 down(g(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(x0))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(x0))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 f_flat(up(x0)) 543.78/241.94 g_flat(up(x0)) 543.78/241.94 543.78/241.94 We have to consider all minimal (P,Q,R)-chains. 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (771) TransformationProof (EQUIVALENT) 543.78/241.94 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(b)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.94 543.78/241.94 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(b)))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(b))))))))) 543.78/241.94 543.78/241.94 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (772) 543.78/241.94 Obligation: 543.78/241.94 Q DP problem: 543.78/241.94 The TRS P consists of the following rules: 543.78/241.94 543.78/241.94 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.94 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.94 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.94 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.94 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.94 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.94 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.94 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.94 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.94 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.94 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.94 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.94 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.94 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.94 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.94 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.94 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.94 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.94 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.94 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.94 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.94 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.94 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.94 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.94 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.94 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.94 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(b)))))))) 543.78/241.94 543.78/241.94 The TRS R consists of the following rules: 543.78/241.94 543.78/241.94 down(a) -> up(f(a)) 543.78/241.94 down(b) -> up(g(b)) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.94 down(f(a)) -> f_flat(down(a)) 543.78/241.94 down(f(b)) -> f_flat(down(b)) 543.78/241.94 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.94 down(f(c)) -> f_flat(down(c)) 543.78/241.94 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.94 down(g(a)) -> g_flat(down(a)) 543.78/241.94 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.94 down(g(b)) -> g_flat(down(b)) 543.78/241.94 down(g(c)) -> g_flat(down(c)) 543.78/241.94 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.94 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.94 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.94 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.94 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.94 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.94 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.94 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.94 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.94 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.94 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.94 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.94 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.94 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.94 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.94 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.94 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.94 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.94 543.78/241.94 The set Q consists of the following terms: 543.78/241.94 543.78/241.94 down(a) 543.78/241.94 down(b) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.94 down(f(a)) 543.78/241.94 down(f(b)) 543.78/241.94 down(f(g(x0))) 543.78/241.94 down(f(c)) 543.78/241.94 down(f(fresh_constant)) 543.78/241.94 down(g(a)) 543.78/241.94 down(g(f(x0))) 543.78/241.94 down(g(b)) 543.78/241.94 down(g(c)) 543.78/241.94 down(g(fresh_constant)) 543.78/241.94 down(f(f(a))) 543.78/241.94 down(f(f(b))) 543.78/241.94 down(f(f(g(x0)))) 543.78/241.94 down(f(f(c))) 543.78/241.94 down(f(f(fresh_constant))) 543.78/241.94 down(g(g(a))) 543.78/241.94 down(g(g(f(x0)))) 543.78/241.94 down(g(g(b))) 543.78/241.94 down(g(g(c))) 543.78/241.94 down(g(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) 543.78/241.94 down(f(f(f(g(x0))))) 543.78/241.94 down(f(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) 543.78/241.94 down(g(g(g(f(x0))))) 543.78/241.94 down(g(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(x0)))))) 543.78/241.94 down(f(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(x0)))))) 543.78/241.94 down(g(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(x0))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(x0))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 f_flat(up(x0)) 543.78/241.94 g_flat(up(x0)) 543.78/241.94 543.78/241.94 We have to consider all minimal (P,Q,R)-chains. 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (773) TransformationProof (EQUIVALENT) 543.78/241.94 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.94 543.78/241.94 (TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant)))))))),TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant))))))))) 543.78/241.94 543.78/241.94 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (774) 543.78/241.94 Obligation: 543.78/241.94 Q DP problem: 543.78/241.94 The TRS P consists of the following rules: 543.78/241.94 543.78/241.94 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.94 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.94 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.94 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.94 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.94 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.94 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.94 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.94 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.94 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.94 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.94 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.94 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.94 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.94 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.94 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.94 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.94 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.94 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.94 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.94 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.94 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.94 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.94 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.94 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.94 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.94 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(b)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(fresh_constant)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant)))))))) 543.78/241.94 543.78/241.94 The TRS R consists of the following rules: 543.78/241.94 543.78/241.94 down(a) -> up(f(a)) 543.78/241.94 down(b) -> up(g(b)) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.94 down(f(a)) -> f_flat(down(a)) 543.78/241.94 down(f(b)) -> f_flat(down(b)) 543.78/241.94 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.94 down(f(c)) -> f_flat(down(c)) 543.78/241.94 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.94 down(g(a)) -> g_flat(down(a)) 543.78/241.94 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.94 down(g(b)) -> g_flat(down(b)) 543.78/241.94 down(g(c)) -> g_flat(down(c)) 543.78/241.94 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.94 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.94 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.94 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.94 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.94 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.94 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.94 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.94 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.94 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.94 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.94 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.94 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.94 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.94 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.94 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.94 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.94 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.94 543.78/241.94 The set Q consists of the following terms: 543.78/241.94 543.78/241.94 down(a) 543.78/241.94 down(b) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.94 down(f(a)) 543.78/241.94 down(f(b)) 543.78/241.94 down(f(g(x0))) 543.78/241.94 down(f(c)) 543.78/241.94 down(f(fresh_constant)) 543.78/241.94 down(g(a)) 543.78/241.94 down(g(f(x0))) 543.78/241.94 down(g(b)) 543.78/241.94 down(g(c)) 543.78/241.94 down(g(fresh_constant)) 543.78/241.94 down(f(f(a))) 543.78/241.94 down(f(f(b))) 543.78/241.94 down(f(f(g(x0)))) 543.78/241.94 down(f(f(c))) 543.78/241.94 down(f(f(fresh_constant))) 543.78/241.94 down(g(g(a))) 543.78/241.94 down(g(g(f(x0)))) 543.78/241.94 down(g(g(b))) 543.78/241.94 down(g(g(c))) 543.78/241.94 down(g(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) 543.78/241.94 down(f(f(f(g(x0))))) 543.78/241.94 down(f(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) 543.78/241.94 down(g(g(g(f(x0))))) 543.78/241.94 down(g(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(x0)))))) 543.78/241.94 down(f(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(x0)))))) 543.78/241.94 down(g(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(x0))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(x0))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 f_flat(up(x0)) 543.78/241.94 g_flat(up(x0)) 543.78/241.94 543.78/241.94 We have to consider all minimal (P,Q,R)-chains. 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (775) DependencyGraphProof (EQUIVALENT) 543.78/241.94 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (776) 543.78/241.94 Obligation: 543.78/241.94 Q DP problem: 543.78/241.94 The TRS P consists of the following rules: 543.78/241.94 543.78/241.94 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.94 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.94 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.94 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.94 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.94 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.94 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.94 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.94 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(a)))))))) 543.78/241.94 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.94 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.94 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.94 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.94 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.94 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.94 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(b)))))))) 543.78/241.94 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.94 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.94 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.94 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.94 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.94 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.94 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.94 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.94 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.94 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.94 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.94 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.94 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.94 543.78/241.94 The TRS R consists of the following rules: 543.78/241.94 543.78/241.94 down(a) -> up(f(a)) 543.78/241.94 down(b) -> up(g(b)) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.94 down(f(a)) -> f_flat(down(a)) 543.78/241.94 down(f(b)) -> f_flat(down(b)) 543.78/241.94 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.94 down(f(c)) -> f_flat(down(c)) 543.78/241.94 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.94 down(g(a)) -> g_flat(down(a)) 543.78/241.94 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.94 down(g(b)) -> g_flat(down(b)) 543.78/241.94 down(g(c)) -> g_flat(down(c)) 543.78/241.94 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.94 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.94 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.94 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.94 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.94 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.94 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.94 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.94 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.94 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.94 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.94 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.94 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.94 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.94 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.94 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.94 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.94 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.94 543.78/241.94 The set Q consists of the following terms: 543.78/241.94 543.78/241.94 down(a) 543.78/241.94 down(b) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.94 down(f(a)) 543.78/241.94 down(f(b)) 543.78/241.94 down(f(g(x0))) 543.78/241.94 down(f(c)) 543.78/241.94 down(f(fresh_constant)) 543.78/241.94 down(g(a)) 543.78/241.94 down(g(f(x0))) 543.78/241.94 down(g(b)) 543.78/241.94 down(g(c)) 543.78/241.94 down(g(fresh_constant)) 543.78/241.94 down(f(f(a))) 543.78/241.94 down(f(f(b))) 543.78/241.94 down(f(f(g(x0)))) 543.78/241.94 down(f(f(c))) 543.78/241.94 down(f(f(fresh_constant))) 543.78/241.94 down(g(g(a))) 543.78/241.94 down(g(g(f(x0)))) 543.78/241.94 down(g(g(b))) 543.78/241.94 down(g(g(c))) 543.78/241.94 down(g(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) 543.78/241.94 down(f(f(f(g(x0))))) 543.78/241.94 down(f(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) 543.78/241.94 down(g(g(g(f(x0))))) 543.78/241.94 down(g(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(x0)))))) 543.78/241.94 down(f(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(x0)))))) 543.78/241.94 down(g(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(x0))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(x0))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) 543.78/241.94 down(g(g(g(g(g(g(c))))))) 543.78/241.94 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.94 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.94 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.94 f_flat(up(x0)) 543.78/241.94 g_flat(up(x0)) 543.78/241.94 543.78/241.94 We have to consider all minimal (P,Q,R)-chains. 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (777) TransformationProof (EQUIVALENT) 543.78/241.94 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(a)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.78/241.94 543.78/241.94 (TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a))))))))) 543.78/241.94 543.78/241.94 543.78/241.94 ---------------------------------------- 543.78/241.94 543.78/241.94 (778) 543.78/241.94 Obligation: 543.78/241.94 Q DP problem: 543.78/241.94 The TRS P consists of the following rules: 543.78/241.94 543.78/241.94 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.94 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.94 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.94 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.94 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.94 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.94 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.94 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.94 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.94 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.94 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.94 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.94 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.94 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.94 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(b)))))))) 543.78/241.94 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.94 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.94 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.94 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.94 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.94 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.94 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.94 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.94 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.94 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.94 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.94 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.94 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.94 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.94 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.94 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.94 543.78/241.94 The TRS R consists of the following rules: 543.78/241.94 543.78/241.94 down(a) -> up(f(a)) 543.78/241.94 down(b) -> up(g(b)) 543.78/241.94 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.94 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.94 down(f(a)) -> f_flat(down(a)) 543.78/241.94 down(f(b)) -> f_flat(down(b)) 543.78/241.94 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.94 down(f(c)) -> f_flat(down(c)) 543.78/241.94 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.94 down(g(a)) -> g_flat(down(a)) 543.78/241.94 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.94 down(g(b)) -> g_flat(down(b)) 543.78/241.94 down(g(c)) -> g_flat(down(c)) 543.78/241.94 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.94 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.94 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.94 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.94 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.94 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.94 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.94 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.94 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.94 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.94 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.94 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.94 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.94 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.94 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.94 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.94 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.94 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.94 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.94 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.94 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.94 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.94 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.94 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.94 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.94 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.94 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.94 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.94 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.94 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.94 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.94 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.94 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.94 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.94 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.94 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.94 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.94 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.94 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.94 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.94 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.94 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.94 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.94 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.94 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.94 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.94 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.94 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.94 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.95 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.95 543.78/241.95 The set Q consists of the following terms: 543.78/241.95 543.78/241.95 down(a) 543.78/241.95 down(b) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.95 down(f(a)) 543.78/241.95 down(f(b)) 543.78/241.95 down(f(g(x0))) 543.78/241.95 down(f(c)) 543.78/241.95 down(f(fresh_constant)) 543.78/241.95 down(g(a)) 543.78/241.95 down(g(f(x0))) 543.78/241.95 down(g(b)) 543.78/241.95 down(g(c)) 543.78/241.95 down(g(fresh_constant)) 543.78/241.95 down(f(f(a))) 543.78/241.95 down(f(f(b))) 543.78/241.95 down(f(f(g(x0)))) 543.78/241.95 down(f(f(c))) 543.78/241.95 down(f(f(fresh_constant))) 543.78/241.95 down(g(g(a))) 543.78/241.95 down(g(g(f(x0)))) 543.78/241.95 down(g(g(b))) 543.78/241.95 down(g(g(c))) 543.78/241.95 down(g(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) 543.78/241.95 down(f(f(f(g(x0))))) 543.78/241.95 down(f(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) 543.78/241.95 down(g(g(g(f(x0))))) 543.78/241.95 down(g(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(x0)))))) 543.78/241.95 down(f(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(x0)))))) 543.78/241.95 down(g(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(x0))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(x0))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 f_flat(up(x0)) 543.78/241.95 g_flat(up(x0)) 543.78/241.95 543.78/241.95 We have to consider all minimal (P,Q,R)-chains. 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (779) TransformationProof (EQUIVALENT) 543.78/241.95 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(b)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.78/241.95 543.78/241.95 (TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b))))))))) 543.78/241.95 543.78/241.95 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (780) 543.78/241.95 Obligation: 543.78/241.95 Q DP problem: 543.78/241.95 The TRS P consists of the following rules: 543.78/241.95 543.78/241.95 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.95 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.95 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.95 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.95 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.95 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.95 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.95 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.95 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.95 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.95 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.95 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.95 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.95 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.95 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.95 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.95 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.95 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.95 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.95 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.95 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.95 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.95 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.95 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.95 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.95 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.95 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.95 543.78/241.95 The TRS R consists of the following rules: 543.78/241.95 543.78/241.95 down(a) -> up(f(a)) 543.78/241.95 down(b) -> up(g(b)) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.95 down(f(a)) -> f_flat(down(a)) 543.78/241.95 down(f(b)) -> f_flat(down(b)) 543.78/241.95 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.95 down(f(c)) -> f_flat(down(c)) 543.78/241.95 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.95 down(g(a)) -> g_flat(down(a)) 543.78/241.95 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.95 down(g(b)) -> g_flat(down(b)) 543.78/241.95 down(g(c)) -> g_flat(down(c)) 543.78/241.95 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.95 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.95 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.95 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.95 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.95 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.95 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.95 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.95 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.95 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.95 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.95 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.95 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.95 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.95 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.95 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.95 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.95 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.95 543.78/241.95 The set Q consists of the following terms: 543.78/241.95 543.78/241.95 down(a) 543.78/241.95 down(b) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.95 down(f(a)) 543.78/241.95 down(f(b)) 543.78/241.95 down(f(g(x0))) 543.78/241.95 down(f(c)) 543.78/241.95 down(f(fresh_constant)) 543.78/241.95 down(g(a)) 543.78/241.95 down(g(f(x0))) 543.78/241.95 down(g(b)) 543.78/241.95 down(g(c)) 543.78/241.95 down(g(fresh_constant)) 543.78/241.95 down(f(f(a))) 543.78/241.95 down(f(f(b))) 543.78/241.95 down(f(f(g(x0)))) 543.78/241.95 down(f(f(c))) 543.78/241.95 down(f(f(fresh_constant))) 543.78/241.95 down(g(g(a))) 543.78/241.95 down(g(g(f(x0)))) 543.78/241.95 down(g(g(b))) 543.78/241.95 down(g(g(c))) 543.78/241.95 down(g(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) 543.78/241.95 down(f(f(f(g(x0))))) 543.78/241.95 down(f(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) 543.78/241.95 down(g(g(g(f(x0))))) 543.78/241.95 down(g(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(x0)))))) 543.78/241.95 down(f(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(x0)))))) 543.78/241.95 down(g(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(x0))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(x0))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 f_flat(up(x0)) 543.78/241.95 g_flat(up(x0)) 543.78/241.95 543.78/241.95 We have to consider all minimal (P,Q,R)-chains. 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (781) TransformationProof (EQUIVALENT) 543.78/241.95 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.95 543.78/241.95 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.78/241.95 543.78/241.95 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (782) 543.78/241.95 Obligation: 543.78/241.95 Q DP problem: 543.78/241.95 The TRS P consists of the following rules: 543.78/241.95 543.78/241.95 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.95 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.95 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.95 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.95 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.95 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.95 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.95 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.95 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.95 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.95 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.95 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.95 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.95 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.95 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.95 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.95 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.95 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.95 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.95 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.95 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.95 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.95 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.95 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.95 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.95 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.95 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.95 543.78/241.95 The TRS R consists of the following rules: 543.78/241.95 543.78/241.95 down(a) -> up(f(a)) 543.78/241.95 down(b) -> up(g(b)) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.95 down(f(a)) -> f_flat(down(a)) 543.78/241.95 down(f(b)) -> f_flat(down(b)) 543.78/241.95 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.95 down(f(c)) -> f_flat(down(c)) 543.78/241.95 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.95 down(g(a)) -> g_flat(down(a)) 543.78/241.95 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.95 down(g(b)) -> g_flat(down(b)) 543.78/241.95 down(g(c)) -> g_flat(down(c)) 543.78/241.95 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.95 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.95 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.95 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.95 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.95 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.95 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.95 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.95 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.95 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.95 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.95 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.95 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.95 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.95 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.95 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.95 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.95 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.95 543.78/241.95 The set Q consists of the following terms: 543.78/241.95 543.78/241.95 down(a) 543.78/241.95 down(b) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.95 down(f(a)) 543.78/241.95 down(f(b)) 543.78/241.95 down(f(g(x0))) 543.78/241.95 down(f(c)) 543.78/241.95 down(f(fresh_constant)) 543.78/241.95 down(g(a)) 543.78/241.95 down(g(f(x0))) 543.78/241.95 down(g(b)) 543.78/241.95 down(g(c)) 543.78/241.95 down(g(fresh_constant)) 543.78/241.95 down(f(f(a))) 543.78/241.95 down(f(f(b))) 543.78/241.95 down(f(f(g(x0)))) 543.78/241.95 down(f(f(c))) 543.78/241.95 down(f(f(fresh_constant))) 543.78/241.95 down(g(g(a))) 543.78/241.95 down(g(g(f(x0)))) 543.78/241.95 down(g(g(b))) 543.78/241.95 down(g(g(c))) 543.78/241.95 down(g(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) 543.78/241.95 down(f(f(f(g(x0))))) 543.78/241.95 down(f(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) 543.78/241.95 down(g(g(g(f(x0))))) 543.78/241.95 down(g(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(x0)))))) 543.78/241.95 down(f(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(x0)))))) 543.78/241.95 down(g(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(x0))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(x0))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 f_flat(up(x0)) 543.78/241.95 g_flat(up(x0)) 543.78/241.95 543.78/241.95 We have to consider all minimal (P,Q,R)-chains. 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (783) TransformationProof (EQUIVALENT) 543.78/241.95 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.95 543.78/241.95 (TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))),TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.78/241.95 543.78/241.95 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (784) 543.78/241.95 Obligation: 543.78/241.95 Q DP problem: 543.78/241.95 The TRS P consists of the following rules: 543.78/241.95 543.78/241.95 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.95 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.95 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.95 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.95 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.95 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.95 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.95 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.95 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.95 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.95 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.95 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.95 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.95 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.95 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.95 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.95 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.95 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.95 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.95 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.95 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.95 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.95 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.95 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.95 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.95 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.95 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.95 543.78/241.95 The TRS R consists of the following rules: 543.78/241.95 543.78/241.95 down(a) -> up(f(a)) 543.78/241.95 down(b) -> up(g(b)) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.95 down(f(a)) -> f_flat(down(a)) 543.78/241.95 down(f(b)) -> f_flat(down(b)) 543.78/241.95 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.95 down(f(c)) -> f_flat(down(c)) 543.78/241.95 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.95 down(g(a)) -> g_flat(down(a)) 543.78/241.95 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.95 down(g(b)) -> g_flat(down(b)) 543.78/241.95 down(g(c)) -> g_flat(down(c)) 543.78/241.95 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.95 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.95 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.95 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.95 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.95 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.95 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.95 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.95 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.95 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.95 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.95 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.95 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.95 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.95 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.95 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.95 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.95 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.95 543.78/241.95 The set Q consists of the following terms: 543.78/241.95 543.78/241.95 down(a) 543.78/241.95 down(b) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.95 down(f(a)) 543.78/241.95 down(f(b)) 543.78/241.95 down(f(g(x0))) 543.78/241.95 down(f(c)) 543.78/241.95 down(f(fresh_constant)) 543.78/241.95 down(g(a)) 543.78/241.95 down(g(f(x0))) 543.78/241.95 down(g(b)) 543.78/241.95 down(g(c)) 543.78/241.95 down(g(fresh_constant)) 543.78/241.95 down(f(f(a))) 543.78/241.95 down(f(f(b))) 543.78/241.95 down(f(f(g(x0)))) 543.78/241.95 down(f(f(c))) 543.78/241.95 down(f(f(fresh_constant))) 543.78/241.95 down(g(g(a))) 543.78/241.95 down(g(g(f(x0)))) 543.78/241.95 down(g(g(b))) 543.78/241.95 down(g(g(c))) 543.78/241.95 down(g(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) 543.78/241.95 down(f(f(f(g(x0))))) 543.78/241.95 down(f(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) 543.78/241.95 down(g(g(g(f(x0))))) 543.78/241.95 down(g(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(x0)))))) 543.78/241.95 down(f(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(x0)))))) 543.78/241.95 down(g(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(x0))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(x0))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 f_flat(up(x0)) 543.78/241.95 g_flat(up(x0)) 543.78/241.95 543.78/241.95 We have to consider all minimal (P,Q,R)-chains. 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (785) TransformationProof (EQUIVALENT) 543.78/241.95 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.95 543.78/241.95 (TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))),TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.78/241.95 543.78/241.95 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (786) 543.78/241.95 Obligation: 543.78/241.95 Q DP problem: 543.78/241.95 The TRS P consists of the following rules: 543.78/241.95 543.78/241.95 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.95 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.95 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.95 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.95 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.95 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.95 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.95 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.95 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.95 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.95 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.95 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.95 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.95 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.95 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.95 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.95 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.95 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.95 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.95 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.95 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.95 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.95 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.95 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.95 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.95 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.95 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.95 543.78/241.95 The TRS R consists of the following rules: 543.78/241.95 543.78/241.95 down(a) -> up(f(a)) 543.78/241.95 down(b) -> up(g(b)) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.95 down(f(a)) -> f_flat(down(a)) 543.78/241.95 down(f(b)) -> f_flat(down(b)) 543.78/241.95 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.95 down(f(c)) -> f_flat(down(c)) 543.78/241.95 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.95 down(g(a)) -> g_flat(down(a)) 543.78/241.95 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.95 down(g(b)) -> g_flat(down(b)) 543.78/241.95 down(g(c)) -> g_flat(down(c)) 543.78/241.95 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.95 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.95 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.95 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.95 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.95 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.95 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.95 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.95 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.95 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.95 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.95 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.95 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.95 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.95 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.95 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.95 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.95 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.95 543.78/241.95 The set Q consists of the following terms: 543.78/241.95 543.78/241.95 down(a) 543.78/241.95 down(b) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.95 down(f(a)) 543.78/241.95 down(f(b)) 543.78/241.95 down(f(g(x0))) 543.78/241.95 down(f(c)) 543.78/241.95 down(f(fresh_constant)) 543.78/241.95 down(g(a)) 543.78/241.95 down(g(f(x0))) 543.78/241.95 down(g(b)) 543.78/241.95 down(g(c)) 543.78/241.95 down(g(fresh_constant)) 543.78/241.95 down(f(f(a))) 543.78/241.95 down(f(f(b))) 543.78/241.95 down(f(f(g(x0)))) 543.78/241.95 down(f(f(c))) 543.78/241.95 down(f(f(fresh_constant))) 543.78/241.95 down(g(g(a))) 543.78/241.95 down(g(g(f(x0)))) 543.78/241.95 down(g(g(b))) 543.78/241.95 down(g(g(c))) 543.78/241.95 down(g(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) 543.78/241.95 down(f(f(f(g(x0))))) 543.78/241.95 down(f(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) 543.78/241.95 down(g(g(g(f(x0))))) 543.78/241.95 down(g(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(x0)))))) 543.78/241.95 down(f(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(x0)))))) 543.78/241.95 down(g(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(x0))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(x0))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 f_flat(up(x0)) 543.78/241.95 g_flat(up(x0)) 543.78/241.95 543.78/241.95 We have to consider all minimal (P,Q,R)-chains. 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (787) TransformationProof (EQUIVALENT) 543.78/241.95 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.95 543.78/241.95 (TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))),TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.78/241.95 543.78/241.95 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (788) 543.78/241.95 Obligation: 543.78/241.95 Q DP problem: 543.78/241.95 The TRS P consists of the following rules: 543.78/241.95 543.78/241.95 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.95 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.95 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.95 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.95 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.95 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.95 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.95 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.95 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.95 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.95 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.95 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.95 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.95 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.95 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.95 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.95 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.95 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.95 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.95 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.95 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.95 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.95 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.95 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.95 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.95 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.95 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.95 543.78/241.95 The TRS R consists of the following rules: 543.78/241.95 543.78/241.95 down(a) -> up(f(a)) 543.78/241.95 down(b) -> up(g(b)) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.95 down(f(a)) -> f_flat(down(a)) 543.78/241.95 down(f(b)) -> f_flat(down(b)) 543.78/241.95 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.95 down(f(c)) -> f_flat(down(c)) 543.78/241.95 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.95 down(g(a)) -> g_flat(down(a)) 543.78/241.95 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.95 down(g(b)) -> g_flat(down(b)) 543.78/241.95 down(g(c)) -> g_flat(down(c)) 543.78/241.95 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.95 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.95 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.95 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.95 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.95 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.95 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.95 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.95 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.95 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.95 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.95 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.95 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.95 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.95 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.95 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.95 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.95 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.95 543.78/241.95 The set Q consists of the following terms: 543.78/241.95 543.78/241.95 down(a) 543.78/241.95 down(b) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.95 down(f(a)) 543.78/241.95 down(f(b)) 543.78/241.95 down(f(g(x0))) 543.78/241.95 down(f(c)) 543.78/241.95 down(f(fresh_constant)) 543.78/241.95 down(g(a)) 543.78/241.95 down(g(f(x0))) 543.78/241.95 down(g(b)) 543.78/241.95 down(g(c)) 543.78/241.95 down(g(fresh_constant)) 543.78/241.95 down(f(f(a))) 543.78/241.95 down(f(f(b))) 543.78/241.95 down(f(f(g(x0)))) 543.78/241.95 down(f(f(c))) 543.78/241.95 down(f(f(fresh_constant))) 543.78/241.95 down(g(g(a))) 543.78/241.95 down(g(g(f(x0)))) 543.78/241.95 down(g(g(b))) 543.78/241.95 down(g(g(c))) 543.78/241.95 down(g(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) 543.78/241.95 down(f(f(f(g(x0))))) 543.78/241.95 down(f(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) 543.78/241.95 down(g(g(g(f(x0))))) 543.78/241.95 down(g(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(x0)))))) 543.78/241.95 down(f(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(x0)))))) 543.78/241.95 down(g(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(x0))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(x0))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 f_flat(up(x0)) 543.78/241.95 g_flat(up(x0)) 543.78/241.95 543.78/241.95 We have to consider all minimal (P,Q,R)-chains. 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (789) TransformationProof (EQUIVALENT) 543.78/241.95 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.95 543.78/241.95 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.78/241.95 543.78/241.95 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (790) 543.78/241.95 Obligation: 543.78/241.95 Q DP problem: 543.78/241.95 The TRS P consists of the following rules: 543.78/241.95 543.78/241.95 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.95 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.95 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.95 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.95 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.95 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.95 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.95 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.95 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.95 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.95 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.95 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.95 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.95 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.95 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.95 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.95 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.95 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.95 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.95 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.95 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.95 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.95 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.95 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.95 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.95 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.95 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.95 543.78/241.95 The TRS R consists of the following rules: 543.78/241.95 543.78/241.95 down(a) -> up(f(a)) 543.78/241.95 down(b) -> up(g(b)) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.95 down(f(a)) -> f_flat(down(a)) 543.78/241.95 down(f(b)) -> f_flat(down(b)) 543.78/241.95 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.95 down(f(c)) -> f_flat(down(c)) 543.78/241.95 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.95 down(g(a)) -> g_flat(down(a)) 543.78/241.95 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.95 down(g(b)) -> g_flat(down(b)) 543.78/241.95 down(g(c)) -> g_flat(down(c)) 543.78/241.95 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.95 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.95 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.95 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.95 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.95 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.95 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.95 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.95 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.95 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.95 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.95 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.95 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.95 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.95 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.95 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.95 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.95 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.95 543.78/241.95 The set Q consists of the following terms: 543.78/241.95 543.78/241.95 down(a) 543.78/241.95 down(b) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.95 down(f(a)) 543.78/241.95 down(f(b)) 543.78/241.95 down(f(g(x0))) 543.78/241.95 down(f(c)) 543.78/241.95 down(f(fresh_constant)) 543.78/241.95 down(g(a)) 543.78/241.95 down(g(f(x0))) 543.78/241.95 down(g(b)) 543.78/241.95 down(g(c)) 543.78/241.95 down(g(fresh_constant)) 543.78/241.95 down(f(f(a))) 543.78/241.95 down(f(f(b))) 543.78/241.95 down(f(f(g(x0)))) 543.78/241.95 down(f(f(c))) 543.78/241.95 down(f(f(fresh_constant))) 543.78/241.95 down(g(g(a))) 543.78/241.95 down(g(g(f(x0)))) 543.78/241.95 down(g(g(b))) 543.78/241.95 down(g(g(c))) 543.78/241.95 down(g(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) 543.78/241.95 down(f(f(f(g(x0))))) 543.78/241.95 down(f(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) 543.78/241.95 down(g(g(g(f(x0))))) 543.78/241.95 down(g(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(x0)))))) 543.78/241.95 down(f(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(x0)))))) 543.78/241.95 down(g(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(x0))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(x0))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 f_flat(up(x0)) 543.78/241.95 g_flat(up(x0)) 543.78/241.95 543.78/241.95 We have to consider all minimal (P,Q,R)-chains. 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (791) TransformationProof (EQUIVALENT) 543.78/241.95 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.95 543.78/241.95 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.78/241.95 543.78/241.95 543.78/241.95 ---------------------------------------- 543.78/241.95 543.78/241.95 (792) 543.78/241.95 Obligation: 543.78/241.95 Q DP problem: 543.78/241.95 The TRS P consists of the following rules: 543.78/241.95 543.78/241.95 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.95 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.95 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.95 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.95 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.95 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.95 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.95 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.95 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.95 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.95 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.95 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.95 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.95 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.95 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.95 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.95 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.95 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.95 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.95 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.95 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.95 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.95 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.95 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.95 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.95 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.95 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.95 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.95 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.95 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.95 543.78/241.95 The TRS R consists of the following rules: 543.78/241.95 543.78/241.95 down(a) -> up(f(a)) 543.78/241.95 down(b) -> up(g(b)) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.95 down(f(a)) -> f_flat(down(a)) 543.78/241.95 down(f(b)) -> f_flat(down(b)) 543.78/241.95 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.95 down(f(c)) -> f_flat(down(c)) 543.78/241.95 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.95 down(g(a)) -> g_flat(down(a)) 543.78/241.95 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.95 down(g(b)) -> g_flat(down(b)) 543.78/241.95 down(g(c)) -> g_flat(down(c)) 543.78/241.95 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.95 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.95 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.95 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.95 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.95 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.95 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.95 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.95 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.95 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.95 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.95 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.95 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.95 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.95 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.95 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.95 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.95 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.95 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.95 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.95 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.95 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.95 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.95 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.95 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.95 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.95 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.95 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.95 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.95 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.95 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.95 543.78/241.95 The set Q consists of the following terms: 543.78/241.95 543.78/241.95 down(a) 543.78/241.95 down(b) 543.78/241.95 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.95 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.95 down(f(a)) 543.78/241.95 down(f(b)) 543.78/241.95 down(f(g(x0))) 543.78/241.95 down(f(c)) 543.78/241.95 down(f(fresh_constant)) 543.78/241.95 down(g(a)) 543.78/241.95 down(g(f(x0))) 543.78/241.95 down(g(b)) 543.78/241.95 down(g(c)) 543.78/241.95 down(g(fresh_constant)) 543.78/241.95 down(f(f(a))) 543.78/241.95 down(f(f(b))) 543.78/241.95 down(f(f(g(x0)))) 543.78/241.95 down(f(f(c))) 543.78/241.95 down(f(f(fresh_constant))) 543.78/241.95 down(g(g(a))) 543.78/241.95 down(g(g(f(x0)))) 543.78/241.95 down(g(g(b))) 543.78/241.95 down(g(g(c))) 543.78/241.95 down(g(g(fresh_constant))) 543.78/241.95 down(f(f(f(a)))) 543.78/241.95 down(f(f(f(b)))) 543.78/241.95 down(f(f(f(g(x0))))) 543.78/241.95 down(f(f(f(c)))) 543.78/241.95 down(f(f(f(fresh_constant)))) 543.78/241.95 down(g(g(g(a)))) 543.78/241.95 down(g(g(g(f(x0))))) 543.78/241.95 down(g(g(g(b)))) 543.78/241.95 down(g(g(g(c)))) 543.78/241.95 down(g(g(g(fresh_constant)))) 543.78/241.95 down(f(f(f(f(a))))) 543.78/241.95 down(f(f(f(f(b))))) 543.78/241.95 down(f(f(f(f(g(x0)))))) 543.78/241.95 down(f(f(f(f(c))))) 543.78/241.95 down(f(f(f(f(fresh_constant))))) 543.78/241.95 down(g(g(g(g(a))))) 543.78/241.95 down(g(g(g(g(f(x0)))))) 543.78/241.95 down(g(g(g(g(b))))) 543.78/241.95 down(g(g(g(g(c))))) 543.78/241.95 down(g(g(g(g(fresh_constant))))) 543.78/241.95 down(f(f(f(f(f(a)))))) 543.78/241.95 down(f(f(f(f(f(b)))))) 543.78/241.95 down(f(f(f(f(f(g(x0))))))) 543.78/241.95 down(f(f(f(f(f(c)))))) 543.78/241.95 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.95 down(g(g(g(g(g(a)))))) 543.78/241.95 down(g(g(g(g(g(f(x0))))))) 543.78/241.95 down(g(g(g(g(g(b)))))) 543.78/241.95 down(g(g(g(g(g(c)))))) 543.78/241.95 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 f_flat(up(x0)) 543.78/241.96 g_flat(up(x0)) 543.78/241.96 543.78/241.96 We have to consider all minimal (P,Q,R)-chains. 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (793) TransformationProof (EQUIVALENT) 543.78/241.96 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.96 543.78/241.96 (TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))),TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.78/241.96 543.78/241.96 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (794) 543.78/241.96 Obligation: 543.78/241.96 Q DP problem: 543.78/241.96 The TRS P consists of the following rules: 543.78/241.96 543.78/241.96 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.96 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.96 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.96 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.96 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.96 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.96 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.96 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.96 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.96 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.96 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.96 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.96 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.96 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.96 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.96 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.96 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.96 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.96 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.96 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.96 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.96 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.96 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.96 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.96 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.96 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.96 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.96 543.78/241.96 The TRS R consists of the following rules: 543.78/241.96 543.78/241.96 down(a) -> up(f(a)) 543.78/241.96 down(b) -> up(g(b)) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.96 down(f(a)) -> f_flat(down(a)) 543.78/241.96 down(f(b)) -> f_flat(down(b)) 543.78/241.96 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.96 down(f(c)) -> f_flat(down(c)) 543.78/241.96 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.96 down(g(a)) -> g_flat(down(a)) 543.78/241.96 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.96 down(g(b)) -> g_flat(down(b)) 543.78/241.96 down(g(c)) -> g_flat(down(c)) 543.78/241.96 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.96 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.96 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.96 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.96 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.96 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.96 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.96 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.96 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.96 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.96 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.96 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.96 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.96 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.96 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.96 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.96 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.96 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.96 543.78/241.96 The set Q consists of the following terms: 543.78/241.96 543.78/241.96 down(a) 543.78/241.96 down(b) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.96 down(f(a)) 543.78/241.96 down(f(b)) 543.78/241.96 down(f(g(x0))) 543.78/241.96 down(f(c)) 543.78/241.96 down(f(fresh_constant)) 543.78/241.96 down(g(a)) 543.78/241.96 down(g(f(x0))) 543.78/241.96 down(g(b)) 543.78/241.96 down(g(c)) 543.78/241.96 down(g(fresh_constant)) 543.78/241.96 down(f(f(a))) 543.78/241.96 down(f(f(b))) 543.78/241.96 down(f(f(g(x0)))) 543.78/241.96 down(f(f(c))) 543.78/241.96 down(f(f(fresh_constant))) 543.78/241.96 down(g(g(a))) 543.78/241.96 down(g(g(f(x0)))) 543.78/241.96 down(g(g(b))) 543.78/241.96 down(g(g(c))) 543.78/241.96 down(g(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) 543.78/241.96 down(f(f(f(g(x0))))) 543.78/241.96 down(f(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) 543.78/241.96 down(g(g(g(f(x0))))) 543.78/241.96 down(g(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(x0)))))) 543.78/241.96 down(f(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(x0)))))) 543.78/241.96 down(g(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(x0))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(x0))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 f_flat(up(x0)) 543.78/241.96 g_flat(up(x0)) 543.78/241.96 543.78/241.96 We have to consider all minimal (P,Q,R)-chains. 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (795) TransformationProof (EQUIVALENT) 543.78/241.96 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.96 543.78/241.96 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.78/241.96 543.78/241.96 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (796) 543.78/241.96 Obligation: 543.78/241.96 Q DP problem: 543.78/241.96 The TRS P consists of the following rules: 543.78/241.96 543.78/241.96 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.96 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.96 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.96 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.96 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.96 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.96 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.96 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.96 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.96 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.96 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.96 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.96 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.96 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.96 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.96 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.96 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.96 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.96 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.96 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.96 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.96 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.96 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.96 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.96 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.96 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.96 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.96 543.78/241.96 The TRS R consists of the following rules: 543.78/241.96 543.78/241.96 down(a) -> up(f(a)) 543.78/241.96 down(b) -> up(g(b)) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.96 down(f(a)) -> f_flat(down(a)) 543.78/241.96 down(f(b)) -> f_flat(down(b)) 543.78/241.96 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.96 down(f(c)) -> f_flat(down(c)) 543.78/241.96 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.96 down(g(a)) -> g_flat(down(a)) 543.78/241.96 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.96 down(g(b)) -> g_flat(down(b)) 543.78/241.96 down(g(c)) -> g_flat(down(c)) 543.78/241.96 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.96 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.96 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.96 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.96 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.96 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.96 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.96 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.96 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.96 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.96 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.96 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.96 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.96 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.96 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.96 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.96 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.96 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.96 543.78/241.96 The set Q consists of the following terms: 543.78/241.96 543.78/241.96 down(a) 543.78/241.96 down(b) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.96 down(f(a)) 543.78/241.96 down(f(b)) 543.78/241.96 down(f(g(x0))) 543.78/241.96 down(f(c)) 543.78/241.96 down(f(fresh_constant)) 543.78/241.96 down(g(a)) 543.78/241.96 down(g(f(x0))) 543.78/241.96 down(g(b)) 543.78/241.96 down(g(c)) 543.78/241.96 down(g(fresh_constant)) 543.78/241.96 down(f(f(a))) 543.78/241.96 down(f(f(b))) 543.78/241.96 down(f(f(g(x0)))) 543.78/241.96 down(f(f(c))) 543.78/241.96 down(f(f(fresh_constant))) 543.78/241.96 down(g(g(a))) 543.78/241.96 down(g(g(f(x0)))) 543.78/241.96 down(g(g(b))) 543.78/241.96 down(g(g(c))) 543.78/241.96 down(g(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) 543.78/241.96 down(f(f(f(g(x0))))) 543.78/241.96 down(f(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) 543.78/241.96 down(g(g(g(f(x0))))) 543.78/241.96 down(g(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(x0)))))) 543.78/241.96 down(f(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(x0)))))) 543.78/241.96 down(g(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(x0))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(x0))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 f_flat(up(x0)) 543.78/241.96 g_flat(up(x0)) 543.78/241.96 543.78/241.96 We have to consider all minimal (P,Q,R)-chains. 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (797) TransformationProof (EQUIVALENT) 543.78/241.96 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.96 543.78/241.96 (TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))),TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.78/241.96 543.78/241.96 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (798) 543.78/241.96 Obligation: 543.78/241.96 Q DP problem: 543.78/241.96 The TRS P consists of the following rules: 543.78/241.96 543.78/241.96 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.96 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.96 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.96 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.96 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.96 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.96 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.96 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.96 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.96 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.96 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.96 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.96 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.96 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.96 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.96 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.96 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.96 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.96 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.96 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.96 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.96 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.96 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.96 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.96 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.96 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.96 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.96 543.78/241.96 The TRS R consists of the following rules: 543.78/241.96 543.78/241.96 down(a) -> up(f(a)) 543.78/241.96 down(b) -> up(g(b)) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.96 down(f(a)) -> f_flat(down(a)) 543.78/241.96 down(f(b)) -> f_flat(down(b)) 543.78/241.96 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.96 down(f(c)) -> f_flat(down(c)) 543.78/241.96 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.96 down(g(a)) -> g_flat(down(a)) 543.78/241.96 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.96 down(g(b)) -> g_flat(down(b)) 543.78/241.96 down(g(c)) -> g_flat(down(c)) 543.78/241.96 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.96 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.96 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.96 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.96 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.96 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.96 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.96 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.96 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.96 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.96 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.96 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.96 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.96 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.96 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.96 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.96 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.96 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.96 543.78/241.96 The set Q consists of the following terms: 543.78/241.96 543.78/241.96 down(a) 543.78/241.96 down(b) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.96 down(f(a)) 543.78/241.96 down(f(b)) 543.78/241.96 down(f(g(x0))) 543.78/241.96 down(f(c)) 543.78/241.96 down(f(fresh_constant)) 543.78/241.96 down(g(a)) 543.78/241.96 down(g(f(x0))) 543.78/241.96 down(g(b)) 543.78/241.96 down(g(c)) 543.78/241.96 down(g(fresh_constant)) 543.78/241.96 down(f(f(a))) 543.78/241.96 down(f(f(b))) 543.78/241.96 down(f(f(g(x0)))) 543.78/241.96 down(f(f(c))) 543.78/241.96 down(f(f(fresh_constant))) 543.78/241.96 down(g(g(a))) 543.78/241.96 down(g(g(f(x0)))) 543.78/241.96 down(g(g(b))) 543.78/241.96 down(g(g(c))) 543.78/241.96 down(g(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) 543.78/241.96 down(f(f(f(g(x0))))) 543.78/241.96 down(f(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) 543.78/241.96 down(g(g(g(f(x0))))) 543.78/241.96 down(g(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(x0)))))) 543.78/241.96 down(f(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(x0)))))) 543.78/241.96 down(g(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(x0))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(x0))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 f_flat(up(x0)) 543.78/241.96 g_flat(up(x0)) 543.78/241.96 543.78/241.96 We have to consider all minimal (P,Q,R)-chains. 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (799) TransformationProof (EQUIVALENT) 543.78/241.96 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.96 543.78/241.96 (TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))),TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.78/241.96 543.78/241.96 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (800) 543.78/241.96 Obligation: 543.78/241.96 Q DP problem: 543.78/241.96 The TRS P consists of the following rules: 543.78/241.96 543.78/241.96 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.96 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.96 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.96 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.96 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.96 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.96 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.96 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.96 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.96 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.96 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.96 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.96 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.96 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.96 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.96 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.96 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.96 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.96 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.96 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.96 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.96 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.96 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.96 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.96 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.96 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.96 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.96 543.78/241.96 The TRS R consists of the following rules: 543.78/241.96 543.78/241.96 down(a) -> up(f(a)) 543.78/241.96 down(b) -> up(g(b)) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.96 down(f(a)) -> f_flat(down(a)) 543.78/241.96 down(f(b)) -> f_flat(down(b)) 543.78/241.96 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.96 down(f(c)) -> f_flat(down(c)) 543.78/241.96 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.96 down(g(a)) -> g_flat(down(a)) 543.78/241.96 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.96 down(g(b)) -> g_flat(down(b)) 543.78/241.96 down(g(c)) -> g_flat(down(c)) 543.78/241.96 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.96 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.96 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.96 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.96 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.96 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.96 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.96 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.96 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.96 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.96 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.96 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.96 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.96 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.96 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.96 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.96 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.96 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.96 543.78/241.96 The set Q consists of the following terms: 543.78/241.96 543.78/241.96 down(a) 543.78/241.96 down(b) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.96 down(f(a)) 543.78/241.96 down(f(b)) 543.78/241.96 down(f(g(x0))) 543.78/241.96 down(f(c)) 543.78/241.96 down(f(fresh_constant)) 543.78/241.96 down(g(a)) 543.78/241.96 down(g(f(x0))) 543.78/241.96 down(g(b)) 543.78/241.96 down(g(c)) 543.78/241.96 down(g(fresh_constant)) 543.78/241.96 down(f(f(a))) 543.78/241.96 down(f(f(b))) 543.78/241.96 down(f(f(g(x0)))) 543.78/241.96 down(f(f(c))) 543.78/241.96 down(f(f(fresh_constant))) 543.78/241.96 down(g(g(a))) 543.78/241.96 down(g(g(f(x0)))) 543.78/241.96 down(g(g(b))) 543.78/241.96 down(g(g(c))) 543.78/241.96 down(g(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) 543.78/241.96 down(f(f(f(g(x0))))) 543.78/241.96 down(f(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) 543.78/241.96 down(g(g(g(f(x0))))) 543.78/241.96 down(g(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(x0)))))) 543.78/241.96 down(f(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(x0)))))) 543.78/241.96 down(g(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(x0))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(x0))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 f_flat(up(x0)) 543.78/241.96 g_flat(up(x0)) 543.78/241.96 543.78/241.96 We have to consider all minimal (P,Q,R)-chains. 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (801) TransformationProof (EQUIVALENT) 543.78/241.96 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.96 543.78/241.96 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.78/241.96 543.78/241.96 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (802) 543.78/241.96 Obligation: 543.78/241.96 Q DP problem: 543.78/241.96 The TRS P consists of the following rules: 543.78/241.96 543.78/241.96 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.96 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.96 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.96 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.96 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.96 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.96 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.96 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.96 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.96 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.96 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.96 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.96 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.96 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.96 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.96 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.96 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.96 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.96 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.96 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.96 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.96 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.96 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.96 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.96 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.96 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.96 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.96 543.78/241.96 The TRS R consists of the following rules: 543.78/241.96 543.78/241.96 down(a) -> up(f(a)) 543.78/241.96 down(b) -> up(g(b)) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.96 down(f(a)) -> f_flat(down(a)) 543.78/241.96 down(f(b)) -> f_flat(down(b)) 543.78/241.96 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.96 down(f(c)) -> f_flat(down(c)) 543.78/241.96 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.96 down(g(a)) -> g_flat(down(a)) 543.78/241.96 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.96 down(g(b)) -> g_flat(down(b)) 543.78/241.96 down(g(c)) -> g_flat(down(c)) 543.78/241.96 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.96 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.96 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.96 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.96 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.96 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.96 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.96 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.96 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.96 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.96 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.96 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.96 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.96 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.96 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.96 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.96 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.96 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.96 543.78/241.96 The set Q consists of the following terms: 543.78/241.96 543.78/241.96 down(a) 543.78/241.96 down(b) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.96 down(f(a)) 543.78/241.96 down(f(b)) 543.78/241.96 down(f(g(x0))) 543.78/241.96 down(f(c)) 543.78/241.96 down(f(fresh_constant)) 543.78/241.96 down(g(a)) 543.78/241.96 down(g(f(x0))) 543.78/241.96 down(g(b)) 543.78/241.96 down(g(c)) 543.78/241.96 down(g(fresh_constant)) 543.78/241.96 down(f(f(a))) 543.78/241.96 down(f(f(b))) 543.78/241.96 down(f(f(g(x0)))) 543.78/241.96 down(f(f(c))) 543.78/241.96 down(f(f(fresh_constant))) 543.78/241.96 down(g(g(a))) 543.78/241.96 down(g(g(f(x0)))) 543.78/241.96 down(g(g(b))) 543.78/241.96 down(g(g(c))) 543.78/241.96 down(g(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) 543.78/241.96 down(f(f(f(g(x0))))) 543.78/241.96 down(f(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) 543.78/241.96 down(g(g(g(f(x0))))) 543.78/241.96 down(g(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(x0)))))) 543.78/241.96 down(f(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(x0)))))) 543.78/241.96 down(g(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(x0))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(x0))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 f_flat(up(x0)) 543.78/241.96 g_flat(up(x0)) 543.78/241.96 543.78/241.96 We have to consider all minimal (P,Q,R)-chains. 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (803) TransformationProof (EQUIVALENT) 543.78/241.96 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.96 543.78/241.96 (TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))),TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.78/241.96 543.78/241.96 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (804) 543.78/241.96 Obligation: 543.78/241.96 Q DP problem: 543.78/241.96 The TRS P consists of the following rules: 543.78/241.96 543.78/241.96 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.96 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.96 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.96 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.96 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.96 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.96 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.96 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.96 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.96 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.96 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.96 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.96 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.96 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.96 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.96 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.96 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.96 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.96 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.96 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.96 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.96 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.96 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.96 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.96 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.96 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.96 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.96 543.78/241.96 The TRS R consists of the following rules: 543.78/241.96 543.78/241.96 down(a) -> up(f(a)) 543.78/241.96 down(b) -> up(g(b)) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.96 down(f(a)) -> f_flat(down(a)) 543.78/241.96 down(f(b)) -> f_flat(down(b)) 543.78/241.96 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.96 down(f(c)) -> f_flat(down(c)) 543.78/241.96 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.96 down(g(a)) -> g_flat(down(a)) 543.78/241.96 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.96 down(g(b)) -> g_flat(down(b)) 543.78/241.96 down(g(c)) -> g_flat(down(c)) 543.78/241.96 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.96 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.96 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.96 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.96 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.96 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.96 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.96 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.96 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.96 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.96 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.96 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.96 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.96 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.96 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.96 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.96 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.96 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.96 543.78/241.96 The set Q consists of the following terms: 543.78/241.96 543.78/241.96 down(a) 543.78/241.96 down(b) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.96 down(f(a)) 543.78/241.96 down(f(b)) 543.78/241.96 down(f(g(x0))) 543.78/241.96 down(f(c)) 543.78/241.96 down(f(fresh_constant)) 543.78/241.96 down(g(a)) 543.78/241.96 down(g(f(x0))) 543.78/241.96 down(g(b)) 543.78/241.96 down(g(c)) 543.78/241.96 down(g(fresh_constant)) 543.78/241.96 down(f(f(a))) 543.78/241.96 down(f(f(b))) 543.78/241.96 down(f(f(g(x0)))) 543.78/241.96 down(f(f(c))) 543.78/241.96 down(f(f(fresh_constant))) 543.78/241.96 down(g(g(a))) 543.78/241.96 down(g(g(f(x0)))) 543.78/241.96 down(g(g(b))) 543.78/241.96 down(g(g(c))) 543.78/241.96 down(g(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) 543.78/241.96 down(f(f(f(g(x0))))) 543.78/241.96 down(f(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) 543.78/241.96 down(g(g(g(f(x0))))) 543.78/241.96 down(g(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(x0)))))) 543.78/241.96 down(f(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(x0)))))) 543.78/241.96 down(g(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(x0))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(x0))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 f_flat(up(x0)) 543.78/241.96 g_flat(up(x0)) 543.78/241.96 543.78/241.96 We have to consider all minimal (P,Q,R)-chains. 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (805) TransformationProof (EQUIVALENT) 543.78/241.96 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.96 543.78/241.96 (TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))),TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.78/241.96 543.78/241.96 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (806) 543.78/241.96 Obligation: 543.78/241.96 Q DP problem: 543.78/241.96 The TRS P consists of the following rules: 543.78/241.96 543.78/241.96 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.96 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.96 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.96 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.96 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.96 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.96 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.96 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.96 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.96 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.96 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.96 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.96 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.96 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.96 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.96 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.96 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.96 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.96 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.96 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.96 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.96 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.96 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.96 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.96 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.96 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.96 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.96 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.96 543.78/241.96 The TRS R consists of the following rules: 543.78/241.96 543.78/241.96 down(a) -> up(f(a)) 543.78/241.96 down(b) -> up(g(b)) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.96 down(f(a)) -> f_flat(down(a)) 543.78/241.96 down(f(b)) -> f_flat(down(b)) 543.78/241.96 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.96 down(f(c)) -> f_flat(down(c)) 543.78/241.96 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.96 down(g(a)) -> g_flat(down(a)) 543.78/241.96 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.96 down(g(b)) -> g_flat(down(b)) 543.78/241.96 down(g(c)) -> g_flat(down(c)) 543.78/241.96 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.96 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.96 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.96 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.96 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.96 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.96 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.96 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.96 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.96 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.96 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.96 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.96 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.96 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.96 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.96 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.96 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.96 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.96 543.78/241.96 The set Q consists of the following terms: 543.78/241.96 543.78/241.96 down(a) 543.78/241.96 down(b) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.96 down(f(a)) 543.78/241.96 down(f(b)) 543.78/241.96 down(f(g(x0))) 543.78/241.96 down(f(c)) 543.78/241.96 down(f(fresh_constant)) 543.78/241.96 down(g(a)) 543.78/241.96 down(g(f(x0))) 543.78/241.96 down(g(b)) 543.78/241.96 down(g(c)) 543.78/241.96 down(g(fresh_constant)) 543.78/241.96 down(f(f(a))) 543.78/241.96 down(f(f(b))) 543.78/241.96 down(f(f(g(x0)))) 543.78/241.96 down(f(f(c))) 543.78/241.96 down(f(f(fresh_constant))) 543.78/241.96 down(g(g(a))) 543.78/241.96 down(g(g(f(x0)))) 543.78/241.96 down(g(g(b))) 543.78/241.96 down(g(g(c))) 543.78/241.96 down(g(g(fresh_constant))) 543.78/241.96 down(f(f(f(a)))) 543.78/241.96 down(f(f(f(b)))) 543.78/241.96 down(f(f(f(g(x0))))) 543.78/241.96 down(f(f(f(c)))) 543.78/241.96 down(f(f(f(fresh_constant)))) 543.78/241.96 down(g(g(g(a)))) 543.78/241.96 down(g(g(g(f(x0))))) 543.78/241.96 down(g(g(g(b)))) 543.78/241.96 down(g(g(g(c)))) 543.78/241.96 down(g(g(g(fresh_constant)))) 543.78/241.96 down(f(f(f(f(a))))) 543.78/241.96 down(f(f(f(f(b))))) 543.78/241.96 down(f(f(f(f(g(x0)))))) 543.78/241.96 down(f(f(f(f(c))))) 543.78/241.96 down(f(f(f(f(fresh_constant))))) 543.78/241.96 down(g(g(g(g(a))))) 543.78/241.96 down(g(g(g(g(f(x0)))))) 543.78/241.96 down(g(g(g(g(b))))) 543.78/241.96 down(g(g(g(g(c))))) 543.78/241.96 down(g(g(g(g(fresh_constant))))) 543.78/241.96 down(f(f(f(f(f(a)))))) 543.78/241.96 down(f(f(f(f(f(b)))))) 543.78/241.96 down(f(f(f(f(f(g(x0))))))) 543.78/241.96 down(f(f(f(f(f(c)))))) 543.78/241.96 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.96 down(g(g(g(g(g(a)))))) 543.78/241.96 down(g(g(g(g(g(f(x0))))))) 543.78/241.96 down(g(g(g(g(g(b)))))) 543.78/241.96 down(g(g(g(g(g(c)))))) 543.78/241.96 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.96 down(f(f(f(f(f(f(a))))))) 543.78/241.96 down(f(f(f(f(f(f(b))))))) 543.78/241.96 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.96 down(f(f(f(f(f(f(c))))))) 543.78/241.96 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.96 down(g(g(g(g(g(g(a))))))) 543.78/241.96 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.96 down(g(g(g(g(g(g(b))))))) 543.78/241.96 down(g(g(g(g(g(g(c))))))) 543.78/241.96 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.96 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.96 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.96 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.96 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.96 f_flat(up(x0)) 543.78/241.96 g_flat(up(x0)) 543.78/241.96 543.78/241.96 We have to consider all minimal (P,Q,R)-chains. 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (807) TransformationProof (EQUIVALENT) 543.78/241.96 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.96 543.78/241.96 (TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))),TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.78/241.96 543.78/241.96 543.78/241.96 ---------------------------------------- 543.78/241.96 543.78/241.96 (808) 543.78/241.96 Obligation: 543.78/241.96 Q DP problem: 543.78/241.96 The TRS P consists of the following rules: 543.78/241.96 543.78/241.96 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.96 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.96 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.96 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.96 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.96 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.96 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.96 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.96 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.96 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.96 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.96 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.96 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.96 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.96 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.96 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.96 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.96 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.96 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.96 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.96 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.96 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.96 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.97 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.97 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.97 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.97 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.97 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.97 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.78/241.97 543.78/241.97 The TRS R consists of the following rules: 543.78/241.97 543.78/241.97 down(a) -> up(f(a)) 543.78/241.97 down(b) -> up(g(b)) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.97 down(f(a)) -> f_flat(down(a)) 543.78/241.97 down(f(b)) -> f_flat(down(b)) 543.78/241.97 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.97 down(f(c)) -> f_flat(down(c)) 543.78/241.97 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.97 down(g(a)) -> g_flat(down(a)) 543.78/241.97 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.97 down(g(b)) -> g_flat(down(b)) 543.78/241.97 down(g(c)) -> g_flat(down(c)) 543.78/241.97 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.97 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.97 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.97 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.97 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.97 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.97 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.97 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.97 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.97 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.97 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.97 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.97 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.97 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.97 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.97 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.97 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.97 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.97 543.78/241.97 The set Q consists of the following terms: 543.78/241.97 543.78/241.97 down(a) 543.78/241.97 down(b) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.97 down(f(a)) 543.78/241.97 down(f(b)) 543.78/241.97 down(f(g(x0))) 543.78/241.97 down(f(c)) 543.78/241.97 down(f(fresh_constant)) 543.78/241.97 down(g(a)) 543.78/241.97 down(g(f(x0))) 543.78/241.97 down(g(b)) 543.78/241.97 down(g(c)) 543.78/241.97 down(g(fresh_constant)) 543.78/241.97 down(f(f(a))) 543.78/241.97 down(f(f(b))) 543.78/241.97 down(f(f(g(x0)))) 543.78/241.97 down(f(f(c))) 543.78/241.97 down(f(f(fresh_constant))) 543.78/241.97 down(g(g(a))) 543.78/241.97 down(g(g(f(x0)))) 543.78/241.97 down(g(g(b))) 543.78/241.97 down(g(g(c))) 543.78/241.97 down(g(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) 543.78/241.97 down(f(f(f(g(x0))))) 543.78/241.97 down(f(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) 543.78/241.97 down(g(g(g(f(x0))))) 543.78/241.97 down(g(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(x0)))))) 543.78/241.97 down(f(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(x0)))))) 543.78/241.97 down(g(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(x0))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(x0))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 f_flat(up(x0)) 543.78/241.97 g_flat(up(x0)) 543.78/241.97 543.78/241.97 We have to consider all minimal (P,Q,R)-chains. 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (809) TransformationProof (EQUIVALENT) 543.78/241.97 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(a))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.97 543.78/241.97 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a)))))))))))) 543.78/241.97 543.78/241.97 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (810) 543.78/241.97 Obligation: 543.78/241.97 Q DP problem: 543.78/241.97 The TRS P consists of the following rules: 543.78/241.97 543.78/241.97 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.97 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.97 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.97 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.97 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.97 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.97 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.97 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.97 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.97 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.97 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.97 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.97 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.97 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.97 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.97 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.97 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.97 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.97 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.97 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.97 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.97 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.97 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.97 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.97 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.97 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.97 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.78/241.97 543.78/241.97 The TRS R consists of the following rules: 543.78/241.97 543.78/241.97 down(a) -> up(f(a)) 543.78/241.97 down(b) -> up(g(b)) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.97 down(f(a)) -> f_flat(down(a)) 543.78/241.97 down(f(b)) -> f_flat(down(b)) 543.78/241.97 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.97 down(f(c)) -> f_flat(down(c)) 543.78/241.97 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.97 down(g(a)) -> g_flat(down(a)) 543.78/241.97 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.97 down(g(b)) -> g_flat(down(b)) 543.78/241.97 down(g(c)) -> g_flat(down(c)) 543.78/241.97 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.97 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.97 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.97 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.97 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.97 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.97 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.97 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.97 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.97 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.97 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.97 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.97 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.97 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.97 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.97 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.97 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.97 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.97 543.78/241.97 The set Q consists of the following terms: 543.78/241.97 543.78/241.97 down(a) 543.78/241.97 down(b) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.97 down(f(a)) 543.78/241.97 down(f(b)) 543.78/241.97 down(f(g(x0))) 543.78/241.97 down(f(c)) 543.78/241.97 down(f(fresh_constant)) 543.78/241.97 down(g(a)) 543.78/241.97 down(g(f(x0))) 543.78/241.97 down(g(b)) 543.78/241.97 down(g(c)) 543.78/241.97 down(g(fresh_constant)) 543.78/241.97 down(f(f(a))) 543.78/241.97 down(f(f(b))) 543.78/241.97 down(f(f(g(x0)))) 543.78/241.97 down(f(f(c))) 543.78/241.97 down(f(f(fresh_constant))) 543.78/241.97 down(g(g(a))) 543.78/241.97 down(g(g(f(x0)))) 543.78/241.97 down(g(g(b))) 543.78/241.97 down(g(g(c))) 543.78/241.97 down(g(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) 543.78/241.97 down(f(f(f(g(x0))))) 543.78/241.97 down(f(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) 543.78/241.97 down(g(g(g(f(x0))))) 543.78/241.97 down(g(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(x0)))))) 543.78/241.97 down(f(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(x0)))))) 543.78/241.97 down(g(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(x0))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(x0))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 f_flat(up(x0)) 543.78/241.97 g_flat(up(x0)) 543.78/241.97 543.78/241.97 We have to consider all minimal (P,Q,R)-chains. 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (811) TransformationProof (EQUIVALENT) 543.78/241.97 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(b))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.97 543.78/241.97 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b)))))))))))) 543.78/241.97 543.78/241.97 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (812) 543.78/241.97 Obligation: 543.78/241.97 Q DP problem: 543.78/241.97 The TRS P consists of the following rules: 543.78/241.97 543.78/241.97 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.97 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.97 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.97 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.97 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.97 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.97 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.97 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.97 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.97 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.97 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.97 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.97 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.97 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.97 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.97 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.97 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.97 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.97 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.97 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.97 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.97 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.97 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.97 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.97 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.97 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.97 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.78/241.97 543.78/241.97 The TRS R consists of the following rules: 543.78/241.97 543.78/241.97 down(a) -> up(f(a)) 543.78/241.97 down(b) -> up(g(b)) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.97 down(f(a)) -> f_flat(down(a)) 543.78/241.97 down(f(b)) -> f_flat(down(b)) 543.78/241.97 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.97 down(f(c)) -> f_flat(down(c)) 543.78/241.97 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.97 down(g(a)) -> g_flat(down(a)) 543.78/241.97 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.97 down(g(b)) -> g_flat(down(b)) 543.78/241.97 down(g(c)) -> g_flat(down(c)) 543.78/241.97 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.97 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.97 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.97 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.97 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.97 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.97 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.97 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.97 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.97 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.97 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.97 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.97 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.97 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.97 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.97 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.97 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.97 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.97 543.78/241.97 The set Q consists of the following terms: 543.78/241.97 543.78/241.97 down(a) 543.78/241.97 down(b) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.97 down(f(a)) 543.78/241.97 down(f(b)) 543.78/241.97 down(f(g(x0))) 543.78/241.97 down(f(c)) 543.78/241.97 down(f(fresh_constant)) 543.78/241.97 down(g(a)) 543.78/241.97 down(g(f(x0))) 543.78/241.97 down(g(b)) 543.78/241.97 down(g(c)) 543.78/241.97 down(g(fresh_constant)) 543.78/241.97 down(f(f(a))) 543.78/241.97 down(f(f(b))) 543.78/241.97 down(f(f(g(x0)))) 543.78/241.97 down(f(f(c))) 543.78/241.97 down(f(f(fresh_constant))) 543.78/241.97 down(g(g(a))) 543.78/241.97 down(g(g(f(x0)))) 543.78/241.97 down(g(g(b))) 543.78/241.97 down(g(g(c))) 543.78/241.97 down(g(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) 543.78/241.97 down(f(f(f(g(x0))))) 543.78/241.97 down(f(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) 543.78/241.97 down(g(g(g(f(x0))))) 543.78/241.97 down(g(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(x0)))))) 543.78/241.97 down(f(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(x0)))))) 543.78/241.97 down(g(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(x0))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(x0))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 f_flat(up(x0)) 543.78/241.97 g_flat(up(x0)) 543.78/241.97 543.78/241.97 We have to consider all minimal (P,Q,R)-chains. 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (813) TransformationProof (EQUIVALENT) 543.78/241.97 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(g(x0)))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.97 543.78/241.97 (TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0))))))))))))) 543.78/241.97 543.78/241.97 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (814) 543.78/241.97 Obligation: 543.78/241.97 Q DP problem: 543.78/241.97 The TRS P consists of the following rules: 543.78/241.97 543.78/241.97 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.97 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.97 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.97 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.97 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.97 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.97 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.97 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.97 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.97 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.97 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.97 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.97 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.97 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.97 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.97 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.97 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.97 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.97 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.97 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.97 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.97 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.97 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.97 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.97 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.97 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.97 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.78/241.97 543.78/241.97 The TRS R consists of the following rules: 543.78/241.97 543.78/241.97 down(a) -> up(f(a)) 543.78/241.97 down(b) -> up(g(b)) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.97 down(f(a)) -> f_flat(down(a)) 543.78/241.97 down(f(b)) -> f_flat(down(b)) 543.78/241.97 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.97 down(f(c)) -> f_flat(down(c)) 543.78/241.97 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.97 down(g(a)) -> g_flat(down(a)) 543.78/241.97 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.97 down(g(b)) -> g_flat(down(b)) 543.78/241.97 down(g(c)) -> g_flat(down(c)) 543.78/241.97 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.97 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.97 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.97 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.97 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.97 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.97 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.97 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.97 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.97 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.97 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.97 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.97 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.97 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.97 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.97 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.97 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.97 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.97 543.78/241.97 The set Q consists of the following terms: 543.78/241.97 543.78/241.97 down(a) 543.78/241.97 down(b) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.97 down(f(a)) 543.78/241.97 down(f(b)) 543.78/241.97 down(f(g(x0))) 543.78/241.97 down(f(c)) 543.78/241.97 down(f(fresh_constant)) 543.78/241.97 down(g(a)) 543.78/241.97 down(g(f(x0))) 543.78/241.97 down(g(b)) 543.78/241.97 down(g(c)) 543.78/241.97 down(g(fresh_constant)) 543.78/241.97 down(f(f(a))) 543.78/241.97 down(f(f(b))) 543.78/241.97 down(f(f(g(x0)))) 543.78/241.97 down(f(f(c))) 543.78/241.97 down(f(f(fresh_constant))) 543.78/241.97 down(g(g(a))) 543.78/241.97 down(g(g(f(x0)))) 543.78/241.97 down(g(g(b))) 543.78/241.97 down(g(g(c))) 543.78/241.97 down(g(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) 543.78/241.97 down(f(f(f(g(x0))))) 543.78/241.97 down(f(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) 543.78/241.97 down(g(g(g(f(x0))))) 543.78/241.97 down(g(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(x0)))))) 543.78/241.97 down(f(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(x0)))))) 543.78/241.97 down(g(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(x0))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(x0))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 f_flat(up(x0)) 543.78/241.97 g_flat(up(x0)) 543.78/241.97 543.78/241.97 We have to consider all minimal (P,Q,R)-chains. 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (815) TransformationProof (EQUIVALENT) 543.78/241.97 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.97 543.78/241.97 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.78/241.97 543.78/241.97 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (816) 543.78/241.97 Obligation: 543.78/241.97 Q DP problem: 543.78/241.97 The TRS P consists of the following rules: 543.78/241.97 543.78/241.97 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.97 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.97 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.97 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.97 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.97 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.97 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.97 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.97 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.97 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.97 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.97 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.97 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.97 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.97 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.97 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.97 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.97 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.97 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.97 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.97 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.97 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.97 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.97 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.97 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.97 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.97 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.78/241.97 543.78/241.97 The TRS R consists of the following rules: 543.78/241.97 543.78/241.97 down(a) -> up(f(a)) 543.78/241.97 down(b) -> up(g(b)) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.97 down(f(a)) -> f_flat(down(a)) 543.78/241.97 down(f(b)) -> f_flat(down(b)) 543.78/241.97 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.97 down(f(c)) -> f_flat(down(c)) 543.78/241.97 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.97 down(g(a)) -> g_flat(down(a)) 543.78/241.97 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.97 down(g(b)) -> g_flat(down(b)) 543.78/241.97 down(g(c)) -> g_flat(down(c)) 543.78/241.97 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.97 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.97 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.97 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.97 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.97 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.97 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.97 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.97 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.97 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.97 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.97 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.97 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.97 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.97 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.97 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.97 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.97 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.97 543.78/241.97 The set Q consists of the following terms: 543.78/241.97 543.78/241.97 down(a) 543.78/241.97 down(b) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.97 down(f(a)) 543.78/241.97 down(f(b)) 543.78/241.97 down(f(g(x0))) 543.78/241.97 down(f(c)) 543.78/241.97 down(f(fresh_constant)) 543.78/241.97 down(g(a)) 543.78/241.97 down(g(f(x0))) 543.78/241.97 down(g(b)) 543.78/241.97 down(g(c)) 543.78/241.97 down(g(fresh_constant)) 543.78/241.97 down(f(f(a))) 543.78/241.97 down(f(f(b))) 543.78/241.97 down(f(f(g(x0)))) 543.78/241.97 down(f(f(c))) 543.78/241.97 down(f(f(fresh_constant))) 543.78/241.97 down(g(g(a))) 543.78/241.97 down(g(g(f(x0)))) 543.78/241.97 down(g(g(b))) 543.78/241.97 down(g(g(c))) 543.78/241.97 down(g(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) 543.78/241.97 down(f(f(f(g(x0))))) 543.78/241.97 down(f(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) 543.78/241.97 down(g(g(g(f(x0))))) 543.78/241.97 down(g(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(x0)))))) 543.78/241.97 down(f(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(x0)))))) 543.78/241.97 down(g(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(x0))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(x0))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 f_flat(up(x0)) 543.78/241.97 g_flat(up(x0)) 543.78/241.97 543.78/241.97 We have to consider all minimal (P,Q,R)-chains. 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (817) TransformationProof (EQUIVALENT) 543.78/241.97 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.97 543.78/241.97 (TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))),TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.78/241.97 543.78/241.97 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (818) 543.78/241.97 Obligation: 543.78/241.97 Q DP problem: 543.78/241.97 The TRS P consists of the following rules: 543.78/241.97 543.78/241.97 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.97 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.97 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.97 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.97 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.97 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.97 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.97 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.97 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.97 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.97 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.97 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.97 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.97 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.97 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.97 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.97 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.97 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.97 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.97 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.97 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.97 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.97 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.97 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.97 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.97 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.97 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.78/241.97 543.78/241.97 The TRS R consists of the following rules: 543.78/241.97 543.78/241.97 down(a) -> up(f(a)) 543.78/241.97 down(b) -> up(g(b)) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.97 down(f(a)) -> f_flat(down(a)) 543.78/241.97 down(f(b)) -> f_flat(down(b)) 543.78/241.97 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.97 down(f(c)) -> f_flat(down(c)) 543.78/241.97 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.97 down(g(a)) -> g_flat(down(a)) 543.78/241.97 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.97 down(g(b)) -> g_flat(down(b)) 543.78/241.97 down(g(c)) -> g_flat(down(c)) 543.78/241.97 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.97 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.97 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.97 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.97 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.97 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.97 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.97 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.97 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.97 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.97 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.97 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.97 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.97 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.97 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.97 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.97 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.97 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.97 543.78/241.97 The set Q consists of the following terms: 543.78/241.97 543.78/241.97 down(a) 543.78/241.97 down(b) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.97 down(f(a)) 543.78/241.97 down(f(b)) 543.78/241.97 down(f(g(x0))) 543.78/241.97 down(f(c)) 543.78/241.97 down(f(fresh_constant)) 543.78/241.97 down(g(a)) 543.78/241.97 down(g(f(x0))) 543.78/241.97 down(g(b)) 543.78/241.97 down(g(c)) 543.78/241.97 down(g(fresh_constant)) 543.78/241.97 down(f(f(a))) 543.78/241.97 down(f(f(b))) 543.78/241.97 down(f(f(g(x0)))) 543.78/241.97 down(f(f(c))) 543.78/241.97 down(f(f(fresh_constant))) 543.78/241.97 down(g(g(a))) 543.78/241.97 down(g(g(f(x0)))) 543.78/241.97 down(g(g(b))) 543.78/241.97 down(g(g(c))) 543.78/241.97 down(g(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) 543.78/241.97 down(f(f(f(g(x0))))) 543.78/241.97 down(f(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) 543.78/241.97 down(g(g(g(f(x0))))) 543.78/241.97 down(g(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(x0)))))) 543.78/241.97 down(f(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(x0)))))) 543.78/241.97 down(g(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(x0))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(x0))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 f_flat(up(x0)) 543.78/241.97 g_flat(up(x0)) 543.78/241.97 543.78/241.97 We have to consider all minimal (P,Q,R)-chains. 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (819) TransformationProof (EQUIVALENT) 543.78/241.97 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.97 543.78/241.97 (TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))),TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.78/241.97 543.78/241.97 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (820) 543.78/241.97 Obligation: 543.78/241.97 Q DP problem: 543.78/241.97 The TRS P consists of the following rules: 543.78/241.97 543.78/241.97 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.97 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.97 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.97 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.97 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.97 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.97 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.97 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.97 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.97 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.97 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.97 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.97 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.97 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.97 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.97 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.97 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.97 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.97 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.97 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.97 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.97 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.97 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.97 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.97 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.97 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.97 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.78/241.97 543.78/241.97 The TRS R consists of the following rules: 543.78/241.97 543.78/241.97 down(a) -> up(f(a)) 543.78/241.97 down(b) -> up(g(b)) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.97 down(f(a)) -> f_flat(down(a)) 543.78/241.97 down(f(b)) -> f_flat(down(b)) 543.78/241.97 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.97 down(f(c)) -> f_flat(down(c)) 543.78/241.97 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.97 down(g(a)) -> g_flat(down(a)) 543.78/241.97 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.97 down(g(b)) -> g_flat(down(b)) 543.78/241.97 down(g(c)) -> g_flat(down(c)) 543.78/241.97 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.97 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.97 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.97 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.97 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.97 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.97 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.97 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.97 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.97 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.97 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.97 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.97 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.97 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.97 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.97 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.97 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.97 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.97 543.78/241.97 The set Q consists of the following terms: 543.78/241.97 543.78/241.97 down(a) 543.78/241.97 down(b) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.97 down(f(a)) 543.78/241.97 down(f(b)) 543.78/241.97 down(f(g(x0))) 543.78/241.97 down(f(c)) 543.78/241.97 down(f(fresh_constant)) 543.78/241.97 down(g(a)) 543.78/241.97 down(g(f(x0))) 543.78/241.97 down(g(b)) 543.78/241.97 down(g(c)) 543.78/241.97 down(g(fresh_constant)) 543.78/241.97 down(f(f(a))) 543.78/241.97 down(f(f(b))) 543.78/241.97 down(f(f(g(x0)))) 543.78/241.97 down(f(f(c))) 543.78/241.97 down(f(f(fresh_constant))) 543.78/241.97 down(g(g(a))) 543.78/241.97 down(g(g(f(x0)))) 543.78/241.97 down(g(g(b))) 543.78/241.97 down(g(g(c))) 543.78/241.97 down(g(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) 543.78/241.97 down(f(f(f(g(x0))))) 543.78/241.97 down(f(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) 543.78/241.97 down(g(g(g(f(x0))))) 543.78/241.97 down(g(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(x0)))))) 543.78/241.97 down(f(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) 543.78/241.97 down(g(g(g(g(a))))) 543.78/241.97 down(g(g(g(g(f(x0)))))) 543.78/241.97 down(g(g(g(g(b))))) 543.78/241.97 down(g(g(g(g(c))))) 543.78/241.97 down(g(g(g(g(fresh_constant))))) 543.78/241.97 down(f(f(f(f(f(a)))))) 543.78/241.97 down(f(f(f(f(f(b)))))) 543.78/241.97 down(f(f(f(f(f(g(x0))))))) 543.78/241.97 down(f(f(f(f(f(c)))))) 543.78/241.97 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.97 down(g(g(g(g(g(a)))))) 543.78/241.97 down(g(g(g(g(g(f(x0))))))) 543.78/241.97 down(g(g(g(g(g(b)))))) 543.78/241.97 down(g(g(g(g(g(c)))))) 543.78/241.97 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.97 down(f(f(f(f(f(f(a))))))) 543.78/241.97 down(f(f(f(f(f(f(b))))))) 543.78/241.97 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.97 down(f(f(f(f(f(f(c))))))) 543.78/241.97 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.97 down(g(g(g(g(g(g(a))))))) 543.78/241.97 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.97 down(g(g(g(g(g(g(b))))))) 543.78/241.97 down(g(g(g(g(g(g(c))))))) 543.78/241.97 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.97 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.97 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.97 f_flat(up(x0)) 543.78/241.97 g_flat(up(x0)) 543.78/241.97 543.78/241.97 We have to consider all minimal (P,Q,R)-chains. 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (821) TransformationProof (EQUIVALENT) 543.78/241.97 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(a))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.97 543.78/241.97 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a)))))))))))) 543.78/241.97 543.78/241.97 543.78/241.97 ---------------------------------------- 543.78/241.97 543.78/241.97 (822) 543.78/241.97 Obligation: 543.78/241.97 Q DP problem: 543.78/241.97 The TRS P consists of the following rules: 543.78/241.97 543.78/241.97 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.97 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.97 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.97 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.97 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.97 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.97 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.97 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.97 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.97 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.97 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.97 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.97 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.97 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.97 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.97 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.97 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.97 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.97 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.97 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.97 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.97 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.97 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.97 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.97 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.97 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.97 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.97 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.78/241.97 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.78/241.97 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.78/241.97 543.78/241.97 The TRS R consists of the following rules: 543.78/241.97 543.78/241.97 down(a) -> up(f(a)) 543.78/241.97 down(b) -> up(g(b)) 543.78/241.97 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.97 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.97 down(f(a)) -> f_flat(down(a)) 543.78/241.97 down(f(b)) -> f_flat(down(b)) 543.78/241.97 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.97 down(f(c)) -> f_flat(down(c)) 543.78/241.97 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.97 down(g(a)) -> g_flat(down(a)) 543.78/241.97 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.97 down(g(b)) -> g_flat(down(b)) 543.78/241.97 down(g(c)) -> g_flat(down(c)) 543.78/241.97 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.97 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.97 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.97 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.97 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.97 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.97 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.97 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.97 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.97 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.97 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.97 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.97 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.97 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.97 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.97 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.97 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.97 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.97 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.97 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.97 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.97 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.97 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.97 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.97 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.97 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.98 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.98 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.98 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.98 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.98 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.98 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.98 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.98 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.98 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.98 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.98 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.98 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.98 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.98 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.98 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.98 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.98 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.98 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.98 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.98 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.98 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.98 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.98 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.98 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.98 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.98 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.98 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.98 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.98 543.78/241.98 The set Q consists of the following terms: 543.78/241.98 543.78/241.98 down(a) 543.78/241.98 down(b) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.98 down(f(a)) 543.78/241.98 down(f(b)) 543.78/241.98 down(f(g(x0))) 543.78/241.98 down(f(c)) 543.78/241.98 down(f(fresh_constant)) 543.78/241.98 down(g(a)) 543.78/241.98 down(g(f(x0))) 543.78/241.98 down(g(b)) 543.78/241.98 down(g(c)) 543.78/241.98 down(g(fresh_constant)) 543.78/241.98 down(f(f(a))) 543.78/241.98 down(f(f(b))) 543.78/241.98 down(f(f(g(x0)))) 543.78/241.98 down(f(f(c))) 543.78/241.98 down(f(f(fresh_constant))) 543.78/241.98 down(g(g(a))) 543.78/241.98 down(g(g(f(x0)))) 543.78/241.98 down(g(g(b))) 543.78/241.98 down(g(g(c))) 543.78/241.98 down(g(g(fresh_constant))) 543.78/241.98 down(f(f(f(a)))) 543.78/241.98 down(f(f(f(b)))) 543.78/241.98 down(f(f(f(g(x0))))) 543.78/241.98 down(f(f(f(c)))) 543.78/241.98 down(f(f(f(fresh_constant)))) 543.78/241.98 down(g(g(g(a)))) 543.78/241.98 down(g(g(g(f(x0))))) 543.78/241.98 down(g(g(g(b)))) 543.78/241.98 down(g(g(g(c)))) 543.78/241.98 down(g(g(g(fresh_constant)))) 543.78/241.98 down(f(f(f(f(a))))) 543.78/241.98 down(f(f(f(f(b))))) 543.78/241.98 down(f(f(f(f(g(x0)))))) 543.78/241.98 down(f(f(f(f(c))))) 543.78/241.98 down(f(f(f(f(fresh_constant))))) 543.78/241.98 down(g(g(g(g(a))))) 543.78/241.98 down(g(g(g(g(f(x0)))))) 543.78/241.98 down(g(g(g(g(b))))) 543.78/241.98 down(g(g(g(g(c))))) 543.78/241.98 down(g(g(g(g(fresh_constant))))) 543.78/241.98 down(f(f(f(f(f(a)))))) 543.78/241.98 down(f(f(f(f(f(b)))))) 543.78/241.98 down(f(f(f(f(f(g(x0))))))) 543.78/241.98 down(f(f(f(f(f(c)))))) 543.78/241.98 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.98 down(g(g(g(g(g(a)))))) 543.78/241.98 down(g(g(g(g(g(f(x0))))))) 543.78/241.98 down(g(g(g(g(g(b)))))) 543.78/241.98 down(g(g(g(g(g(c)))))) 543.78/241.98 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.98 down(f(f(f(f(f(f(a))))))) 543.78/241.98 down(f(f(f(f(f(f(b))))))) 543.78/241.98 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.98 down(f(f(f(f(f(f(c))))))) 543.78/241.98 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.98 down(g(g(g(g(g(g(a))))))) 543.78/241.98 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.98 down(g(g(g(g(g(g(b))))))) 543.78/241.98 down(g(g(g(g(g(g(c))))))) 543.78/241.98 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.98 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.98 f_flat(up(x0)) 543.78/241.98 g_flat(up(x0)) 543.78/241.98 543.78/241.98 We have to consider all minimal (P,Q,R)-chains. 543.78/241.98 ---------------------------------------- 543.78/241.98 543.78/241.98 (823) TransformationProof (EQUIVALENT) 543.78/241.98 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(f(x0)))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.98 543.78/241.98 (TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0))))))))))))) 543.78/241.98 543.78/241.98 543.78/241.98 ---------------------------------------- 543.78/241.98 543.78/241.98 (824) 543.78/241.98 Obligation: 543.78/241.98 Q DP problem: 543.78/241.98 The TRS P consists of the following rules: 543.78/241.98 543.78/241.98 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.98 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.98 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.98 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.98 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.98 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.98 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.98 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.98 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.98 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.98 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.98 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.98 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.98 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.98 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.98 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.98 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.98 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.98 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.98 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.98 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.98 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.98 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.98 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.98 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.98 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.98 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.98 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.78/241.98 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.78/241.98 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.78/241.98 543.78/241.98 The TRS R consists of the following rules: 543.78/241.98 543.78/241.98 down(a) -> up(f(a)) 543.78/241.98 down(b) -> up(g(b)) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.78/241.98 down(f(a)) -> f_flat(down(a)) 543.78/241.98 down(f(b)) -> f_flat(down(b)) 543.78/241.98 down(f(g(y4))) -> f_flat(down(g(y4))) 543.78/241.98 down(f(c)) -> f_flat(down(c)) 543.78/241.98 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.78/241.98 down(g(a)) -> g_flat(down(a)) 543.78/241.98 down(g(f(y6))) -> g_flat(down(f(y6))) 543.78/241.98 down(g(b)) -> g_flat(down(b)) 543.78/241.98 down(g(c)) -> g_flat(down(c)) 543.78/241.98 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.78/241.98 down(f(f(a))) -> f_flat(down(f(a))) 543.78/241.98 down(f(f(b))) -> f_flat(down(f(b))) 543.78/241.98 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.78/241.98 down(f(f(c))) -> f_flat(down(f(c))) 543.78/241.98 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.78/241.98 down(g(g(a))) -> g_flat(down(g(a))) 543.78/241.98 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.78/241.98 down(g(g(b))) -> g_flat(down(g(b))) 543.78/241.98 down(g(g(c))) -> g_flat(down(g(c))) 543.78/241.98 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.78/241.98 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.78/241.98 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.78/241.98 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.78/241.98 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.78/241.98 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.78/241.98 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.78/241.98 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.78/241.98 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.78/241.98 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.78/241.98 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.78/241.98 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.78/241.98 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.78/241.98 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.78/241.98 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.78/241.98 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.78/241.98 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.78/241.98 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.78/241.98 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.78/241.98 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.78/241.98 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.78/241.98 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.78/241.98 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.78/241.98 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.78/241.98 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.78/241.98 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.78/241.98 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.78/241.98 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.78/241.98 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.78/241.98 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.78/241.98 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.78/241.98 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.78/241.98 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.78/241.98 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.78/241.98 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.78/241.98 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.78/241.98 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.78/241.98 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.78/241.98 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.78/241.98 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.78/241.98 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.78/241.98 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.98 g_flat(up(x_1)) -> up(g(x_1)) 543.78/241.98 f_flat(up(x_1)) -> up(f(x_1)) 543.78/241.98 543.78/241.98 The set Q consists of the following terms: 543.78/241.98 543.78/241.98 down(a) 543.78/241.98 down(b) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.78/241.98 down(f(a)) 543.78/241.98 down(f(b)) 543.78/241.98 down(f(g(x0))) 543.78/241.98 down(f(c)) 543.78/241.98 down(f(fresh_constant)) 543.78/241.98 down(g(a)) 543.78/241.98 down(g(f(x0))) 543.78/241.98 down(g(b)) 543.78/241.98 down(g(c)) 543.78/241.98 down(g(fresh_constant)) 543.78/241.98 down(f(f(a))) 543.78/241.98 down(f(f(b))) 543.78/241.98 down(f(f(g(x0)))) 543.78/241.98 down(f(f(c))) 543.78/241.98 down(f(f(fresh_constant))) 543.78/241.98 down(g(g(a))) 543.78/241.98 down(g(g(f(x0)))) 543.78/241.98 down(g(g(b))) 543.78/241.98 down(g(g(c))) 543.78/241.98 down(g(g(fresh_constant))) 543.78/241.98 down(f(f(f(a)))) 543.78/241.98 down(f(f(f(b)))) 543.78/241.98 down(f(f(f(g(x0))))) 543.78/241.98 down(f(f(f(c)))) 543.78/241.98 down(f(f(f(fresh_constant)))) 543.78/241.98 down(g(g(g(a)))) 543.78/241.98 down(g(g(g(f(x0))))) 543.78/241.98 down(g(g(g(b)))) 543.78/241.98 down(g(g(g(c)))) 543.78/241.98 down(g(g(g(fresh_constant)))) 543.78/241.98 down(f(f(f(f(a))))) 543.78/241.98 down(f(f(f(f(b))))) 543.78/241.98 down(f(f(f(f(g(x0)))))) 543.78/241.98 down(f(f(f(f(c))))) 543.78/241.98 down(f(f(f(f(fresh_constant))))) 543.78/241.98 down(g(g(g(g(a))))) 543.78/241.98 down(g(g(g(g(f(x0)))))) 543.78/241.98 down(g(g(g(g(b))))) 543.78/241.98 down(g(g(g(g(c))))) 543.78/241.98 down(g(g(g(g(fresh_constant))))) 543.78/241.98 down(f(f(f(f(f(a)))))) 543.78/241.98 down(f(f(f(f(f(b)))))) 543.78/241.98 down(f(f(f(f(f(g(x0))))))) 543.78/241.98 down(f(f(f(f(f(c)))))) 543.78/241.98 down(f(f(f(f(f(fresh_constant)))))) 543.78/241.98 down(g(g(g(g(g(a)))))) 543.78/241.98 down(g(g(g(g(g(f(x0))))))) 543.78/241.98 down(g(g(g(g(g(b)))))) 543.78/241.98 down(g(g(g(g(g(c)))))) 543.78/241.98 down(g(g(g(g(g(fresh_constant)))))) 543.78/241.98 down(f(f(f(f(f(f(a))))))) 543.78/241.98 down(f(f(f(f(f(f(b))))))) 543.78/241.98 down(f(f(f(f(f(f(g(x0)))))))) 543.78/241.98 down(f(f(f(f(f(f(c))))))) 543.78/241.98 down(f(f(f(f(f(f(fresh_constant))))))) 543.78/241.98 down(g(g(g(g(g(g(a))))))) 543.78/241.98 down(g(g(g(g(g(g(f(x0)))))))) 543.78/241.98 down(g(g(g(g(g(g(b))))))) 543.78/241.98 down(g(g(g(g(g(g(c))))))) 543.78/241.98 down(g(g(g(g(g(g(fresh_constant))))))) 543.78/241.98 down(f(f(f(f(f(f(f(a)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(b)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(g(x0))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(c)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(a)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(f(x0))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(b)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(c)))))))) 543.78/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(a))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(b))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(c))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(a))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(b))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(c))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.78/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.78/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.78/241.98 f_flat(up(x0)) 543.78/241.98 g_flat(up(x0)) 543.78/241.98 543.78/241.98 We have to consider all minimal (P,Q,R)-chains. 543.78/241.98 ---------------------------------------- 543.78/241.98 543.78/241.98 (825) TransformationProof (EQUIVALENT) 543.78/241.98 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(c))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.78/241.98 543.78/241.98 (TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c)))))))))))) 543.78/241.98 543.78/241.98 543.78/241.98 ---------------------------------------- 543.78/241.98 543.78/241.98 (826) 543.78/241.98 Obligation: 543.78/241.98 Q DP problem: 543.78/241.98 The TRS P consists of the following rules: 543.78/241.98 543.78/241.98 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.78/241.98 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.78/241.98 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.78/241.98 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.78/241.98 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.78/241.98 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.78/241.98 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.78/241.98 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.78/241.98 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.78/241.98 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.78/241.98 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.78/241.98 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.78/241.98 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.78/241.98 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.78/241.98 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.78/241.98 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.78/241.98 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.78/241.98 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.78/241.98 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.78/241.98 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.78/241.98 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.78/241.98 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) 543.78/241.98 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.78/241.98 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.78/241.98 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.78/241.98 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.78/241.98 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.78/241.98 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.78/241.98 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.78/241.98 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.98 543.84/241.98 The TRS R consists of the following rules: 543.84/241.98 543.84/241.98 down(a) -> up(f(a)) 543.84/241.98 down(b) -> up(g(b)) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.98 down(f(a)) -> f_flat(down(a)) 543.84/241.98 down(f(b)) -> f_flat(down(b)) 543.84/241.98 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.98 down(f(c)) -> f_flat(down(c)) 543.84/241.98 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.98 down(g(a)) -> g_flat(down(a)) 543.84/241.98 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.98 down(g(b)) -> g_flat(down(b)) 543.84/241.98 down(g(c)) -> g_flat(down(c)) 543.84/241.98 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.98 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.98 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.98 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.98 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.98 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.98 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.98 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.98 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.98 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.98 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.98 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.98 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.98 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.98 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.98 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.98 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.98 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.98 543.84/241.98 The set Q consists of the following terms: 543.84/241.98 543.84/241.98 down(a) 543.84/241.98 down(b) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.98 down(f(a)) 543.84/241.98 down(f(b)) 543.84/241.98 down(f(g(x0))) 543.84/241.98 down(f(c)) 543.84/241.98 down(f(fresh_constant)) 543.84/241.98 down(g(a)) 543.84/241.98 down(g(f(x0))) 543.84/241.98 down(g(b)) 543.84/241.98 down(g(c)) 543.84/241.98 down(g(fresh_constant)) 543.84/241.98 down(f(f(a))) 543.84/241.98 down(f(f(b))) 543.84/241.98 down(f(f(g(x0)))) 543.84/241.98 down(f(f(c))) 543.84/241.98 down(f(f(fresh_constant))) 543.84/241.98 down(g(g(a))) 543.84/241.98 down(g(g(f(x0)))) 543.84/241.98 down(g(g(b))) 543.84/241.98 down(g(g(c))) 543.84/241.98 down(g(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) 543.84/241.98 down(f(f(f(g(x0))))) 543.84/241.98 down(f(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) 543.84/241.98 down(g(g(g(f(x0))))) 543.84/241.98 down(g(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(x0)))))) 543.84/241.98 down(f(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(x0)))))) 543.84/241.98 down(g(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(x0))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(x0))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 f_flat(up(x0)) 543.84/241.98 g_flat(up(x0)) 543.84/241.98 543.84/241.98 We have to consider all minimal (P,Q,R)-chains. 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (827) TransformationProof (EQUIVALENT) 543.84/241.98 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(f(fresh_constant))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.98 543.84/241.98 (TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant)))))))))))) 543.84/241.98 543.84/241.98 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (828) 543.84/241.98 Obligation: 543.84/241.98 Q DP problem: 543.84/241.98 The TRS P consists of the following rules: 543.84/241.98 543.84/241.98 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.98 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.98 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.98 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.98 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.98 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.98 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.98 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.98 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.98 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.98 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.98 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.98 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.98 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.98 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.98 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.98 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.98 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.98 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.98 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.98 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.98 TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) 543.84/241.98 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.84/241.98 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.84/241.98 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.84/241.98 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.98 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.98 543.84/241.98 The TRS R consists of the following rules: 543.84/241.98 543.84/241.98 down(a) -> up(f(a)) 543.84/241.98 down(b) -> up(g(b)) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.98 down(f(a)) -> f_flat(down(a)) 543.84/241.98 down(f(b)) -> f_flat(down(b)) 543.84/241.98 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.98 down(f(c)) -> f_flat(down(c)) 543.84/241.98 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.98 down(g(a)) -> g_flat(down(a)) 543.84/241.98 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.98 down(g(b)) -> g_flat(down(b)) 543.84/241.98 down(g(c)) -> g_flat(down(c)) 543.84/241.98 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.98 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.98 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.98 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.98 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.98 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.98 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.98 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.98 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.98 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.98 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.98 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.98 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.98 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.98 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.98 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.98 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.98 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.98 543.84/241.98 The set Q consists of the following terms: 543.84/241.98 543.84/241.98 down(a) 543.84/241.98 down(b) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.98 down(f(a)) 543.84/241.98 down(f(b)) 543.84/241.98 down(f(g(x0))) 543.84/241.98 down(f(c)) 543.84/241.98 down(f(fresh_constant)) 543.84/241.98 down(g(a)) 543.84/241.98 down(g(f(x0))) 543.84/241.98 down(g(b)) 543.84/241.98 down(g(c)) 543.84/241.98 down(g(fresh_constant)) 543.84/241.98 down(f(f(a))) 543.84/241.98 down(f(f(b))) 543.84/241.98 down(f(f(g(x0)))) 543.84/241.98 down(f(f(c))) 543.84/241.98 down(f(f(fresh_constant))) 543.84/241.98 down(g(g(a))) 543.84/241.98 down(g(g(f(x0)))) 543.84/241.98 down(g(g(b))) 543.84/241.98 down(g(g(c))) 543.84/241.98 down(g(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) 543.84/241.98 down(f(f(f(g(x0))))) 543.84/241.98 down(f(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) 543.84/241.98 down(g(g(g(f(x0))))) 543.84/241.98 down(g(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(x0)))))) 543.84/241.98 down(f(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(x0)))))) 543.84/241.98 down(g(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(x0))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(x0))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 f_flat(up(x0)) 543.84/241.98 g_flat(up(x0)) 543.84/241.98 543.84/241.98 We have to consider all minimal (P,Q,R)-chains. 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (829) TransformationProof (EQUIVALENT) 543.84/241.98 By rewriting [LPAR04] the rule TOP(up(f(f(f(b))))) -> TOP(f_flat(up(f(f(g(b)))))) at position [0] we obtained the following new rules [LPAR04]: 543.84/241.98 543.84/241.98 (TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))),TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b))))))) 543.84/241.98 543.84/241.98 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (830) 543.84/241.98 Obligation: 543.84/241.98 Q DP problem: 543.84/241.98 The TRS P consists of the following rules: 543.84/241.98 543.84/241.98 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.98 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.98 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.98 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.98 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.98 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.98 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.98 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.98 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.98 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.98 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.98 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.98 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.98 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.98 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.98 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.98 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.98 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.98 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.98 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.98 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.98 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) 543.84/241.98 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.84/241.98 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.84/241.98 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.98 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.98 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.98 543.84/241.98 The TRS R consists of the following rules: 543.84/241.98 543.84/241.98 down(a) -> up(f(a)) 543.84/241.98 down(b) -> up(g(b)) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.98 down(f(a)) -> f_flat(down(a)) 543.84/241.98 down(f(b)) -> f_flat(down(b)) 543.84/241.98 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.98 down(f(c)) -> f_flat(down(c)) 543.84/241.98 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.98 down(g(a)) -> g_flat(down(a)) 543.84/241.98 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.98 down(g(b)) -> g_flat(down(b)) 543.84/241.98 down(g(c)) -> g_flat(down(c)) 543.84/241.98 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.98 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.98 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.98 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.98 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.98 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.98 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.98 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.98 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.98 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.98 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.98 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.98 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.98 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.98 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.98 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.98 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.98 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.98 543.84/241.98 The set Q consists of the following terms: 543.84/241.98 543.84/241.98 down(a) 543.84/241.98 down(b) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.98 down(f(a)) 543.84/241.98 down(f(b)) 543.84/241.98 down(f(g(x0))) 543.84/241.98 down(f(c)) 543.84/241.98 down(f(fresh_constant)) 543.84/241.98 down(g(a)) 543.84/241.98 down(g(f(x0))) 543.84/241.98 down(g(b)) 543.84/241.98 down(g(c)) 543.84/241.98 down(g(fresh_constant)) 543.84/241.98 down(f(f(a))) 543.84/241.98 down(f(f(b))) 543.84/241.98 down(f(f(g(x0)))) 543.84/241.98 down(f(f(c))) 543.84/241.98 down(f(f(fresh_constant))) 543.84/241.98 down(g(g(a))) 543.84/241.98 down(g(g(f(x0)))) 543.84/241.98 down(g(g(b))) 543.84/241.98 down(g(g(c))) 543.84/241.98 down(g(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) 543.84/241.98 down(f(f(f(g(x0))))) 543.84/241.98 down(f(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) 543.84/241.98 down(g(g(g(f(x0))))) 543.84/241.98 down(g(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(x0)))))) 543.84/241.98 down(f(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(x0)))))) 543.84/241.98 down(g(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(x0))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(x0))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 f_flat(up(x0)) 543.84/241.98 g_flat(up(x0)) 543.84/241.98 543.84/241.98 We have to consider all minimal (P,Q,R)-chains. 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (831) TransformationProof (EQUIVALENT) 543.84/241.98 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(f_flat(up(f(g(b))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.98 543.84/241.98 (TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))),TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b)))))))) 543.84/241.98 543.84/241.98 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (832) 543.84/241.98 Obligation: 543.84/241.98 Q DP problem: 543.84/241.98 The TRS P consists of the following rules: 543.84/241.98 543.84/241.98 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.98 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.98 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.98 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.98 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.98 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.98 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.98 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.98 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.98 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.98 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.98 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.98 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.98 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.98 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.98 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.98 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.98 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.98 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.98 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.98 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.84/241.98 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.84/241.98 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.98 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.98 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.98 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.98 543.84/241.98 The TRS R consists of the following rules: 543.84/241.98 543.84/241.98 down(a) -> up(f(a)) 543.84/241.98 down(b) -> up(g(b)) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.98 down(f(a)) -> f_flat(down(a)) 543.84/241.98 down(f(b)) -> f_flat(down(b)) 543.84/241.98 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.98 down(f(c)) -> f_flat(down(c)) 543.84/241.98 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.98 down(g(a)) -> g_flat(down(a)) 543.84/241.98 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.98 down(g(b)) -> g_flat(down(b)) 543.84/241.98 down(g(c)) -> g_flat(down(c)) 543.84/241.98 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.98 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.98 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.98 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.98 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.98 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.98 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.98 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.98 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.98 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.98 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.98 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.98 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.98 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.98 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.98 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.98 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.98 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.98 543.84/241.98 The set Q consists of the following terms: 543.84/241.98 543.84/241.98 down(a) 543.84/241.98 down(b) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.98 down(f(a)) 543.84/241.98 down(f(b)) 543.84/241.98 down(f(g(x0))) 543.84/241.98 down(f(c)) 543.84/241.98 down(f(fresh_constant)) 543.84/241.98 down(g(a)) 543.84/241.98 down(g(f(x0))) 543.84/241.98 down(g(b)) 543.84/241.98 down(g(c)) 543.84/241.98 down(g(fresh_constant)) 543.84/241.98 down(f(f(a))) 543.84/241.98 down(f(f(b))) 543.84/241.98 down(f(f(g(x0)))) 543.84/241.98 down(f(f(c))) 543.84/241.98 down(f(f(fresh_constant))) 543.84/241.98 down(g(g(a))) 543.84/241.98 down(g(g(f(x0)))) 543.84/241.98 down(g(g(b))) 543.84/241.98 down(g(g(c))) 543.84/241.98 down(g(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) 543.84/241.98 down(f(f(f(g(x0))))) 543.84/241.98 down(f(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) 543.84/241.98 down(g(g(g(f(x0))))) 543.84/241.98 down(g(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(x0)))))) 543.84/241.98 down(f(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(x0)))))) 543.84/241.98 down(g(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(x0))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(x0))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 f_flat(up(x0)) 543.84/241.98 g_flat(up(x0)) 543.84/241.98 543.84/241.98 We have to consider all minimal (P,Q,R)-chains. 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (833) TransformationProof (EQUIVALENT) 543.84/241.98 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.98 543.84/241.98 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.84/241.98 543.84/241.98 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (834) 543.84/241.98 Obligation: 543.84/241.98 Q DP problem: 543.84/241.98 The TRS P consists of the following rules: 543.84/241.98 543.84/241.98 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.98 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.98 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.98 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.98 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.98 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.98 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.98 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.98 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.98 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.98 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.98 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.98 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.98 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.98 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.98 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.98 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.98 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.98 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.98 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.98 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.84/241.98 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.84/241.98 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.98 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.98 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.98 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.98 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/241.98 543.84/241.98 The TRS R consists of the following rules: 543.84/241.98 543.84/241.98 down(a) -> up(f(a)) 543.84/241.98 down(b) -> up(g(b)) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.98 down(f(a)) -> f_flat(down(a)) 543.84/241.98 down(f(b)) -> f_flat(down(b)) 543.84/241.98 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.98 down(f(c)) -> f_flat(down(c)) 543.84/241.98 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.98 down(g(a)) -> g_flat(down(a)) 543.84/241.98 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.98 down(g(b)) -> g_flat(down(b)) 543.84/241.98 down(g(c)) -> g_flat(down(c)) 543.84/241.98 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.98 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.98 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.98 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.98 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.98 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.98 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.98 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.98 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.98 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.98 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.98 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.98 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.98 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.98 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.98 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.98 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.98 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.98 543.84/241.98 The set Q consists of the following terms: 543.84/241.98 543.84/241.98 down(a) 543.84/241.98 down(b) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.98 down(f(a)) 543.84/241.98 down(f(b)) 543.84/241.98 down(f(g(x0))) 543.84/241.98 down(f(c)) 543.84/241.98 down(f(fresh_constant)) 543.84/241.98 down(g(a)) 543.84/241.98 down(g(f(x0))) 543.84/241.98 down(g(b)) 543.84/241.98 down(g(c)) 543.84/241.98 down(g(fresh_constant)) 543.84/241.98 down(f(f(a))) 543.84/241.98 down(f(f(b))) 543.84/241.98 down(f(f(g(x0)))) 543.84/241.98 down(f(f(c))) 543.84/241.98 down(f(f(fresh_constant))) 543.84/241.98 down(g(g(a))) 543.84/241.98 down(g(g(f(x0)))) 543.84/241.98 down(g(g(b))) 543.84/241.98 down(g(g(c))) 543.84/241.98 down(g(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) 543.84/241.98 down(f(f(f(g(x0))))) 543.84/241.98 down(f(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) 543.84/241.98 down(g(g(g(f(x0))))) 543.84/241.98 down(g(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(x0)))))) 543.84/241.98 down(f(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(x0)))))) 543.84/241.98 down(g(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(x0))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(x0))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 f_flat(up(x0)) 543.84/241.98 g_flat(up(x0)) 543.84/241.98 543.84/241.98 We have to consider all minimal (P,Q,R)-chains. 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (835) TransformationProof (EQUIVALENT) 543.84/241.98 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.98 543.84/241.98 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.84/241.98 543.84/241.98 543.84/241.98 ---------------------------------------- 543.84/241.98 543.84/241.98 (836) 543.84/241.98 Obligation: 543.84/241.98 Q DP problem: 543.84/241.98 The TRS P consists of the following rules: 543.84/241.98 543.84/241.98 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.98 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.98 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.98 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.98 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.98 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.98 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.98 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.98 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.98 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.98 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.98 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.98 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.98 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.98 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.98 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.98 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.98 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.98 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.98 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.98 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.84/241.98 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.84/241.98 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.98 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.98 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.98 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.98 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.98 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/241.98 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/241.98 543.84/241.98 The TRS R consists of the following rules: 543.84/241.98 543.84/241.98 down(a) -> up(f(a)) 543.84/241.98 down(b) -> up(g(b)) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.98 down(f(a)) -> f_flat(down(a)) 543.84/241.98 down(f(b)) -> f_flat(down(b)) 543.84/241.98 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.98 down(f(c)) -> f_flat(down(c)) 543.84/241.98 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.98 down(g(a)) -> g_flat(down(a)) 543.84/241.98 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.98 down(g(b)) -> g_flat(down(b)) 543.84/241.98 down(g(c)) -> g_flat(down(c)) 543.84/241.98 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.98 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.98 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.98 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.98 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.98 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.98 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.98 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.98 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.98 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.98 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.98 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.98 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.98 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.98 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.98 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.98 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.98 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.98 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.98 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.98 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.98 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.98 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.98 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.98 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.98 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.98 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.98 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.98 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.98 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.98 543.84/241.98 The set Q consists of the following terms: 543.84/241.98 543.84/241.98 down(a) 543.84/241.98 down(b) 543.84/241.98 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.98 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.98 down(f(a)) 543.84/241.98 down(f(b)) 543.84/241.98 down(f(g(x0))) 543.84/241.98 down(f(c)) 543.84/241.98 down(f(fresh_constant)) 543.84/241.98 down(g(a)) 543.84/241.98 down(g(f(x0))) 543.84/241.98 down(g(b)) 543.84/241.98 down(g(c)) 543.84/241.98 down(g(fresh_constant)) 543.84/241.98 down(f(f(a))) 543.84/241.98 down(f(f(b))) 543.84/241.98 down(f(f(g(x0)))) 543.84/241.98 down(f(f(c))) 543.84/241.98 down(f(f(fresh_constant))) 543.84/241.98 down(g(g(a))) 543.84/241.98 down(g(g(f(x0)))) 543.84/241.98 down(g(g(b))) 543.84/241.98 down(g(g(c))) 543.84/241.98 down(g(g(fresh_constant))) 543.84/241.98 down(f(f(f(a)))) 543.84/241.98 down(f(f(f(b)))) 543.84/241.98 down(f(f(f(g(x0))))) 543.84/241.98 down(f(f(f(c)))) 543.84/241.98 down(f(f(f(fresh_constant)))) 543.84/241.98 down(g(g(g(a)))) 543.84/241.98 down(g(g(g(f(x0))))) 543.84/241.98 down(g(g(g(b)))) 543.84/241.98 down(g(g(g(c)))) 543.84/241.98 down(g(g(g(fresh_constant)))) 543.84/241.98 down(f(f(f(f(a))))) 543.84/241.98 down(f(f(f(f(b))))) 543.84/241.98 down(f(f(f(f(g(x0)))))) 543.84/241.98 down(f(f(f(f(c))))) 543.84/241.98 down(f(f(f(f(fresh_constant))))) 543.84/241.98 down(g(g(g(g(a))))) 543.84/241.98 down(g(g(g(g(f(x0)))))) 543.84/241.98 down(g(g(g(g(b))))) 543.84/241.98 down(g(g(g(g(c))))) 543.84/241.98 down(g(g(g(g(fresh_constant))))) 543.84/241.98 down(f(f(f(f(f(a)))))) 543.84/241.98 down(f(f(f(f(f(b)))))) 543.84/241.98 down(f(f(f(f(f(g(x0))))))) 543.84/241.98 down(f(f(f(f(f(c)))))) 543.84/241.98 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.98 down(g(g(g(g(g(a)))))) 543.84/241.98 down(g(g(g(g(g(f(x0))))))) 543.84/241.98 down(g(g(g(g(g(b)))))) 543.84/241.98 down(g(g(g(g(g(c)))))) 543.84/241.98 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.98 down(f(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 f_flat(up(x0)) 543.84/241.99 g_flat(up(x0)) 543.84/241.99 543.84/241.99 We have to consider all minimal (P,Q,R)-chains. 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (837) TransformationProof (EQUIVALENT) 543.84/241.99 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.99 543.84/241.99 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.84/241.99 543.84/241.99 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (838) 543.84/241.99 Obligation: 543.84/241.99 Q DP problem: 543.84/241.99 The TRS P consists of the following rules: 543.84/241.99 543.84/241.99 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.99 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.99 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.99 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.99 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.99 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.99 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.99 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.99 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.99 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.99 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.99 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.99 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.99 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.99 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.99 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.99 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.99 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.99 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.99 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.99 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.84/241.99 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.84/241.99 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.99 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.99 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.99 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.99 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/241.99 543.84/241.99 The TRS R consists of the following rules: 543.84/241.99 543.84/241.99 down(a) -> up(f(a)) 543.84/241.99 down(b) -> up(g(b)) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.99 down(f(a)) -> f_flat(down(a)) 543.84/241.99 down(f(b)) -> f_flat(down(b)) 543.84/241.99 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.99 down(f(c)) -> f_flat(down(c)) 543.84/241.99 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.99 down(g(a)) -> g_flat(down(a)) 543.84/241.99 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.99 down(g(b)) -> g_flat(down(b)) 543.84/241.99 down(g(c)) -> g_flat(down(c)) 543.84/241.99 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.99 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.99 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.99 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.99 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.99 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.99 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.99 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.99 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.99 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.99 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.99 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.99 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.99 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.99 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.99 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.99 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.99 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.99 543.84/241.99 The set Q consists of the following terms: 543.84/241.99 543.84/241.99 down(a) 543.84/241.99 down(b) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.99 down(f(a)) 543.84/241.99 down(f(b)) 543.84/241.99 down(f(g(x0))) 543.84/241.99 down(f(c)) 543.84/241.99 down(f(fresh_constant)) 543.84/241.99 down(g(a)) 543.84/241.99 down(g(f(x0))) 543.84/241.99 down(g(b)) 543.84/241.99 down(g(c)) 543.84/241.99 down(g(fresh_constant)) 543.84/241.99 down(f(f(a))) 543.84/241.99 down(f(f(b))) 543.84/241.99 down(f(f(g(x0)))) 543.84/241.99 down(f(f(c))) 543.84/241.99 down(f(f(fresh_constant))) 543.84/241.99 down(g(g(a))) 543.84/241.99 down(g(g(f(x0)))) 543.84/241.99 down(g(g(b))) 543.84/241.99 down(g(g(c))) 543.84/241.99 down(g(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) 543.84/241.99 down(f(f(f(g(x0))))) 543.84/241.99 down(f(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) 543.84/241.99 down(g(g(g(f(x0))))) 543.84/241.99 down(g(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(x0)))))) 543.84/241.99 down(f(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(x0)))))) 543.84/241.99 down(g(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(x0))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(x0))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 f_flat(up(x0)) 543.84/241.99 g_flat(up(x0)) 543.84/241.99 543.84/241.99 We have to consider all minimal (P,Q,R)-chains. 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (839) TransformationProof (EQUIVALENT) 543.84/241.99 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(b))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.99 543.84/241.99 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b)))))))))))) 543.84/241.99 543.84/241.99 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (840) 543.84/241.99 Obligation: 543.84/241.99 Q DP problem: 543.84/241.99 The TRS P consists of the following rules: 543.84/241.99 543.84/241.99 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.99 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.99 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.99 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.99 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.99 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.99 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.99 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.99 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.99 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.99 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.99 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.99 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.99 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.99 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.99 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.99 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.99 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.99 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.99 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.99 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.84/241.99 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.84/241.99 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.99 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.99 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.99 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.99 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/241.99 543.84/241.99 The TRS R consists of the following rules: 543.84/241.99 543.84/241.99 down(a) -> up(f(a)) 543.84/241.99 down(b) -> up(g(b)) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.99 down(f(a)) -> f_flat(down(a)) 543.84/241.99 down(f(b)) -> f_flat(down(b)) 543.84/241.99 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.99 down(f(c)) -> f_flat(down(c)) 543.84/241.99 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.99 down(g(a)) -> g_flat(down(a)) 543.84/241.99 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.99 down(g(b)) -> g_flat(down(b)) 543.84/241.99 down(g(c)) -> g_flat(down(c)) 543.84/241.99 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.99 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.99 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.99 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.99 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.99 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.99 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.99 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.99 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.99 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.99 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.99 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.99 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.99 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.99 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.99 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.99 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.99 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.99 543.84/241.99 The set Q consists of the following terms: 543.84/241.99 543.84/241.99 down(a) 543.84/241.99 down(b) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.99 down(f(a)) 543.84/241.99 down(f(b)) 543.84/241.99 down(f(g(x0))) 543.84/241.99 down(f(c)) 543.84/241.99 down(f(fresh_constant)) 543.84/241.99 down(g(a)) 543.84/241.99 down(g(f(x0))) 543.84/241.99 down(g(b)) 543.84/241.99 down(g(c)) 543.84/241.99 down(g(fresh_constant)) 543.84/241.99 down(f(f(a))) 543.84/241.99 down(f(f(b))) 543.84/241.99 down(f(f(g(x0)))) 543.84/241.99 down(f(f(c))) 543.84/241.99 down(f(f(fresh_constant))) 543.84/241.99 down(g(g(a))) 543.84/241.99 down(g(g(f(x0)))) 543.84/241.99 down(g(g(b))) 543.84/241.99 down(g(g(c))) 543.84/241.99 down(g(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) 543.84/241.99 down(f(f(f(g(x0))))) 543.84/241.99 down(f(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) 543.84/241.99 down(g(g(g(f(x0))))) 543.84/241.99 down(g(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(x0)))))) 543.84/241.99 down(f(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(x0)))))) 543.84/241.99 down(g(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(x0))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(x0))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 f_flat(up(x0)) 543.84/241.99 g_flat(up(x0)) 543.84/241.99 543.84/241.99 We have to consider all minimal (P,Q,R)-chains. 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (841) TransformationProof (EQUIVALENT) 543.84/241.99 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(c))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.99 543.84/241.99 (TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c)))))))))))) 543.84/241.99 543.84/241.99 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (842) 543.84/241.99 Obligation: 543.84/241.99 Q DP problem: 543.84/241.99 The TRS P consists of the following rules: 543.84/241.99 543.84/241.99 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.99 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.99 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.99 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.99 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.99 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.99 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.99 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.99 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.99 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.99 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.99 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.99 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.99 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.99 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.99 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.99 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.99 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.99 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.99 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.99 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) 543.84/241.99 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.84/241.99 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.99 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.99 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.99 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.99 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/241.99 543.84/241.99 The TRS R consists of the following rules: 543.84/241.99 543.84/241.99 down(a) -> up(f(a)) 543.84/241.99 down(b) -> up(g(b)) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.99 down(f(a)) -> f_flat(down(a)) 543.84/241.99 down(f(b)) -> f_flat(down(b)) 543.84/241.99 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.99 down(f(c)) -> f_flat(down(c)) 543.84/241.99 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.99 down(g(a)) -> g_flat(down(a)) 543.84/241.99 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.99 down(g(b)) -> g_flat(down(b)) 543.84/241.99 down(g(c)) -> g_flat(down(c)) 543.84/241.99 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.99 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.99 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.99 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.99 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.99 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.99 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.99 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.99 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.99 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.99 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.99 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.99 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.99 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.99 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.99 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.99 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.99 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.99 543.84/241.99 The set Q consists of the following terms: 543.84/241.99 543.84/241.99 down(a) 543.84/241.99 down(b) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.99 down(f(a)) 543.84/241.99 down(f(b)) 543.84/241.99 down(f(g(x0))) 543.84/241.99 down(f(c)) 543.84/241.99 down(f(fresh_constant)) 543.84/241.99 down(g(a)) 543.84/241.99 down(g(f(x0))) 543.84/241.99 down(g(b)) 543.84/241.99 down(g(c)) 543.84/241.99 down(g(fresh_constant)) 543.84/241.99 down(f(f(a))) 543.84/241.99 down(f(f(b))) 543.84/241.99 down(f(f(g(x0)))) 543.84/241.99 down(f(f(c))) 543.84/241.99 down(f(f(fresh_constant))) 543.84/241.99 down(g(g(a))) 543.84/241.99 down(g(g(f(x0)))) 543.84/241.99 down(g(g(b))) 543.84/241.99 down(g(g(c))) 543.84/241.99 down(g(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) 543.84/241.99 down(f(f(f(g(x0))))) 543.84/241.99 down(f(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) 543.84/241.99 down(g(g(g(f(x0))))) 543.84/241.99 down(g(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(x0)))))) 543.84/241.99 down(f(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(x0)))))) 543.84/241.99 down(g(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(x0))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(x0))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 f_flat(up(x0)) 543.84/241.99 g_flat(up(x0)) 543.84/241.99 543.84/241.99 We have to consider all minimal (P,Q,R)-chains. 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (843) TransformationProof (EQUIVALENT) 543.84/241.99 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(g(fresh_constant))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.99 543.84/241.99 (TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant)))))))))))) 543.84/241.99 543.84/241.99 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (844) 543.84/241.99 Obligation: 543.84/241.99 Q DP problem: 543.84/241.99 The TRS P consists of the following rules: 543.84/241.99 543.84/241.99 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.99 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.99 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.99 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.99 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.99 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.99 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.99 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.99 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.99 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.99 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.99 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.99 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.99 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.99 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.99 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.99 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.99 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.99 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.99 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.99 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.99 TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) 543.84/241.99 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.99 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.99 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.99 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.99 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/241.99 543.84/241.99 The TRS R consists of the following rules: 543.84/241.99 543.84/241.99 down(a) -> up(f(a)) 543.84/241.99 down(b) -> up(g(b)) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.99 down(f(a)) -> f_flat(down(a)) 543.84/241.99 down(f(b)) -> f_flat(down(b)) 543.84/241.99 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.99 down(f(c)) -> f_flat(down(c)) 543.84/241.99 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.99 down(g(a)) -> g_flat(down(a)) 543.84/241.99 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.99 down(g(b)) -> g_flat(down(b)) 543.84/241.99 down(g(c)) -> g_flat(down(c)) 543.84/241.99 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.99 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.99 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.99 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.99 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.99 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.99 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.99 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.99 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.99 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.99 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.99 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.99 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.99 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.99 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.99 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.99 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.99 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.99 543.84/241.99 The set Q consists of the following terms: 543.84/241.99 543.84/241.99 down(a) 543.84/241.99 down(b) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.99 down(f(a)) 543.84/241.99 down(f(b)) 543.84/241.99 down(f(g(x0))) 543.84/241.99 down(f(c)) 543.84/241.99 down(f(fresh_constant)) 543.84/241.99 down(g(a)) 543.84/241.99 down(g(f(x0))) 543.84/241.99 down(g(b)) 543.84/241.99 down(g(c)) 543.84/241.99 down(g(fresh_constant)) 543.84/241.99 down(f(f(a))) 543.84/241.99 down(f(f(b))) 543.84/241.99 down(f(f(g(x0)))) 543.84/241.99 down(f(f(c))) 543.84/241.99 down(f(f(fresh_constant))) 543.84/241.99 down(g(g(a))) 543.84/241.99 down(g(g(f(x0)))) 543.84/241.99 down(g(g(b))) 543.84/241.99 down(g(g(c))) 543.84/241.99 down(g(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) 543.84/241.99 down(f(f(f(g(x0))))) 543.84/241.99 down(f(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) 543.84/241.99 down(g(g(g(f(x0))))) 543.84/241.99 down(g(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(x0)))))) 543.84/241.99 down(f(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(x0)))))) 543.84/241.99 down(g(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(x0))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(x0))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 f_flat(up(x0)) 543.84/241.99 g_flat(up(x0)) 543.84/241.99 543.84/241.99 We have to consider all minimal (P,Q,R)-chains. 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (845) TransformationProof (EQUIVALENT) 543.84/241.99 By rewriting [LPAR04] the rule TOP(up(g(g(g(a))))) -> TOP(g_flat(up(g(g(f(a)))))) at position [0] we obtained the following new rules [LPAR04]: 543.84/241.99 543.84/241.99 (TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))),TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a))))))) 543.84/241.99 543.84/241.99 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (846) 543.84/241.99 Obligation: 543.84/241.99 Q DP problem: 543.84/241.99 The TRS P consists of the following rules: 543.84/241.99 543.84/241.99 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.99 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.99 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.99 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.99 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.99 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.99 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.99 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.99 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.99 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.99 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.99 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.99 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.99 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.99 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.99 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.99 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.99 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.99 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.99 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.99 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.99 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) 543.84/241.99 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.99 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.99 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.99 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/241.99 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/241.99 543.84/241.99 The TRS R consists of the following rules: 543.84/241.99 543.84/241.99 down(a) -> up(f(a)) 543.84/241.99 down(b) -> up(g(b)) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.99 down(f(a)) -> f_flat(down(a)) 543.84/241.99 down(f(b)) -> f_flat(down(b)) 543.84/241.99 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.99 down(f(c)) -> f_flat(down(c)) 543.84/241.99 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.99 down(g(a)) -> g_flat(down(a)) 543.84/241.99 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.99 down(g(b)) -> g_flat(down(b)) 543.84/241.99 down(g(c)) -> g_flat(down(c)) 543.84/241.99 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.99 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.99 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.99 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.99 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.99 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.99 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.99 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.99 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.99 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.99 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.99 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.99 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.99 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.99 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.99 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.99 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.99 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.99 543.84/241.99 The set Q consists of the following terms: 543.84/241.99 543.84/241.99 down(a) 543.84/241.99 down(b) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.99 down(f(a)) 543.84/241.99 down(f(b)) 543.84/241.99 down(f(g(x0))) 543.84/241.99 down(f(c)) 543.84/241.99 down(f(fresh_constant)) 543.84/241.99 down(g(a)) 543.84/241.99 down(g(f(x0))) 543.84/241.99 down(g(b)) 543.84/241.99 down(g(c)) 543.84/241.99 down(g(fresh_constant)) 543.84/241.99 down(f(f(a))) 543.84/241.99 down(f(f(b))) 543.84/241.99 down(f(f(g(x0)))) 543.84/241.99 down(f(f(c))) 543.84/241.99 down(f(f(fresh_constant))) 543.84/241.99 down(g(g(a))) 543.84/241.99 down(g(g(f(x0)))) 543.84/241.99 down(g(g(b))) 543.84/241.99 down(g(g(c))) 543.84/241.99 down(g(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) 543.84/241.99 down(f(f(f(g(x0))))) 543.84/241.99 down(f(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) 543.84/241.99 down(g(g(g(f(x0))))) 543.84/241.99 down(g(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(x0)))))) 543.84/241.99 down(f(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(x0)))))) 543.84/241.99 down(g(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(x0))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(x0))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 f_flat(up(x0)) 543.84/241.99 g_flat(up(x0)) 543.84/241.99 543.84/241.99 We have to consider all minimal (P,Q,R)-chains. 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (847) TransformationProof (EQUIVALENT) 543.84/241.99 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(g_flat(up(g(f(a))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.99 543.84/241.99 (TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))),TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a)))))))) 543.84/241.99 543.84/241.99 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (848) 543.84/241.99 Obligation: 543.84/241.99 Q DP problem: 543.84/241.99 The TRS P consists of the following rules: 543.84/241.99 543.84/241.99 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.99 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.99 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.99 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.99 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.99 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.99 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.99 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.99 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.99 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.99 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.99 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.99 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.99 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.99 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.99 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.99 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.99 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.99 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.99 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.99 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.99 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.99 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.99 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/241.99 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/241.99 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/241.99 543.84/241.99 The TRS R consists of the following rules: 543.84/241.99 543.84/241.99 down(a) -> up(f(a)) 543.84/241.99 down(b) -> up(g(b)) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.99 down(f(a)) -> f_flat(down(a)) 543.84/241.99 down(f(b)) -> f_flat(down(b)) 543.84/241.99 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.99 down(f(c)) -> f_flat(down(c)) 543.84/241.99 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.99 down(g(a)) -> g_flat(down(a)) 543.84/241.99 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.99 down(g(b)) -> g_flat(down(b)) 543.84/241.99 down(g(c)) -> g_flat(down(c)) 543.84/241.99 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.99 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.99 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.99 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.99 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.99 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.99 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.99 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.99 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.99 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.99 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.99 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.99 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.99 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.99 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.99 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.99 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.99 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.99 543.84/241.99 The set Q consists of the following terms: 543.84/241.99 543.84/241.99 down(a) 543.84/241.99 down(b) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.99 down(f(a)) 543.84/241.99 down(f(b)) 543.84/241.99 down(f(g(x0))) 543.84/241.99 down(f(c)) 543.84/241.99 down(f(fresh_constant)) 543.84/241.99 down(g(a)) 543.84/241.99 down(g(f(x0))) 543.84/241.99 down(g(b)) 543.84/241.99 down(g(c)) 543.84/241.99 down(g(fresh_constant)) 543.84/241.99 down(f(f(a))) 543.84/241.99 down(f(f(b))) 543.84/241.99 down(f(f(g(x0)))) 543.84/241.99 down(f(f(c))) 543.84/241.99 down(f(f(fresh_constant))) 543.84/241.99 down(g(g(a))) 543.84/241.99 down(g(g(f(x0)))) 543.84/241.99 down(g(g(b))) 543.84/241.99 down(g(g(c))) 543.84/241.99 down(g(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) 543.84/241.99 down(f(f(f(g(x0))))) 543.84/241.99 down(f(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) 543.84/241.99 down(g(g(g(f(x0))))) 543.84/241.99 down(g(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(x0)))))) 543.84/241.99 down(f(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(x0)))))) 543.84/241.99 down(g(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(x0))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(x0))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 f_flat(up(x0)) 543.84/241.99 g_flat(up(x0)) 543.84/241.99 543.84/241.99 We have to consider all minimal (P,Q,R)-chains. 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (849) TransformationProof (EQUIVALENT) 543.84/241.99 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.99 543.84/241.99 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.84/241.99 543.84/241.99 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (850) 543.84/241.99 Obligation: 543.84/241.99 Q DP problem: 543.84/241.99 The TRS P consists of the following rules: 543.84/241.99 543.84/241.99 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.99 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.99 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.99 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.99 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.99 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.99 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.99 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/241.99 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/241.99 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/241.99 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/241.99 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/241.99 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/241.99 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/241.99 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/241.99 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/241.99 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/241.99 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/241.99 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/241.99 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/241.99 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/241.99 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/241.99 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/241.99 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/241.99 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/241.99 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/241.99 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/241.99 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/241.99 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/241.99 543.84/241.99 The TRS R consists of the following rules: 543.84/241.99 543.84/241.99 down(a) -> up(f(a)) 543.84/241.99 down(b) -> up(g(b)) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/241.99 down(f(a)) -> f_flat(down(a)) 543.84/241.99 down(f(b)) -> f_flat(down(b)) 543.84/241.99 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/241.99 down(f(c)) -> f_flat(down(c)) 543.84/241.99 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/241.99 down(g(a)) -> g_flat(down(a)) 543.84/241.99 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/241.99 down(g(b)) -> g_flat(down(b)) 543.84/241.99 down(g(c)) -> g_flat(down(c)) 543.84/241.99 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/241.99 down(f(f(a))) -> f_flat(down(f(a))) 543.84/241.99 down(f(f(b))) -> f_flat(down(f(b))) 543.84/241.99 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/241.99 down(f(f(c))) -> f_flat(down(f(c))) 543.84/241.99 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/241.99 down(g(g(a))) -> g_flat(down(g(a))) 543.84/241.99 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/241.99 down(g(g(b))) -> g_flat(down(g(b))) 543.84/241.99 down(g(g(c))) -> g_flat(down(g(c))) 543.84/241.99 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/241.99 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/241.99 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/241.99 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/241.99 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/241.99 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/241.99 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 g_flat(up(x_1)) -> up(g(x_1)) 543.84/241.99 f_flat(up(x_1)) -> up(f(x_1)) 543.84/241.99 543.84/241.99 The set Q consists of the following terms: 543.84/241.99 543.84/241.99 down(a) 543.84/241.99 down(b) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/241.99 down(f(a)) 543.84/241.99 down(f(b)) 543.84/241.99 down(f(g(x0))) 543.84/241.99 down(f(c)) 543.84/241.99 down(f(fresh_constant)) 543.84/241.99 down(g(a)) 543.84/241.99 down(g(f(x0))) 543.84/241.99 down(g(b)) 543.84/241.99 down(g(c)) 543.84/241.99 down(g(fresh_constant)) 543.84/241.99 down(f(f(a))) 543.84/241.99 down(f(f(b))) 543.84/241.99 down(f(f(g(x0)))) 543.84/241.99 down(f(f(c))) 543.84/241.99 down(f(f(fresh_constant))) 543.84/241.99 down(g(g(a))) 543.84/241.99 down(g(g(f(x0)))) 543.84/241.99 down(g(g(b))) 543.84/241.99 down(g(g(c))) 543.84/241.99 down(g(g(fresh_constant))) 543.84/241.99 down(f(f(f(a)))) 543.84/241.99 down(f(f(f(b)))) 543.84/241.99 down(f(f(f(g(x0))))) 543.84/241.99 down(f(f(f(c)))) 543.84/241.99 down(f(f(f(fresh_constant)))) 543.84/241.99 down(g(g(g(a)))) 543.84/241.99 down(g(g(g(f(x0))))) 543.84/241.99 down(g(g(g(b)))) 543.84/241.99 down(g(g(g(c)))) 543.84/241.99 down(g(g(g(fresh_constant)))) 543.84/241.99 down(f(f(f(f(a))))) 543.84/241.99 down(f(f(f(f(b))))) 543.84/241.99 down(f(f(f(f(g(x0)))))) 543.84/241.99 down(f(f(f(f(c))))) 543.84/241.99 down(f(f(f(f(fresh_constant))))) 543.84/241.99 down(g(g(g(g(a))))) 543.84/241.99 down(g(g(g(g(f(x0)))))) 543.84/241.99 down(g(g(g(g(b))))) 543.84/241.99 down(g(g(g(g(c))))) 543.84/241.99 down(g(g(g(g(fresh_constant))))) 543.84/241.99 down(f(f(f(f(f(a)))))) 543.84/241.99 down(f(f(f(f(f(b)))))) 543.84/241.99 down(f(f(f(f(f(g(x0))))))) 543.84/241.99 down(f(f(f(f(f(c)))))) 543.84/241.99 down(f(f(f(f(f(fresh_constant)))))) 543.84/241.99 down(g(g(g(g(g(a)))))) 543.84/241.99 down(g(g(g(g(g(f(x0))))))) 543.84/241.99 down(g(g(g(g(g(b)))))) 543.84/241.99 down(g(g(g(g(g(c)))))) 543.84/241.99 down(g(g(g(g(g(fresh_constant)))))) 543.84/241.99 down(f(f(f(f(f(f(a))))))) 543.84/241.99 down(f(f(f(f(f(f(b))))))) 543.84/241.99 down(f(f(f(f(f(f(g(x0)))))))) 543.84/241.99 down(f(f(f(f(f(f(c))))))) 543.84/241.99 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/241.99 down(g(g(g(g(g(g(a))))))) 543.84/241.99 down(g(g(g(g(g(g(f(x0)))))))) 543.84/241.99 down(g(g(g(g(g(g(b))))))) 543.84/241.99 down(g(g(g(g(g(g(c))))))) 543.84/241.99 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/241.99 down(f(f(f(f(f(f(f(a)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(b)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(c)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(a)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(b)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(c)))))))) 543.84/241.99 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/241.99 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/241.99 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/241.99 f_flat(up(x0)) 543.84/241.99 g_flat(up(x0)) 543.84/241.99 543.84/241.99 We have to consider all minimal (P,Q,R)-chains. 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (851) TransformationProof (EQUIVALENT) 543.84/241.99 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/241.99 543.84/241.99 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.84/241.99 543.84/241.99 543.84/241.99 ---------------------------------------- 543.84/241.99 543.84/241.99 (852) 543.84/241.99 Obligation: 543.84/241.99 Q DP problem: 543.84/241.99 The TRS P consists of the following rules: 543.84/241.99 543.84/241.99 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/241.99 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/241.99 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/241.99 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/241.99 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/241.99 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/241.99 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/241.99 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.00 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.00 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.00 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.00 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.00 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.00 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.00 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.00 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.00 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.00 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.00 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.00 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.00 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.00 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.00 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.00 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.00 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.00 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.00 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.00 543.84/242.00 The TRS R consists of the following rules: 543.84/242.00 543.84/242.00 down(a) -> up(f(a)) 543.84/242.00 down(b) -> up(g(b)) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.00 down(f(a)) -> f_flat(down(a)) 543.84/242.00 down(f(b)) -> f_flat(down(b)) 543.84/242.00 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.00 down(f(c)) -> f_flat(down(c)) 543.84/242.00 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.00 down(g(a)) -> g_flat(down(a)) 543.84/242.00 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.00 down(g(b)) -> g_flat(down(b)) 543.84/242.00 down(g(c)) -> g_flat(down(c)) 543.84/242.00 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.00 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.00 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.00 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.00 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.00 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.00 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.00 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.00 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.00 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.00 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.00 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.00 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.00 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.00 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.00 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.00 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.00 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.00 543.84/242.00 The set Q consists of the following terms: 543.84/242.00 543.84/242.00 down(a) 543.84/242.00 down(b) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.00 down(f(a)) 543.84/242.00 down(f(b)) 543.84/242.00 down(f(g(x0))) 543.84/242.00 down(f(c)) 543.84/242.00 down(f(fresh_constant)) 543.84/242.00 down(g(a)) 543.84/242.00 down(g(f(x0))) 543.84/242.00 down(g(b)) 543.84/242.00 down(g(c)) 543.84/242.00 down(g(fresh_constant)) 543.84/242.00 down(f(f(a))) 543.84/242.00 down(f(f(b))) 543.84/242.00 down(f(f(g(x0)))) 543.84/242.00 down(f(f(c))) 543.84/242.00 down(f(f(fresh_constant))) 543.84/242.00 down(g(g(a))) 543.84/242.00 down(g(g(f(x0)))) 543.84/242.00 down(g(g(b))) 543.84/242.00 down(g(g(c))) 543.84/242.00 down(g(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) 543.84/242.00 down(f(f(f(g(x0))))) 543.84/242.00 down(f(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) 543.84/242.00 down(g(g(g(f(x0))))) 543.84/242.00 down(g(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(x0)))))) 543.84/242.00 down(f(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(x0)))))) 543.84/242.00 down(g(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(x0))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(x0))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 f_flat(up(x0)) 543.84/242.00 g_flat(up(x0)) 543.84/242.00 543.84/242.00 We have to consider all minimal (P,Q,R)-chains. 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (853) TransformationProof (EQUIVALENT) 543.84/242.00 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.00 543.84/242.00 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.84/242.00 543.84/242.00 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (854) 543.84/242.00 Obligation: 543.84/242.00 Q DP problem: 543.84/242.00 The TRS P consists of the following rules: 543.84/242.00 543.84/242.00 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.00 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.00 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.00 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.00 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.00 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.00 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.00 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.00 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.00 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.00 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.00 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.00 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.00 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.00 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.00 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.00 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.00 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.00 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.00 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.00 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.00 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.00 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.00 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.00 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.00 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.00 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.00 543.84/242.00 The TRS R consists of the following rules: 543.84/242.00 543.84/242.00 down(a) -> up(f(a)) 543.84/242.00 down(b) -> up(g(b)) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.00 down(f(a)) -> f_flat(down(a)) 543.84/242.00 down(f(b)) -> f_flat(down(b)) 543.84/242.00 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.00 down(f(c)) -> f_flat(down(c)) 543.84/242.00 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.00 down(g(a)) -> g_flat(down(a)) 543.84/242.00 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.00 down(g(b)) -> g_flat(down(b)) 543.84/242.00 down(g(c)) -> g_flat(down(c)) 543.84/242.00 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.00 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.00 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.00 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.00 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.00 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.00 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.00 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.00 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.00 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.00 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.00 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.00 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.00 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.00 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.00 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.00 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.00 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.00 543.84/242.00 The set Q consists of the following terms: 543.84/242.00 543.84/242.00 down(a) 543.84/242.00 down(b) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.00 down(f(a)) 543.84/242.00 down(f(b)) 543.84/242.00 down(f(g(x0))) 543.84/242.00 down(f(c)) 543.84/242.00 down(f(fresh_constant)) 543.84/242.00 down(g(a)) 543.84/242.00 down(g(f(x0))) 543.84/242.00 down(g(b)) 543.84/242.00 down(g(c)) 543.84/242.00 down(g(fresh_constant)) 543.84/242.00 down(f(f(a))) 543.84/242.00 down(f(f(b))) 543.84/242.00 down(f(f(g(x0)))) 543.84/242.00 down(f(f(c))) 543.84/242.00 down(f(f(fresh_constant))) 543.84/242.00 down(g(g(a))) 543.84/242.00 down(g(g(f(x0)))) 543.84/242.00 down(g(g(b))) 543.84/242.00 down(g(g(c))) 543.84/242.00 down(g(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) 543.84/242.00 down(f(f(f(g(x0))))) 543.84/242.00 down(f(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) 543.84/242.00 down(g(g(g(f(x0))))) 543.84/242.00 down(g(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(x0)))))) 543.84/242.00 down(f(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(x0)))))) 543.84/242.00 down(g(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(x0))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(x0))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 f_flat(up(x0)) 543.84/242.00 g_flat(up(x0)) 543.84/242.00 543.84/242.00 We have to consider all minimal (P,Q,R)-chains. 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (855) TransformationProof (EQUIVALENT) 543.84/242.00 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.00 543.84/242.00 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.84/242.00 543.84/242.00 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (856) 543.84/242.00 Obligation: 543.84/242.00 Q DP problem: 543.84/242.00 The TRS P consists of the following rules: 543.84/242.00 543.84/242.00 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.00 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.00 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.00 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.00 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.00 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.00 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.00 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.00 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.00 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.00 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.00 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.00 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.00 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.00 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.00 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.00 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.00 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.00 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.00 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.00 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.00 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.00 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.00 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.00 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.00 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.00 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.00 543.84/242.00 The TRS R consists of the following rules: 543.84/242.00 543.84/242.00 down(a) -> up(f(a)) 543.84/242.00 down(b) -> up(g(b)) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.00 down(f(a)) -> f_flat(down(a)) 543.84/242.00 down(f(b)) -> f_flat(down(b)) 543.84/242.00 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.00 down(f(c)) -> f_flat(down(c)) 543.84/242.00 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.00 down(g(a)) -> g_flat(down(a)) 543.84/242.00 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.00 down(g(b)) -> g_flat(down(b)) 543.84/242.00 down(g(c)) -> g_flat(down(c)) 543.84/242.00 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.00 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.00 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.00 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.00 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.00 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.00 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.00 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.00 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.00 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.00 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.00 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.00 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.00 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.00 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.00 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.00 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.00 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.00 543.84/242.00 The set Q consists of the following terms: 543.84/242.00 543.84/242.00 down(a) 543.84/242.00 down(b) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.00 down(f(a)) 543.84/242.00 down(f(b)) 543.84/242.00 down(f(g(x0))) 543.84/242.00 down(f(c)) 543.84/242.00 down(f(fresh_constant)) 543.84/242.00 down(g(a)) 543.84/242.00 down(g(f(x0))) 543.84/242.00 down(g(b)) 543.84/242.00 down(g(c)) 543.84/242.00 down(g(fresh_constant)) 543.84/242.00 down(f(f(a))) 543.84/242.00 down(f(f(b))) 543.84/242.00 down(f(f(g(x0)))) 543.84/242.00 down(f(f(c))) 543.84/242.00 down(f(f(fresh_constant))) 543.84/242.00 down(g(g(a))) 543.84/242.00 down(g(g(f(x0)))) 543.84/242.00 down(g(g(b))) 543.84/242.00 down(g(g(c))) 543.84/242.00 down(g(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) 543.84/242.00 down(f(f(f(g(x0))))) 543.84/242.00 down(f(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) 543.84/242.00 down(g(g(g(f(x0))))) 543.84/242.00 down(g(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(x0)))))) 543.84/242.00 down(f(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(x0)))))) 543.84/242.00 down(g(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(x0))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(x0))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 f_flat(up(x0)) 543.84/242.00 g_flat(up(x0)) 543.84/242.00 543.84/242.00 We have to consider all minimal (P,Q,R)-chains. 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (857) TransformationProof (EQUIVALENT) 543.84/242.00 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.00 543.84/242.00 (TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))),TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.84/242.00 543.84/242.00 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (858) 543.84/242.00 Obligation: 543.84/242.00 Q DP problem: 543.84/242.00 The TRS P consists of the following rules: 543.84/242.00 543.84/242.00 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.00 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.00 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.00 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.00 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.00 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.00 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.00 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.00 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.00 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.00 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.00 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.00 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.00 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.00 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.00 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.00 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.00 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.00 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.00 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.00 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.00 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.00 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.00 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.00 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.00 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.00 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.00 543.84/242.00 The TRS R consists of the following rules: 543.84/242.00 543.84/242.00 down(a) -> up(f(a)) 543.84/242.00 down(b) -> up(g(b)) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.00 down(f(a)) -> f_flat(down(a)) 543.84/242.00 down(f(b)) -> f_flat(down(b)) 543.84/242.00 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.00 down(f(c)) -> f_flat(down(c)) 543.84/242.00 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.00 down(g(a)) -> g_flat(down(a)) 543.84/242.00 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.00 down(g(b)) -> g_flat(down(b)) 543.84/242.00 down(g(c)) -> g_flat(down(c)) 543.84/242.00 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.00 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.00 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.00 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.00 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.00 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.00 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.00 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.00 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.00 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.00 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.00 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.00 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.00 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.00 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.00 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.00 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.00 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.00 543.84/242.00 The set Q consists of the following terms: 543.84/242.00 543.84/242.00 down(a) 543.84/242.00 down(b) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.00 down(f(a)) 543.84/242.00 down(f(b)) 543.84/242.00 down(f(g(x0))) 543.84/242.00 down(f(c)) 543.84/242.00 down(f(fresh_constant)) 543.84/242.00 down(g(a)) 543.84/242.00 down(g(f(x0))) 543.84/242.00 down(g(b)) 543.84/242.00 down(g(c)) 543.84/242.00 down(g(fresh_constant)) 543.84/242.00 down(f(f(a))) 543.84/242.00 down(f(f(b))) 543.84/242.00 down(f(f(g(x0)))) 543.84/242.00 down(f(f(c))) 543.84/242.00 down(f(f(fresh_constant))) 543.84/242.00 down(g(g(a))) 543.84/242.00 down(g(g(f(x0)))) 543.84/242.00 down(g(g(b))) 543.84/242.00 down(g(g(c))) 543.84/242.00 down(g(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) 543.84/242.00 down(f(f(f(g(x0))))) 543.84/242.00 down(f(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) 543.84/242.00 down(g(g(g(f(x0))))) 543.84/242.00 down(g(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(x0)))))) 543.84/242.00 down(f(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(x0)))))) 543.84/242.00 down(g(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(x0))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(x0))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 f_flat(up(x0)) 543.84/242.00 g_flat(up(x0)) 543.84/242.00 543.84/242.00 We have to consider all minimal (P,Q,R)-chains. 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (859) TransformationProof (EQUIVALENT) 543.84/242.00 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.00 543.84/242.00 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.84/242.00 543.84/242.00 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (860) 543.84/242.00 Obligation: 543.84/242.00 Q DP problem: 543.84/242.00 The TRS P consists of the following rules: 543.84/242.00 543.84/242.00 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.00 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.00 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.00 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.00 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.00 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.00 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.00 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.00 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.00 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.00 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.00 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.00 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.00 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.00 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.00 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.00 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.00 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.00 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.00 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.00 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.00 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.00 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.00 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.00 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.00 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.00 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) 543.84/242.00 543.84/242.00 The TRS R consists of the following rules: 543.84/242.00 543.84/242.00 down(a) -> up(f(a)) 543.84/242.00 down(b) -> up(g(b)) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.00 down(f(a)) -> f_flat(down(a)) 543.84/242.00 down(f(b)) -> f_flat(down(b)) 543.84/242.00 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.00 down(f(c)) -> f_flat(down(c)) 543.84/242.00 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.00 down(g(a)) -> g_flat(down(a)) 543.84/242.00 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.00 down(g(b)) -> g_flat(down(b)) 543.84/242.00 down(g(c)) -> g_flat(down(c)) 543.84/242.00 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.00 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.00 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.00 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.00 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.00 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.00 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.00 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.00 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.00 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.00 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.00 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.00 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.00 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.00 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.00 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.00 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.00 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.00 543.84/242.00 The set Q consists of the following terms: 543.84/242.00 543.84/242.00 down(a) 543.84/242.00 down(b) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.00 down(f(a)) 543.84/242.00 down(f(b)) 543.84/242.00 down(f(g(x0))) 543.84/242.00 down(f(c)) 543.84/242.00 down(f(fresh_constant)) 543.84/242.00 down(g(a)) 543.84/242.00 down(g(f(x0))) 543.84/242.00 down(g(b)) 543.84/242.00 down(g(c)) 543.84/242.00 down(g(fresh_constant)) 543.84/242.00 down(f(f(a))) 543.84/242.00 down(f(f(b))) 543.84/242.00 down(f(f(g(x0)))) 543.84/242.00 down(f(f(c))) 543.84/242.00 down(f(f(fresh_constant))) 543.84/242.00 down(g(g(a))) 543.84/242.00 down(g(g(f(x0)))) 543.84/242.00 down(g(g(b))) 543.84/242.00 down(g(g(c))) 543.84/242.00 down(g(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) 543.84/242.00 down(f(f(f(g(x0))))) 543.84/242.00 down(f(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) 543.84/242.00 down(g(g(g(f(x0))))) 543.84/242.00 down(g(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(x0)))))) 543.84/242.00 down(f(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(x0)))))) 543.84/242.00 down(g(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(x0))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(x0))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 f_flat(up(x0)) 543.84/242.00 g_flat(up(x0)) 543.84/242.00 543.84/242.00 We have to consider all minimal (P,Q,R)-chains. 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (861) TransformationProof (EQUIVALENT) 543.84/242.00 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(a))))))) -> TOP(f_flat(up(f(f(f(f(f(a)))))))) at position [0] we obtained the following new rules [LPAR04]: 543.84/242.00 543.84/242.00 (TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))),TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a))))))))) 543.84/242.00 543.84/242.00 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (862) 543.84/242.00 Obligation: 543.84/242.00 Q DP problem: 543.84/242.00 The TRS P consists of the following rules: 543.84/242.00 543.84/242.00 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.00 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.00 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.00 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.00 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.00 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.00 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.00 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.00 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.00 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.00 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.00 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.00 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.00 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.00 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.00 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.00 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.00 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.00 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.00 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.00 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.00 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.00 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.00 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.00 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.00 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.00 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.00 543.84/242.00 The TRS R consists of the following rules: 543.84/242.00 543.84/242.00 down(a) -> up(f(a)) 543.84/242.00 down(b) -> up(g(b)) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.00 down(f(a)) -> f_flat(down(a)) 543.84/242.00 down(f(b)) -> f_flat(down(b)) 543.84/242.00 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.00 down(f(c)) -> f_flat(down(c)) 543.84/242.00 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.00 down(g(a)) -> g_flat(down(a)) 543.84/242.00 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.00 down(g(b)) -> g_flat(down(b)) 543.84/242.00 down(g(c)) -> g_flat(down(c)) 543.84/242.00 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.00 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.00 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.00 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.00 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.00 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.00 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.00 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.00 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.00 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.00 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.00 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.00 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.00 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.00 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.00 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.00 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.00 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.00 543.84/242.00 The set Q consists of the following terms: 543.84/242.00 543.84/242.00 down(a) 543.84/242.00 down(b) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.00 down(f(a)) 543.84/242.00 down(f(b)) 543.84/242.00 down(f(g(x0))) 543.84/242.00 down(f(c)) 543.84/242.00 down(f(fresh_constant)) 543.84/242.00 down(g(a)) 543.84/242.00 down(g(f(x0))) 543.84/242.00 down(g(b)) 543.84/242.00 down(g(c)) 543.84/242.00 down(g(fresh_constant)) 543.84/242.00 down(f(f(a))) 543.84/242.00 down(f(f(b))) 543.84/242.00 down(f(f(g(x0)))) 543.84/242.00 down(f(f(c))) 543.84/242.00 down(f(f(fresh_constant))) 543.84/242.00 down(g(g(a))) 543.84/242.00 down(g(g(f(x0)))) 543.84/242.00 down(g(g(b))) 543.84/242.00 down(g(g(c))) 543.84/242.00 down(g(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) 543.84/242.00 down(f(f(f(g(x0))))) 543.84/242.00 down(f(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) 543.84/242.00 down(g(g(g(f(x0))))) 543.84/242.00 down(g(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(x0)))))) 543.84/242.00 down(f(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(x0)))))) 543.84/242.00 down(g(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(x0))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(x0))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 f_flat(up(x0)) 543.84/242.00 g_flat(up(x0)) 543.84/242.00 543.84/242.00 We have to consider all minimal (P,Q,R)-chains. 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (863) TransformationProof (EQUIVALENT) 543.84/242.00 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(b))))))) -> TOP(g_flat(up(g(g(g(g(g(b)))))))) at position [0] we obtained the following new rules [LPAR04]: 543.84/242.00 543.84/242.00 (TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))),TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b))))))))) 543.84/242.00 543.84/242.00 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (864) 543.84/242.00 Obligation: 543.84/242.00 Q DP problem: 543.84/242.00 The TRS P consists of the following rules: 543.84/242.00 543.84/242.00 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.00 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.00 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.00 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.00 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.00 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.00 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.00 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.00 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.00 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.00 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.00 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.00 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.00 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.00 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.00 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.00 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.00 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.00 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.00 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.00 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.00 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.00 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.00 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.00 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.00 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.00 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.00 543.84/242.00 The TRS R consists of the following rules: 543.84/242.00 543.84/242.00 down(a) -> up(f(a)) 543.84/242.00 down(b) -> up(g(b)) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.00 down(f(a)) -> f_flat(down(a)) 543.84/242.00 down(f(b)) -> f_flat(down(b)) 543.84/242.00 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.00 down(f(c)) -> f_flat(down(c)) 543.84/242.00 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.00 down(g(a)) -> g_flat(down(a)) 543.84/242.00 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.00 down(g(b)) -> g_flat(down(b)) 543.84/242.00 down(g(c)) -> g_flat(down(c)) 543.84/242.00 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.00 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.00 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.00 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.00 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.00 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.00 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.00 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.00 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.00 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.00 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.00 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.00 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.00 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.00 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.00 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.00 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.00 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.00 543.84/242.00 The set Q consists of the following terms: 543.84/242.00 543.84/242.00 down(a) 543.84/242.00 down(b) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.00 down(f(a)) 543.84/242.00 down(f(b)) 543.84/242.00 down(f(g(x0))) 543.84/242.00 down(f(c)) 543.84/242.00 down(f(fresh_constant)) 543.84/242.00 down(g(a)) 543.84/242.00 down(g(f(x0))) 543.84/242.00 down(g(b)) 543.84/242.00 down(g(c)) 543.84/242.00 down(g(fresh_constant)) 543.84/242.00 down(f(f(a))) 543.84/242.00 down(f(f(b))) 543.84/242.00 down(f(f(g(x0)))) 543.84/242.00 down(f(f(c))) 543.84/242.00 down(f(f(fresh_constant))) 543.84/242.00 down(g(g(a))) 543.84/242.00 down(g(g(f(x0)))) 543.84/242.00 down(g(g(b))) 543.84/242.00 down(g(g(c))) 543.84/242.00 down(g(g(fresh_constant))) 543.84/242.00 down(f(f(f(a)))) 543.84/242.00 down(f(f(f(b)))) 543.84/242.00 down(f(f(f(g(x0))))) 543.84/242.00 down(f(f(f(c)))) 543.84/242.00 down(f(f(f(fresh_constant)))) 543.84/242.00 down(g(g(g(a)))) 543.84/242.00 down(g(g(g(f(x0))))) 543.84/242.00 down(g(g(g(b)))) 543.84/242.00 down(g(g(g(c)))) 543.84/242.00 down(g(g(g(fresh_constant)))) 543.84/242.00 down(f(f(f(f(a))))) 543.84/242.00 down(f(f(f(f(b))))) 543.84/242.00 down(f(f(f(f(g(x0)))))) 543.84/242.00 down(f(f(f(f(c))))) 543.84/242.00 down(f(f(f(f(fresh_constant))))) 543.84/242.00 down(g(g(g(g(a))))) 543.84/242.00 down(g(g(g(g(f(x0)))))) 543.84/242.00 down(g(g(g(g(b))))) 543.84/242.00 down(g(g(g(g(c))))) 543.84/242.00 down(g(g(g(g(fresh_constant))))) 543.84/242.00 down(f(f(f(f(f(a)))))) 543.84/242.00 down(f(f(f(f(f(b)))))) 543.84/242.00 down(f(f(f(f(f(g(x0))))))) 543.84/242.00 down(f(f(f(f(f(c)))))) 543.84/242.00 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.00 down(g(g(g(g(g(a)))))) 543.84/242.00 down(g(g(g(g(g(f(x0))))))) 543.84/242.00 down(g(g(g(g(g(b)))))) 543.84/242.00 down(g(g(g(g(g(c)))))) 543.84/242.00 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.00 down(f(f(f(f(f(f(a))))))) 543.84/242.00 down(f(f(f(f(f(f(b))))))) 543.84/242.00 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.00 down(f(f(f(f(f(f(c))))))) 543.84/242.00 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.00 down(g(g(g(g(g(g(a))))))) 543.84/242.00 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.00 down(g(g(g(g(g(g(b))))))) 543.84/242.00 down(g(g(g(g(g(g(c))))))) 543.84/242.00 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.00 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.00 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.00 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.00 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.00 f_flat(up(x0)) 543.84/242.00 g_flat(up(x0)) 543.84/242.00 543.84/242.00 We have to consider all minimal (P,Q,R)-chains. 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (865) TransformationProof (EQUIVALENT) 543.84/242.00 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.00 543.84/242.00 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.84/242.00 543.84/242.00 543.84/242.00 ---------------------------------------- 543.84/242.00 543.84/242.00 (866) 543.84/242.00 Obligation: 543.84/242.00 Q DP problem: 543.84/242.00 The TRS P consists of the following rules: 543.84/242.00 543.84/242.00 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.00 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.00 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.00 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.00 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.00 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.00 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.00 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.00 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.00 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.00 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.00 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.00 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.00 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.00 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.00 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.00 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.00 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.00 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.00 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.00 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.00 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.00 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.00 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.00 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.00 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.00 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) 543.84/242.00 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.00 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.00 543.84/242.00 The TRS R consists of the following rules: 543.84/242.00 543.84/242.00 down(a) -> up(f(a)) 543.84/242.00 down(b) -> up(g(b)) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.01 down(f(a)) -> f_flat(down(a)) 543.84/242.01 down(f(b)) -> f_flat(down(b)) 543.84/242.01 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.01 down(f(c)) -> f_flat(down(c)) 543.84/242.01 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.01 down(g(a)) -> g_flat(down(a)) 543.84/242.01 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.01 down(g(b)) -> g_flat(down(b)) 543.84/242.01 down(g(c)) -> g_flat(down(c)) 543.84/242.01 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.01 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.01 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.01 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.01 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.01 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.01 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.01 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.01 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.01 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.01 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.01 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.01 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.01 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.01 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.01 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.01 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.01 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.01 543.84/242.01 The set Q consists of the following terms: 543.84/242.01 543.84/242.01 down(a) 543.84/242.01 down(b) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.01 down(f(a)) 543.84/242.01 down(f(b)) 543.84/242.01 down(f(g(x0))) 543.84/242.01 down(f(c)) 543.84/242.01 down(f(fresh_constant)) 543.84/242.01 down(g(a)) 543.84/242.01 down(g(f(x0))) 543.84/242.01 down(g(b)) 543.84/242.01 down(g(c)) 543.84/242.01 down(g(fresh_constant)) 543.84/242.01 down(f(f(a))) 543.84/242.01 down(f(f(b))) 543.84/242.01 down(f(f(g(x0)))) 543.84/242.01 down(f(f(c))) 543.84/242.01 down(f(f(fresh_constant))) 543.84/242.01 down(g(g(a))) 543.84/242.01 down(g(g(f(x0)))) 543.84/242.01 down(g(g(b))) 543.84/242.01 down(g(g(c))) 543.84/242.01 down(g(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) 543.84/242.01 down(f(f(f(g(x0))))) 543.84/242.01 down(f(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) 543.84/242.01 down(g(g(g(f(x0))))) 543.84/242.01 down(g(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(x0)))))) 543.84/242.01 down(f(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(x0)))))) 543.84/242.01 down(g(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(x0))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(x0))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 f_flat(up(x0)) 543.84/242.01 g_flat(up(x0)) 543.84/242.01 543.84/242.01 We have to consider all minimal (P,Q,R)-chains. 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (867) TransformationProof (EQUIVALENT) 543.84/242.01 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.01 543.84/242.01 (TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))),TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.84/242.01 543.84/242.01 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (868) 543.84/242.01 Obligation: 543.84/242.01 Q DP problem: 543.84/242.01 The TRS P consists of the following rules: 543.84/242.01 543.84/242.01 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.01 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.01 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.01 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.01 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.01 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.01 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.01 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.01 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.01 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.01 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.01 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.01 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.01 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.01 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.01 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.01 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.01 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.01 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.01 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.01 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.01 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.01 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.01 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.01 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.01 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.01 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.01 543.84/242.01 The TRS R consists of the following rules: 543.84/242.01 543.84/242.01 down(a) -> up(f(a)) 543.84/242.01 down(b) -> up(g(b)) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.01 down(f(a)) -> f_flat(down(a)) 543.84/242.01 down(f(b)) -> f_flat(down(b)) 543.84/242.01 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.01 down(f(c)) -> f_flat(down(c)) 543.84/242.01 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.01 down(g(a)) -> g_flat(down(a)) 543.84/242.01 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.01 down(g(b)) -> g_flat(down(b)) 543.84/242.01 down(g(c)) -> g_flat(down(c)) 543.84/242.01 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.01 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.01 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.01 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.01 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.01 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.01 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.01 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.01 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.01 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.01 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.01 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.01 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.01 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.01 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.01 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.01 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.01 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.01 543.84/242.01 The set Q consists of the following terms: 543.84/242.01 543.84/242.01 down(a) 543.84/242.01 down(b) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.01 down(f(a)) 543.84/242.01 down(f(b)) 543.84/242.01 down(f(g(x0))) 543.84/242.01 down(f(c)) 543.84/242.01 down(f(fresh_constant)) 543.84/242.01 down(g(a)) 543.84/242.01 down(g(f(x0))) 543.84/242.01 down(g(b)) 543.84/242.01 down(g(c)) 543.84/242.01 down(g(fresh_constant)) 543.84/242.01 down(f(f(a))) 543.84/242.01 down(f(f(b))) 543.84/242.01 down(f(f(g(x0)))) 543.84/242.01 down(f(f(c))) 543.84/242.01 down(f(f(fresh_constant))) 543.84/242.01 down(g(g(a))) 543.84/242.01 down(g(g(f(x0)))) 543.84/242.01 down(g(g(b))) 543.84/242.01 down(g(g(c))) 543.84/242.01 down(g(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) 543.84/242.01 down(f(f(f(g(x0))))) 543.84/242.01 down(f(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) 543.84/242.01 down(g(g(g(f(x0))))) 543.84/242.01 down(g(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(x0)))))) 543.84/242.01 down(f(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(x0)))))) 543.84/242.01 down(g(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(x0))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(x0))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 f_flat(up(x0)) 543.84/242.01 g_flat(up(x0)) 543.84/242.01 543.84/242.01 We have to consider all minimal (P,Q,R)-chains. 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (869) TransformationProof (EQUIVALENT) 543.84/242.01 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.01 543.84/242.01 (TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c))))))))),TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c)))))))))) 543.84/242.01 543.84/242.01 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (870) 543.84/242.01 Obligation: 543.84/242.01 Q DP problem: 543.84/242.01 The TRS P consists of the following rules: 543.84/242.01 543.84/242.01 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.01 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.01 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.01 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.01 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.01 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.01 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.01 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.01 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.01 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.01 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.01 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.01 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.01 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.01 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.01 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.01 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.01 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.01 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.01 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.01 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.01 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.01 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.01 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.01 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.01 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.01 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(c))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c))))))))) 543.84/242.01 543.84/242.01 The TRS R consists of the following rules: 543.84/242.01 543.84/242.01 down(a) -> up(f(a)) 543.84/242.01 down(b) -> up(g(b)) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.01 down(f(a)) -> f_flat(down(a)) 543.84/242.01 down(f(b)) -> f_flat(down(b)) 543.84/242.01 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.01 down(f(c)) -> f_flat(down(c)) 543.84/242.01 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.01 down(g(a)) -> g_flat(down(a)) 543.84/242.01 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.01 down(g(b)) -> g_flat(down(b)) 543.84/242.01 down(g(c)) -> g_flat(down(c)) 543.84/242.01 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.01 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.01 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.01 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.01 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.01 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.01 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.01 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.01 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.01 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.01 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.01 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.01 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.01 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.01 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.01 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.01 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.01 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.01 543.84/242.01 The set Q consists of the following terms: 543.84/242.01 543.84/242.01 down(a) 543.84/242.01 down(b) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.01 down(f(a)) 543.84/242.01 down(f(b)) 543.84/242.01 down(f(g(x0))) 543.84/242.01 down(f(c)) 543.84/242.01 down(f(fresh_constant)) 543.84/242.01 down(g(a)) 543.84/242.01 down(g(f(x0))) 543.84/242.01 down(g(b)) 543.84/242.01 down(g(c)) 543.84/242.01 down(g(fresh_constant)) 543.84/242.01 down(f(f(a))) 543.84/242.01 down(f(f(b))) 543.84/242.01 down(f(f(g(x0)))) 543.84/242.01 down(f(f(c))) 543.84/242.01 down(f(f(fresh_constant))) 543.84/242.01 down(g(g(a))) 543.84/242.01 down(g(g(f(x0)))) 543.84/242.01 down(g(g(b))) 543.84/242.01 down(g(g(c))) 543.84/242.01 down(g(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) 543.84/242.01 down(f(f(f(g(x0))))) 543.84/242.01 down(f(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) 543.84/242.01 down(g(g(g(f(x0))))) 543.84/242.01 down(g(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(x0)))))) 543.84/242.01 down(f(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(x0)))))) 543.84/242.01 down(g(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(x0))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(x0))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 f_flat(up(x0)) 543.84/242.01 g_flat(up(x0)) 543.84/242.01 543.84/242.01 We have to consider all minimal (P,Q,R)-chains. 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (871) DependencyGraphProof (EQUIVALENT) 543.84/242.01 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (872) 543.84/242.01 Obligation: 543.84/242.01 Q DP problem: 543.84/242.01 The TRS P consists of the following rules: 543.84/242.01 543.84/242.01 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.01 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.01 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.01 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.01 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.01 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.01 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.01 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.01 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) 543.84/242.01 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.01 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.01 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.01 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.01 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.01 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.01 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) 543.84/242.01 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.01 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.01 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.01 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.01 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.01 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.01 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.01 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.01 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.01 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.01 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.01 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.01 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.01 543.84/242.01 The TRS R consists of the following rules: 543.84/242.01 543.84/242.01 down(a) -> up(f(a)) 543.84/242.01 down(b) -> up(g(b)) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.01 down(f(a)) -> f_flat(down(a)) 543.84/242.01 down(f(b)) -> f_flat(down(b)) 543.84/242.01 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.01 down(f(c)) -> f_flat(down(c)) 543.84/242.01 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.01 down(g(a)) -> g_flat(down(a)) 543.84/242.01 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.01 down(g(b)) -> g_flat(down(b)) 543.84/242.01 down(g(c)) -> g_flat(down(c)) 543.84/242.01 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.01 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.01 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.01 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.01 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.01 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.01 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.01 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.01 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.01 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.01 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.01 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.01 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.01 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.01 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.01 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.01 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.01 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.01 543.84/242.01 The set Q consists of the following terms: 543.84/242.01 543.84/242.01 down(a) 543.84/242.01 down(b) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.01 down(f(a)) 543.84/242.01 down(f(b)) 543.84/242.01 down(f(g(x0))) 543.84/242.01 down(f(c)) 543.84/242.01 down(f(fresh_constant)) 543.84/242.01 down(g(a)) 543.84/242.01 down(g(f(x0))) 543.84/242.01 down(g(b)) 543.84/242.01 down(g(c)) 543.84/242.01 down(g(fresh_constant)) 543.84/242.01 down(f(f(a))) 543.84/242.01 down(f(f(b))) 543.84/242.01 down(f(f(g(x0)))) 543.84/242.01 down(f(f(c))) 543.84/242.01 down(f(f(fresh_constant))) 543.84/242.01 down(g(g(a))) 543.84/242.01 down(g(g(f(x0)))) 543.84/242.01 down(g(g(b))) 543.84/242.01 down(g(g(c))) 543.84/242.01 down(g(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) 543.84/242.01 down(f(f(f(g(x0))))) 543.84/242.01 down(f(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) 543.84/242.01 down(g(g(g(f(x0))))) 543.84/242.01 down(g(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(x0)))))) 543.84/242.01 down(f(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(x0)))))) 543.84/242.01 down(g(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(x0))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(x0))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 f_flat(up(x0)) 543.84/242.01 g_flat(up(x0)) 543.84/242.01 543.84/242.01 We have to consider all minimal (P,Q,R)-chains. 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (873) TransformationProof (EQUIVALENT) 543.84/242.01 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.01 543.84/242.01 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) 543.84/242.01 543.84/242.01 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (874) 543.84/242.01 Obligation: 543.84/242.01 Q DP problem: 543.84/242.01 The TRS P consists of the following rules: 543.84/242.01 543.84/242.01 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.01 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.01 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.01 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.01 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.01 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.01 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.01 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.01 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.01 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.01 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.01 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.01 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.01 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.01 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.01 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) 543.84/242.01 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.01 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.01 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.01 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.01 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.01 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.01 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.01 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.01 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.01 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.01 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.01 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.01 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))) 543.84/242.01 543.84/242.01 The TRS R consists of the following rules: 543.84/242.01 543.84/242.01 down(a) -> up(f(a)) 543.84/242.01 down(b) -> up(g(b)) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.01 down(f(a)) -> f_flat(down(a)) 543.84/242.01 down(f(b)) -> f_flat(down(b)) 543.84/242.01 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.01 down(f(c)) -> f_flat(down(c)) 543.84/242.01 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.01 down(g(a)) -> g_flat(down(a)) 543.84/242.01 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.01 down(g(b)) -> g_flat(down(b)) 543.84/242.01 down(g(c)) -> g_flat(down(c)) 543.84/242.01 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.01 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.01 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.01 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.01 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.01 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.01 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.01 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.01 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.01 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.01 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.01 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.01 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.01 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.01 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.01 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.01 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.01 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.01 543.84/242.01 The set Q consists of the following terms: 543.84/242.01 543.84/242.01 down(a) 543.84/242.01 down(b) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.01 down(f(a)) 543.84/242.01 down(f(b)) 543.84/242.01 down(f(g(x0))) 543.84/242.01 down(f(c)) 543.84/242.01 down(f(fresh_constant)) 543.84/242.01 down(g(a)) 543.84/242.01 down(g(f(x0))) 543.84/242.01 down(g(b)) 543.84/242.01 down(g(c)) 543.84/242.01 down(g(fresh_constant)) 543.84/242.01 down(f(f(a))) 543.84/242.01 down(f(f(b))) 543.84/242.01 down(f(f(g(x0)))) 543.84/242.01 down(f(f(c))) 543.84/242.01 down(f(f(fresh_constant))) 543.84/242.01 down(g(g(a))) 543.84/242.01 down(g(g(f(x0)))) 543.84/242.01 down(g(g(b))) 543.84/242.01 down(g(g(c))) 543.84/242.01 down(g(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) 543.84/242.01 down(f(f(f(g(x0))))) 543.84/242.01 down(f(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) 543.84/242.01 down(g(g(g(f(x0))))) 543.84/242.01 down(g(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(x0)))))) 543.84/242.01 down(f(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(x0)))))) 543.84/242.01 down(g(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(x0))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(x0))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 f_flat(up(x0)) 543.84/242.01 g_flat(up(x0)) 543.84/242.01 543.84/242.01 We have to consider all minimal (P,Q,R)-chains. 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (875) TransformationProof (EQUIVALENT) 543.84/242.01 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.01 543.84/242.01 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) 543.84/242.01 543.84/242.01 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (876) 543.84/242.01 Obligation: 543.84/242.01 Q DP problem: 543.84/242.01 The TRS P consists of the following rules: 543.84/242.01 543.84/242.01 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.01 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.01 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.01 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.01 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.01 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.01 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.01 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.01 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.01 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.01 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.01 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.01 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.01 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.01 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.01 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.01 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.01 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.01 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.01 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.01 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.01 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.01 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.01 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.01 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.01 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.01 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.01 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.01 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))) 543.84/242.01 543.84/242.01 The TRS R consists of the following rules: 543.84/242.01 543.84/242.01 down(a) -> up(f(a)) 543.84/242.01 down(b) -> up(g(b)) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.01 down(f(a)) -> f_flat(down(a)) 543.84/242.01 down(f(b)) -> f_flat(down(b)) 543.84/242.01 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.01 down(f(c)) -> f_flat(down(c)) 543.84/242.01 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.01 down(g(a)) -> g_flat(down(a)) 543.84/242.01 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.01 down(g(b)) -> g_flat(down(b)) 543.84/242.01 down(g(c)) -> g_flat(down(c)) 543.84/242.01 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.01 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.01 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.01 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.01 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.01 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.01 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.01 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.01 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.01 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.01 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.01 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.01 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.01 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.01 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.01 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.01 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.01 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.01 543.84/242.01 The set Q consists of the following terms: 543.84/242.01 543.84/242.01 down(a) 543.84/242.01 down(b) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.01 down(f(a)) 543.84/242.01 down(f(b)) 543.84/242.01 down(f(g(x0))) 543.84/242.01 down(f(c)) 543.84/242.01 down(f(fresh_constant)) 543.84/242.01 down(g(a)) 543.84/242.01 down(g(f(x0))) 543.84/242.01 down(g(b)) 543.84/242.01 down(g(c)) 543.84/242.01 down(g(fresh_constant)) 543.84/242.01 down(f(f(a))) 543.84/242.01 down(f(f(b))) 543.84/242.01 down(f(f(g(x0)))) 543.84/242.01 down(f(f(c))) 543.84/242.01 down(f(f(fresh_constant))) 543.84/242.01 down(g(g(a))) 543.84/242.01 down(g(g(f(x0)))) 543.84/242.01 down(g(g(b))) 543.84/242.01 down(g(g(c))) 543.84/242.01 down(g(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) 543.84/242.01 down(f(f(f(g(x0))))) 543.84/242.01 down(f(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) 543.84/242.01 down(g(g(g(f(x0))))) 543.84/242.01 down(g(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(x0)))))) 543.84/242.01 down(f(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(x0)))))) 543.84/242.01 down(g(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(x0))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(x0))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 f_flat(up(x0)) 543.84/242.01 g_flat(up(x0)) 543.84/242.01 543.84/242.01 We have to consider all minimal (P,Q,R)-chains. 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (877) TransformationProof (EQUIVALENT) 543.84/242.01 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.01 543.84/242.01 (TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant))))))))),TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant)))))))))) 543.84/242.01 543.84/242.01 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (878) 543.84/242.01 Obligation: 543.84/242.01 Q DP problem: 543.84/242.01 The TRS P consists of the following rules: 543.84/242.01 543.84/242.01 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.01 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.01 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.01 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.01 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.01 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.01 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.01 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.01 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.01 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.01 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.01 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.01 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.01 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.01 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.01 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.01 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.01 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.01 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.01 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.01 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.01 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.01 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.01 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.01 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.01 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.01 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.01 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.01 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(fresh_constant))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant))))))))) 543.84/242.01 543.84/242.01 The TRS R consists of the following rules: 543.84/242.01 543.84/242.01 down(a) -> up(f(a)) 543.84/242.01 down(b) -> up(g(b)) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.01 down(f(a)) -> f_flat(down(a)) 543.84/242.01 down(f(b)) -> f_flat(down(b)) 543.84/242.01 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.01 down(f(c)) -> f_flat(down(c)) 543.84/242.01 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.01 down(g(a)) -> g_flat(down(a)) 543.84/242.01 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.01 down(g(b)) -> g_flat(down(b)) 543.84/242.01 down(g(c)) -> g_flat(down(c)) 543.84/242.01 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.01 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.01 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.01 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.01 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.01 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.01 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.01 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.01 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.01 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.01 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.01 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.01 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.01 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.01 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.01 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.01 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.01 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.01 543.84/242.01 The set Q consists of the following terms: 543.84/242.01 543.84/242.01 down(a) 543.84/242.01 down(b) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.01 down(f(a)) 543.84/242.01 down(f(b)) 543.84/242.01 down(f(g(x0))) 543.84/242.01 down(f(c)) 543.84/242.01 down(f(fresh_constant)) 543.84/242.01 down(g(a)) 543.84/242.01 down(g(f(x0))) 543.84/242.01 down(g(b)) 543.84/242.01 down(g(c)) 543.84/242.01 down(g(fresh_constant)) 543.84/242.01 down(f(f(a))) 543.84/242.01 down(f(f(b))) 543.84/242.01 down(f(f(g(x0)))) 543.84/242.01 down(f(f(c))) 543.84/242.01 down(f(f(fresh_constant))) 543.84/242.01 down(g(g(a))) 543.84/242.01 down(g(g(f(x0)))) 543.84/242.01 down(g(g(b))) 543.84/242.01 down(g(g(c))) 543.84/242.01 down(g(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) 543.84/242.01 down(f(f(f(g(x0))))) 543.84/242.01 down(f(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) 543.84/242.01 down(g(g(g(f(x0))))) 543.84/242.01 down(g(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(x0)))))) 543.84/242.01 down(f(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(x0)))))) 543.84/242.01 down(g(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(x0))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(x0))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.01 f_flat(up(x0)) 543.84/242.01 g_flat(up(x0)) 543.84/242.01 543.84/242.01 We have to consider all minimal (P,Q,R)-chains. 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (879) DependencyGraphProof (EQUIVALENT) 543.84/242.01 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.84/242.01 ---------------------------------------- 543.84/242.01 543.84/242.01 (880) 543.84/242.01 Obligation: 543.84/242.01 Q DP problem: 543.84/242.01 The TRS P consists of the following rules: 543.84/242.01 543.84/242.01 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.01 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.01 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.01 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.01 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.01 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.01 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.01 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.01 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))) 543.84/242.01 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.01 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.01 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.01 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.01 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.01 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.01 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))) 543.84/242.01 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.01 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.01 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.01 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.01 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.01 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.01 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.01 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.01 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.01 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.01 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.01 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.01 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.01 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.01 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.01 543.84/242.01 The TRS R consists of the following rules: 543.84/242.01 543.84/242.01 down(a) -> up(f(a)) 543.84/242.01 down(b) -> up(g(b)) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.01 down(f(a)) -> f_flat(down(a)) 543.84/242.01 down(f(b)) -> f_flat(down(b)) 543.84/242.01 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.01 down(f(c)) -> f_flat(down(c)) 543.84/242.01 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.01 down(g(a)) -> g_flat(down(a)) 543.84/242.01 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.01 down(g(b)) -> g_flat(down(b)) 543.84/242.01 down(g(c)) -> g_flat(down(c)) 543.84/242.01 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.01 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.01 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.01 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.01 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.01 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.01 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.01 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.01 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.01 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.01 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.01 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.01 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.01 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.01 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.01 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.01 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.01 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.01 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.01 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.01 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.01 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.01 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.01 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.01 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.01 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.01 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.01 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.01 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.01 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.01 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.01 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.01 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.01 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.01 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.01 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.01 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.01 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.01 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.01 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.01 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.01 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.01 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.01 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.01 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.01 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.01 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.01 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.01 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.01 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.01 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.01 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.01 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.01 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.01 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.02 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.02 543.84/242.02 The set Q consists of the following terms: 543.84/242.02 543.84/242.02 down(a) 543.84/242.02 down(b) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.02 down(f(a)) 543.84/242.02 down(f(b)) 543.84/242.02 down(f(g(x0))) 543.84/242.02 down(f(c)) 543.84/242.02 down(f(fresh_constant)) 543.84/242.02 down(g(a)) 543.84/242.02 down(g(f(x0))) 543.84/242.02 down(g(b)) 543.84/242.02 down(g(c)) 543.84/242.02 down(g(fresh_constant)) 543.84/242.02 down(f(f(a))) 543.84/242.02 down(f(f(b))) 543.84/242.02 down(f(f(g(x0)))) 543.84/242.02 down(f(f(c))) 543.84/242.02 down(f(f(fresh_constant))) 543.84/242.02 down(g(g(a))) 543.84/242.02 down(g(g(f(x0)))) 543.84/242.02 down(g(g(b))) 543.84/242.02 down(g(g(c))) 543.84/242.02 down(g(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) 543.84/242.02 down(f(f(f(g(x0))))) 543.84/242.02 down(f(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) 543.84/242.02 down(g(g(g(f(x0))))) 543.84/242.02 down(g(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(x0)))))) 543.84/242.02 down(f(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(x0)))))) 543.84/242.02 down(g(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(x0))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(x0))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 f_flat(up(x0)) 543.84/242.02 g_flat(up(x0)) 543.84/242.02 543.84/242.02 We have to consider all minimal (P,Q,R)-chains. 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (881) TransformationProof (EQUIVALENT) 543.84/242.02 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.02 543.84/242.02 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))) 543.84/242.02 543.84/242.02 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (882) 543.84/242.02 Obligation: 543.84/242.02 Q DP problem: 543.84/242.02 The TRS P consists of the following rules: 543.84/242.02 543.84/242.02 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.02 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.02 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.02 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.02 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.02 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.02 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.02 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.02 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.02 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.02 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.02 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.02 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.02 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.02 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.02 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))) 543.84/242.02 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.02 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.02 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.02 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.02 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.02 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.02 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.02 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.02 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.02 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.02 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.02 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.02 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) 543.84/242.02 543.84/242.02 The TRS R consists of the following rules: 543.84/242.02 543.84/242.02 down(a) -> up(f(a)) 543.84/242.02 down(b) -> up(g(b)) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.02 down(f(a)) -> f_flat(down(a)) 543.84/242.02 down(f(b)) -> f_flat(down(b)) 543.84/242.02 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.02 down(f(c)) -> f_flat(down(c)) 543.84/242.02 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.02 down(g(a)) -> g_flat(down(a)) 543.84/242.02 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.02 down(g(b)) -> g_flat(down(b)) 543.84/242.02 down(g(c)) -> g_flat(down(c)) 543.84/242.02 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.02 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.02 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.02 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.02 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.02 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.02 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.02 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.02 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.02 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.02 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.02 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.02 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.02 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.02 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.02 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.02 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.02 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.02 543.84/242.02 The set Q consists of the following terms: 543.84/242.02 543.84/242.02 down(a) 543.84/242.02 down(b) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.02 down(f(a)) 543.84/242.02 down(f(b)) 543.84/242.02 down(f(g(x0))) 543.84/242.02 down(f(c)) 543.84/242.02 down(f(fresh_constant)) 543.84/242.02 down(g(a)) 543.84/242.02 down(g(f(x0))) 543.84/242.02 down(g(b)) 543.84/242.02 down(g(c)) 543.84/242.02 down(g(fresh_constant)) 543.84/242.02 down(f(f(a))) 543.84/242.02 down(f(f(b))) 543.84/242.02 down(f(f(g(x0)))) 543.84/242.02 down(f(f(c))) 543.84/242.02 down(f(f(fresh_constant))) 543.84/242.02 down(g(g(a))) 543.84/242.02 down(g(g(f(x0)))) 543.84/242.02 down(g(g(b))) 543.84/242.02 down(g(g(c))) 543.84/242.02 down(g(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) 543.84/242.02 down(f(f(f(g(x0))))) 543.84/242.02 down(f(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) 543.84/242.02 down(g(g(g(f(x0))))) 543.84/242.02 down(g(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(x0)))))) 543.84/242.02 down(f(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(x0)))))) 543.84/242.02 down(g(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(x0))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(x0))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 f_flat(up(x0)) 543.84/242.02 g_flat(up(x0)) 543.84/242.02 543.84/242.02 We have to consider all minimal (P,Q,R)-chains. 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (883) TransformationProof (EQUIVALENT) 543.84/242.02 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.02 543.84/242.02 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))) 543.84/242.02 543.84/242.02 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (884) 543.84/242.02 Obligation: 543.84/242.02 Q DP problem: 543.84/242.02 The TRS P consists of the following rules: 543.84/242.02 543.84/242.02 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.02 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.02 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.02 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.02 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.02 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.02 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.02 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.02 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.02 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.02 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.02 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.02 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.02 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.02 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.02 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.02 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.02 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.02 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.02 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.02 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.02 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.02 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.02 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.02 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.02 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.02 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.02 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.02 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) 543.84/242.02 543.84/242.02 The TRS R consists of the following rules: 543.84/242.02 543.84/242.02 down(a) -> up(f(a)) 543.84/242.02 down(b) -> up(g(b)) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.02 down(f(a)) -> f_flat(down(a)) 543.84/242.02 down(f(b)) -> f_flat(down(b)) 543.84/242.02 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.02 down(f(c)) -> f_flat(down(c)) 543.84/242.02 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.02 down(g(a)) -> g_flat(down(a)) 543.84/242.02 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.02 down(g(b)) -> g_flat(down(b)) 543.84/242.02 down(g(c)) -> g_flat(down(c)) 543.84/242.02 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.02 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.02 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.02 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.02 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.02 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.02 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.02 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.02 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.02 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.02 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.02 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.02 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.02 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.02 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.02 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.02 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.02 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.02 543.84/242.02 The set Q consists of the following terms: 543.84/242.02 543.84/242.02 down(a) 543.84/242.02 down(b) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.02 down(f(a)) 543.84/242.02 down(f(b)) 543.84/242.02 down(f(g(x0))) 543.84/242.02 down(f(c)) 543.84/242.02 down(f(fresh_constant)) 543.84/242.02 down(g(a)) 543.84/242.02 down(g(f(x0))) 543.84/242.02 down(g(b)) 543.84/242.02 down(g(c)) 543.84/242.02 down(g(fresh_constant)) 543.84/242.02 down(f(f(a))) 543.84/242.02 down(f(f(b))) 543.84/242.02 down(f(f(g(x0)))) 543.84/242.02 down(f(f(c))) 543.84/242.02 down(f(f(fresh_constant))) 543.84/242.02 down(g(g(a))) 543.84/242.02 down(g(g(f(x0)))) 543.84/242.02 down(g(g(b))) 543.84/242.02 down(g(g(c))) 543.84/242.02 down(g(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) 543.84/242.02 down(f(f(f(g(x0))))) 543.84/242.02 down(f(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) 543.84/242.02 down(g(g(g(f(x0))))) 543.84/242.02 down(g(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(x0)))))) 543.84/242.02 down(f(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(x0)))))) 543.84/242.02 down(g(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(x0))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(x0))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 f_flat(up(x0)) 543.84/242.02 g_flat(up(x0)) 543.84/242.02 543.84/242.02 We have to consider all minimal (P,Q,R)-chains. 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (885) TransformationProof (EQUIVALENT) 543.84/242.02 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.02 543.84/242.02 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.84/242.02 543.84/242.02 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (886) 543.84/242.02 Obligation: 543.84/242.02 Q DP problem: 543.84/242.02 The TRS P consists of the following rules: 543.84/242.02 543.84/242.02 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.02 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.02 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.02 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.02 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.02 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.02 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.02 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.02 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.02 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.02 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.02 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.02 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.02 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.02 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.02 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.02 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.02 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.02 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.02 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.02 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.02 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.02 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.02 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.02 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.02 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.02 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.02 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.02 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.02 543.84/242.02 The TRS R consists of the following rules: 543.84/242.02 543.84/242.02 down(a) -> up(f(a)) 543.84/242.02 down(b) -> up(g(b)) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.02 down(f(a)) -> f_flat(down(a)) 543.84/242.02 down(f(b)) -> f_flat(down(b)) 543.84/242.02 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.02 down(f(c)) -> f_flat(down(c)) 543.84/242.02 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.02 down(g(a)) -> g_flat(down(a)) 543.84/242.02 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.02 down(g(b)) -> g_flat(down(b)) 543.84/242.02 down(g(c)) -> g_flat(down(c)) 543.84/242.02 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.02 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.02 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.02 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.02 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.02 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.02 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.02 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.02 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.02 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.02 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.02 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.02 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.02 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.02 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.02 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.02 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.02 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.02 543.84/242.02 The set Q consists of the following terms: 543.84/242.02 543.84/242.02 down(a) 543.84/242.02 down(b) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.02 down(f(a)) 543.84/242.02 down(f(b)) 543.84/242.02 down(f(g(x0))) 543.84/242.02 down(f(c)) 543.84/242.02 down(f(fresh_constant)) 543.84/242.02 down(g(a)) 543.84/242.02 down(g(f(x0))) 543.84/242.02 down(g(b)) 543.84/242.02 down(g(c)) 543.84/242.02 down(g(fresh_constant)) 543.84/242.02 down(f(f(a))) 543.84/242.02 down(f(f(b))) 543.84/242.02 down(f(f(g(x0)))) 543.84/242.02 down(f(f(c))) 543.84/242.02 down(f(f(fresh_constant))) 543.84/242.02 down(g(g(a))) 543.84/242.02 down(g(g(f(x0)))) 543.84/242.02 down(g(g(b))) 543.84/242.02 down(g(g(c))) 543.84/242.02 down(g(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) 543.84/242.02 down(f(f(f(g(x0))))) 543.84/242.02 down(f(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) 543.84/242.02 down(g(g(g(f(x0))))) 543.84/242.02 down(g(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(x0)))))) 543.84/242.02 down(f(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(x0)))))) 543.84/242.02 down(g(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(x0))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(x0))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 f_flat(up(x0)) 543.84/242.02 g_flat(up(x0)) 543.84/242.02 543.84/242.02 We have to consider all minimal (P,Q,R)-chains. 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (887) TransformationProof (EQUIVALENT) 543.84/242.02 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.02 543.84/242.02 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.84/242.02 543.84/242.02 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (888) 543.84/242.02 Obligation: 543.84/242.02 Q DP problem: 543.84/242.02 The TRS P consists of the following rules: 543.84/242.02 543.84/242.02 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.02 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.02 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.02 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.02 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.02 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.02 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.02 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.02 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.02 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.02 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.02 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.02 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.02 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.02 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.02 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.02 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.02 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.02 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.02 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.02 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.02 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.02 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.02 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.02 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.02 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.02 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.02 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.02 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.02 543.84/242.02 The TRS R consists of the following rules: 543.84/242.02 543.84/242.02 down(a) -> up(f(a)) 543.84/242.02 down(b) -> up(g(b)) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.02 down(f(a)) -> f_flat(down(a)) 543.84/242.02 down(f(b)) -> f_flat(down(b)) 543.84/242.02 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.02 down(f(c)) -> f_flat(down(c)) 543.84/242.02 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.02 down(g(a)) -> g_flat(down(a)) 543.84/242.02 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.02 down(g(b)) -> g_flat(down(b)) 543.84/242.02 down(g(c)) -> g_flat(down(c)) 543.84/242.02 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.02 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.02 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.02 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.02 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.02 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.02 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.02 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.02 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.02 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.02 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.02 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.02 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.02 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.02 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.02 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.02 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.02 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.02 543.84/242.02 The set Q consists of the following terms: 543.84/242.02 543.84/242.02 down(a) 543.84/242.02 down(b) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.02 down(f(a)) 543.84/242.02 down(f(b)) 543.84/242.02 down(f(g(x0))) 543.84/242.02 down(f(c)) 543.84/242.02 down(f(fresh_constant)) 543.84/242.02 down(g(a)) 543.84/242.02 down(g(f(x0))) 543.84/242.02 down(g(b)) 543.84/242.02 down(g(c)) 543.84/242.02 down(g(fresh_constant)) 543.84/242.02 down(f(f(a))) 543.84/242.02 down(f(f(b))) 543.84/242.02 down(f(f(g(x0)))) 543.84/242.02 down(f(f(c))) 543.84/242.02 down(f(f(fresh_constant))) 543.84/242.02 down(g(g(a))) 543.84/242.02 down(g(g(f(x0)))) 543.84/242.02 down(g(g(b))) 543.84/242.02 down(g(g(c))) 543.84/242.02 down(g(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) 543.84/242.02 down(f(f(f(g(x0))))) 543.84/242.02 down(f(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) 543.84/242.02 down(g(g(g(f(x0))))) 543.84/242.02 down(g(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(x0)))))) 543.84/242.02 down(f(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(x0)))))) 543.84/242.02 down(g(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(x0))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(x0))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 f_flat(up(x0)) 543.84/242.02 g_flat(up(x0)) 543.84/242.02 543.84/242.02 We have to consider all minimal (P,Q,R)-chains. 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (889) TransformationProof (EQUIVALENT) 543.84/242.02 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.02 543.84/242.02 (TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))),TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.84/242.02 543.84/242.02 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (890) 543.84/242.02 Obligation: 543.84/242.02 Q DP problem: 543.84/242.02 The TRS P consists of the following rules: 543.84/242.02 543.84/242.02 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.02 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.02 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.02 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.02 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.02 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.02 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.02 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.02 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.02 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.02 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.02 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.02 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.02 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.02 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.02 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.02 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.02 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.02 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.02 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.02 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.02 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.02 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.02 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.02 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.02 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.02 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.02 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.02 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.02 543.84/242.02 The TRS R consists of the following rules: 543.84/242.02 543.84/242.02 down(a) -> up(f(a)) 543.84/242.02 down(b) -> up(g(b)) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.02 down(f(a)) -> f_flat(down(a)) 543.84/242.02 down(f(b)) -> f_flat(down(b)) 543.84/242.02 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.02 down(f(c)) -> f_flat(down(c)) 543.84/242.02 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.02 down(g(a)) -> g_flat(down(a)) 543.84/242.02 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.02 down(g(b)) -> g_flat(down(b)) 543.84/242.02 down(g(c)) -> g_flat(down(c)) 543.84/242.02 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.02 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.02 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.02 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.02 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.02 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.02 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.02 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.02 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.02 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.02 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.02 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.02 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.02 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.02 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.02 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.02 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.02 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.02 543.84/242.02 The set Q consists of the following terms: 543.84/242.02 543.84/242.02 down(a) 543.84/242.02 down(b) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.02 down(f(a)) 543.84/242.02 down(f(b)) 543.84/242.02 down(f(g(x0))) 543.84/242.02 down(f(c)) 543.84/242.02 down(f(fresh_constant)) 543.84/242.02 down(g(a)) 543.84/242.02 down(g(f(x0))) 543.84/242.02 down(g(b)) 543.84/242.02 down(g(c)) 543.84/242.02 down(g(fresh_constant)) 543.84/242.02 down(f(f(a))) 543.84/242.02 down(f(f(b))) 543.84/242.02 down(f(f(g(x0)))) 543.84/242.02 down(f(f(c))) 543.84/242.02 down(f(f(fresh_constant))) 543.84/242.02 down(g(g(a))) 543.84/242.02 down(g(g(f(x0)))) 543.84/242.02 down(g(g(b))) 543.84/242.02 down(g(g(c))) 543.84/242.02 down(g(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) 543.84/242.02 down(f(f(f(g(x0))))) 543.84/242.02 down(f(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) 543.84/242.02 down(g(g(g(f(x0))))) 543.84/242.02 down(g(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(x0)))))) 543.84/242.02 down(f(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(x0)))))) 543.84/242.02 down(g(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(x0))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(x0))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 f_flat(up(x0)) 543.84/242.02 g_flat(up(x0)) 543.84/242.02 543.84/242.02 We have to consider all minimal (P,Q,R)-chains. 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (891) TransformationProof (EQUIVALENT) 543.84/242.02 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.02 543.84/242.02 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.84/242.02 543.84/242.02 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (892) 543.84/242.02 Obligation: 543.84/242.02 Q DP problem: 543.84/242.02 The TRS P consists of the following rules: 543.84/242.02 543.84/242.02 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.02 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.02 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.02 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.02 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.02 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.02 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.02 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.02 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.02 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.02 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.02 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.02 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.02 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.02 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.02 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.02 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.02 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.02 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.02 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.02 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.02 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.02 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.02 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.02 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.02 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.02 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.02 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.02 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.02 543.84/242.02 The TRS R consists of the following rules: 543.84/242.02 543.84/242.02 down(a) -> up(f(a)) 543.84/242.02 down(b) -> up(g(b)) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.02 down(f(a)) -> f_flat(down(a)) 543.84/242.02 down(f(b)) -> f_flat(down(b)) 543.84/242.02 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.02 down(f(c)) -> f_flat(down(c)) 543.84/242.02 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.02 down(g(a)) -> g_flat(down(a)) 543.84/242.02 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.02 down(g(b)) -> g_flat(down(b)) 543.84/242.02 down(g(c)) -> g_flat(down(c)) 543.84/242.02 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.02 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.02 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.02 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.02 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.02 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.02 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.02 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.02 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.02 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.02 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.02 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.02 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.02 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.02 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.02 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.02 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.02 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.02 543.84/242.02 The set Q consists of the following terms: 543.84/242.02 543.84/242.02 down(a) 543.84/242.02 down(b) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.02 down(f(a)) 543.84/242.02 down(f(b)) 543.84/242.02 down(f(g(x0))) 543.84/242.02 down(f(c)) 543.84/242.02 down(f(fresh_constant)) 543.84/242.02 down(g(a)) 543.84/242.02 down(g(f(x0))) 543.84/242.02 down(g(b)) 543.84/242.02 down(g(c)) 543.84/242.02 down(g(fresh_constant)) 543.84/242.02 down(f(f(a))) 543.84/242.02 down(f(f(b))) 543.84/242.02 down(f(f(g(x0)))) 543.84/242.02 down(f(f(c))) 543.84/242.02 down(f(f(fresh_constant))) 543.84/242.02 down(g(g(a))) 543.84/242.02 down(g(g(f(x0)))) 543.84/242.02 down(g(g(b))) 543.84/242.02 down(g(g(c))) 543.84/242.02 down(g(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) 543.84/242.02 down(f(f(f(g(x0))))) 543.84/242.02 down(f(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) 543.84/242.02 down(g(g(g(f(x0))))) 543.84/242.02 down(g(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(x0)))))) 543.84/242.02 down(f(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(x0)))))) 543.84/242.02 down(g(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(x0))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(x0))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 f_flat(up(x0)) 543.84/242.02 g_flat(up(x0)) 543.84/242.02 543.84/242.02 We have to consider all minimal (P,Q,R)-chains. 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (893) TransformationProof (EQUIVALENT) 543.84/242.02 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.02 543.84/242.02 (TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c))))))))),TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c)))))))))) 543.84/242.02 543.84/242.02 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (894) 543.84/242.02 Obligation: 543.84/242.02 Q DP problem: 543.84/242.02 The TRS P consists of the following rules: 543.84/242.02 543.84/242.02 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.02 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.02 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.02 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.02 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.02 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.02 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.02 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.02 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.02 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.02 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.02 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.02 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.02 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.02 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.02 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.02 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.02 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.02 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.02 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.02 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.02 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.02 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.02 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.02 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.02 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.02 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.02 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.02 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.02 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.02 TOP(up(g(g(g(g(g(g(g(c))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c))))))))) 543.84/242.02 543.84/242.02 The TRS R consists of the following rules: 543.84/242.02 543.84/242.02 down(a) -> up(f(a)) 543.84/242.02 down(b) -> up(g(b)) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.02 down(f(a)) -> f_flat(down(a)) 543.84/242.02 down(f(b)) -> f_flat(down(b)) 543.84/242.02 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.02 down(f(c)) -> f_flat(down(c)) 543.84/242.02 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.02 down(g(a)) -> g_flat(down(a)) 543.84/242.02 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.02 down(g(b)) -> g_flat(down(b)) 543.84/242.02 down(g(c)) -> g_flat(down(c)) 543.84/242.02 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.02 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.02 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.02 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.02 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.02 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.02 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.02 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.02 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.02 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.02 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.02 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.02 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.02 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.02 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.02 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.02 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.02 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.02 543.84/242.02 The set Q consists of the following terms: 543.84/242.02 543.84/242.02 down(a) 543.84/242.02 down(b) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.02 down(f(a)) 543.84/242.02 down(f(b)) 543.84/242.02 down(f(g(x0))) 543.84/242.02 down(f(c)) 543.84/242.02 down(f(fresh_constant)) 543.84/242.02 down(g(a)) 543.84/242.02 down(g(f(x0))) 543.84/242.02 down(g(b)) 543.84/242.02 down(g(c)) 543.84/242.02 down(g(fresh_constant)) 543.84/242.02 down(f(f(a))) 543.84/242.02 down(f(f(b))) 543.84/242.02 down(f(f(g(x0)))) 543.84/242.02 down(f(f(c))) 543.84/242.02 down(f(f(fresh_constant))) 543.84/242.02 down(g(g(a))) 543.84/242.02 down(g(g(f(x0)))) 543.84/242.02 down(g(g(b))) 543.84/242.02 down(g(g(c))) 543.84/242.02 down(g(g(fresh_constant))) 543.84/242.02 down(f(f(f(a)))) 543.84/242.02 down(f(f(f(b)))) 543.84/242.02 down(f(f(f(g(x0))))) 543.84/242.02 down(f(f(f(c)))) 543.84/242.02 down(f(f(f(fresh_constant)))) 543.84/242.02 down(g(g(g(a)))) 543.84/242.02 down(g(g(g(f(x0))))) 543.84/242.02 down(g(g(g(b)))) 543.84/242.02 down(g(g(g(c)))) 543.84/242.02 down(g(g(g(fresh_constant)))) 543.84/242.02 down(f(f(f(f(a))))) 543.84/242.02 down(f(f(f(f(b))))) 543.84/242.02 down(f(f(f(f(g(x0)))))) 543.84/242.02 down(f(f(f(f(c))))) 543.84/242.02 down(f(f(f(f(fresh_constant))))) 543.84/242.02 down(g(g(g(g(a))))) 543.84/242.02 down(g(g(g(g(f(x0)))))) 543.84/242.02 down(g(g(g(g(b))))) 543.84/242.02 down(g(g(g(g(c))))) 543.84/242.02 down(g(g(g(g(fresh_constant))))) 543.84/242.02 down(f(f(f(f(f(a)))))) 543.84/242.02 down(f(f(f(f(f(b)))))) 543.84/242.02 down(f(f(f(f(f(g(x0))))))) 543.84/242.02 down(f(f(f(f(f(c)))))) 543.84/242.02 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.02 down(g(g(g(g(g(a)))))) 543.84/242.02 down(g(g(g(g(g(f(x0))))))) 543.84/242.02 down(g(g(g(g(g(b)))))) 543.84/242.02 down(g(g(g(g(g(c)))))) 543.84/242.02 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.02 down(f(f(f(f(f(f(a))))))) 543.84/242.02 down(f(f(f(f(f(f(b))))))) 543.84/242.02 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.02 down(f(f(f(f(f(f(c))))))) 543.84/242.02 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.02 down(g(g(g(g(g(g(a))))))) 543.84/242.02 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.02 down(g(g(g(g(g(g(b))))))) 543.84/242.02 down(g(g(g(g(g(g(c))))))) 543.84/242.02 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.02 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.02 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.02 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.02 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.02 f_flat(up(x0)) 543.84/242.02 g_flat(up(x0)) 543.84/242.02 543.84/242.02 We have to consider all minimal (P,Q,R)-chains. 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (895) DependencyGraphProof (EQUIVALENT) 543.84/242.02 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.84/242.02 ---------------------------------------- 543.84/242.02 543.84/242.02 (896) 543.84/242.02 Obligation: 543.84/242.02 Q DP problem: 543.84/242.02 The TRS P consists of the following rules: 543.84/242.02 543.84/242.02 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.02 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.02 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.02 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.03 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.03 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.03 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.03 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.03 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) 543.84/242.03 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.03 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.03 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.03 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.03 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.03 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.03 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) 543.84/242.03 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.03 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.03 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.03 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.03 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.03 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.03 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.03 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.03 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.03 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.03 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.03 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.03 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.03 543.84/242.03 The TRS R consists of the following rules: 543.84/242.03 543.84/242.03 down(a) -> up(f(a)) 543.84/242.03 down(b) -> up(g(b)) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.03 down(f(a)) -> f_flat(down(a)) 543.84/242.03 down(f(b)) -> f_flat(down(b)) 543.84/242.03 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.03 down(f(c)) -> f_flat(down(c)) 543.84/242.03 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.03 down(g(a)) -> g_flat(down(a)) 543.84/242.03 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.03 down(g(b)) -> g_flat(down(b)) 543.84/242.03 down(g(c)) -> g_flat(down(c)) 543.84/242.03 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.03 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.03 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.03 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.03 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.03 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.03 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.03 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.03 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.03 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.03 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.03 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.03 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.03 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.03 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.03 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.03 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.03 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.03 543.84/242.03 The set Q consists of the following terms: 543.84/242.03 543.84/242.03 down(a) 543.84/242.03 down(b) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.03 down(f(a)) 543.84/242.03 down(f(b)) 543.84/242.03 down(f(g(x0))) 543.84/242.03 down(f(c)) 543.84/242.03 down(f(fresh_constant)) 543.84/242.03 down(g(a)) 543.84/242.03 down(g(f(x0))) 543.84/242.03 down(g(b)) 543.84/242.03 down(g(c)) 543.84/242.03 down(g(fresh_constant)) 543.84/242.03 down(f(f(a))) 543.84/242.03 down(f(f(b))) 543.84/242.03 down(f(f(g(x0)))) 543.84/242.03 down(f(f(c))) 543.84/242.03 down(f(f(fresh_constant))) 543.84/242.03 down(g(g(a))) 543.84/242.03 down(g(g(f(x0)))) 543.84/242.03 down(g(g(b))) 543.84/242.03 down(g(g(c))) 543.84/242.03 down(g(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) 543.84/242.03 down(f(f(f(g(x0))))) 543.84/242.03 down(f(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) 543.84/242.03 down(g(g(g(f(x0))))) 543.84/242.03 down(g(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(x0)))))) 543.84/242.03 down(f(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(x0)))))) 543.84/242.03 down(g(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(x0))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(x0))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 f_flat(up(x0)) 543.84/242.03 g_flat(up(x0)) 543.84/242.03 543.84/242.03 We have to consider all minimal (P,Q,R)-chains. 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (897) TransformationProof (EQUIVALENT) 543.84/242.03 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.03 543.84/242.03 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.84/242.03 543.84/242.03 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (898) 543.84/242.03 Obligation: 543.84/242.03 Q DP problem: 543.84/242.03 The TRS P consists of the following rules: 543.84/242.03 543.84/242.03 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.03 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.03 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.03 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.03 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.03 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.03 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.03 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.03 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.03 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.03 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.03 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.03 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.03 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.03 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.03 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) 543.84/242.03 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.03 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.03 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.03 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.03 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.03 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.03 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.03 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.03 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.03 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.03 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.03 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.03 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))) 543.84/242.03 543.84/242.03 The TRS R consists of the following rules: 543.84/242.03 543.84/242.03 down(a) -> up(f(a)) 543.84/242.03 down(b) -> up(g(b)) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.03 down(f(a)) -> f_flat(down(a)) 543.84/242.03 down(f(b)) -> f_flat(down(b)) 543.84/242.03 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.03 down(f(c)) -> f_flat(down(c)) 543.84/242.03 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.03 down(g(a)) -> g_flat(down(a)) 543.84/242.03 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.03 down(g(b)) -> g_flat(down(b)) 543.84/242.03 down(g(c)) -> g_flat(down(c)) 543.84/242.03 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.03 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.03 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.03 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.03 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.03 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.03 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.03 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.03 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.03 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.03 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.03 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.03 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.03 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.03 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.03 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.03 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.03 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.03 543.84/242.03 The set Q consists of the following terms: 543.84/242.03 543.84/242.03 down(a) 543.84/242.03 down(b) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.03 down(f(a)) 543.84/242.03 down(f(b)) 543.84/242.03 down(f(g(x0))) 543.84/242.03 down(f(c)) 543.84/242.03 down(f(fresh_constant)) 543.84/242.03 down(g(a)) 543.84/242.03 down(g(f(x0))) 543.84/242.03 down(g(b)) 543.84/242.03 down(g(c)) 543.84/242.03 down(g(fresh_constant)) 543.84/242.03 down(f(f(a))) 543.84/242.03 down(f(f(b))) 543.84/242.03 down(f(f(g(x0)))) 543.84/242.03 down(f(f(c))) 543.84/242.03 down(f(f(fresh_constant))) 543.84/242.03 down(g(g(a))) 543.84/242.03 down(g(g(f(x0)))) 543.84/242.03 down(g(g(b))) 543.84/242.03 down(g(g(c))) 543.84/242.03 down(g(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) 543.84/242.03 down(f(f(f(g(x0))))) 543.84/242.03 down(f(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) 543.84/242.03 down(g(g(g(f(x0))))) 543.84/242.03 down(g(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(x0)))))) 543.84/242.03 down(f(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(x0)))))) 543.84/242.03 down(g(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(x0))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(x0))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 f_flat(up(x0)) 543.84/242.03 g_flat(up(x0)) 543.84/242.03 543.84/242.03 We have to consider all minimal (P,Q,R)-chains. 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (899) TransformationProof (EQUIVALENT) 543.84/242.03 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.03 543.84/242.03 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.84/242.03 543.84/242.03 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (900) 543.84/242.03 Obligation: 543.84/242.03 Q DP problem: 543.84/242.03 The TRS P consists of the following rules: 543.84/242.03 543.84/242.03 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.03 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.03 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.03 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.03 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.03 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.03 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.03 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.03 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.03 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.03 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.03 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.03 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.03 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.03 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.03 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.03 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.03 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.03 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.03 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.03 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.03 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.03 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.03 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.03 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.03 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.03 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.03 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.03 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))) 543.84/242.03 543.84/242.03 The TRS R consists of the following rules: 543.84/242.03 543.84/242.03 down(a) -> up(f(a)) 543.84/242.03 down(b) -> up(g(b)) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.03 down(f(a)) -> f_flat(down(a)) 543.84/242.03 down(f(b)) -> f_flat(down(b)) 543.84/242.03 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.03 down(f(c)) -> f_flat(down(c)) 543.84/242.03 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.03 down(g(a)) -> g_flat(down(a)) 543.84/242.03 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.03 down(g(b)) -> g_flat(down(b)) 543.84/242.03 down(g(c)) -> g_flat(down(c)) 543.84/242.03 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.03 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.03 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.03 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.03 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.03 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.03 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.03 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.03 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.03 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.03 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.03 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.03 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.03 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.03 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.03 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.03 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.03 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.03 543.84/242.03 The set Q consists of the following terms: 543.84/242.03 543.84/242.03 down(a) 543.84/242.03 down(b) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.03 down(f(a)) 543.84/242.03 down(f(b)) 543.84/242.03 down(f(g(x0))) 543.84/242.03 down(f(c)) 543.84/242.03 down(f(fresh_constant)) 543.84/242.03 down(g(a)) 543.84/242.03 down(g(f(x0))) 543.84/242.03 down(g(b)) 543.84/242.03 down(g(c)) 543.84/242.03 down(g(fresh_constant)) 543.84/242.03 down(f(f(a))) 543.84/242.03 down(f(f(b))) 543.84/242.03 down(f(f(g(x0)))) 543.84/242.03 down(f(f(c))) 543.84/242.03 down(f(f(fresh_constant))) 543.84/242.03 down(g(g(a))) 543.84/242.03 down(g(g(f(x0)))) 543.84/242.03 down(g(g(b))) 543.84/242.03 down(g(g(c))) 543.84/242.03 down(g(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) 543.84/242.03 down(f(f(f(g(x0))))) 543.84/242.03 down(f(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) 543.84/242.03 down(g(g(g(f(x0))))) 543.84/242.03 down(g(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(x0)))))) 543.84/242.03 down(f(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(x0)))))) 543.84/242.03 down(g(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(x0))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(x0))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 f_flat(up(x0)) 543.84/242.03 g_flat(up(x0)) 543.84/242.03 543.84/242.03 We have to consider all minimal (P,Q,R)-chains. 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (901) TransformationProof (EQUIVALENT) 543.84/242.03 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.03 543.84/242.03 (TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant))))))))),TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant)))))))))) 543.84/242.03 543.84/242.03 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (902) 543.84/242.03 Obligation: 543.84/242.03 Q DP problem: 543.84/242.03 The TRS P consists of the following rules: 543.84/242.03 543.84/242.03 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.03 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.03 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.03 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.03 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.03 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.03 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.03 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.03 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.03 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.03 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.03 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.03 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.03 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.03 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.03 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.03 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.03 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.03 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.03 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.03 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.03 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.03 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.03 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.03 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.03 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.03 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.03 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.03 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(fresh_constant))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant))))))))) 543.84/242.03 543.84/242.03 The TRS R consists of the following rules: 543.84/242.03 543.84/242.03 down(a) -> up(f(a)) 543.84/242.03 down(b) -> up(g(b)) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.03 down(f(a)) -> f_flat(down(a)) 543.84/242.03 down(f(b)) -> f_flat(down(b)) 543.84/242.03 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.03 down(f(c)) -> f_flat(down(c)) 543.84/242.03 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.03 down(g(a)) -> g_flat(down(a)) 543.84/242.03 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.03 down(g(b)) -> g_flat(down(b)) 543.84/242.03 down(g(c)) -> g_flat(down(c)) 543.84/242.03 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.03 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.03 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.03 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.03 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.03 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.03 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.03 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.03 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.03 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.03 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.03 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.03 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.03 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.03 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.03 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.03 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.03 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.03 543.84/242.03 The set Q consists of the following terms: 543.84/242.03 543.84/242.03 down(a) 543.84/242.03 down(b) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.03 down(f(a)) 543.84/242.03 down(f(b)) 543.84/242.03 down(f(g(x0))) 543.84/242.03 down(f(c)) 543.84/242.03 down(f(fresh_constant)) 543.84/242.03 down(g(a)) 543.84/242.03 down(g(f(x0))) 543.84/242.03 down(g(b)) 543.84/242.03 down(g(c)) 543.84/242.03 down(g(fresh_constant)) 543.84/242.03 down(f(f(a))) 543.84/242.03 down(f(f(b))) 543.84/242.03 down(f(f(g(x0)))) 543.84/242.03 down(f(f(c))) 543.84/242.03 down(f(f(fresh_constant))) 543.84/242.03 down(g(g(a))) 543.84/242.03 down(g(g(f(x0)))) 543.84/242.03 down(g(g(b))) 543.84/242.03 down(g(g(c))) 543.84/242.03 down(g(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) 543.84/242.03 down(f(f(f(g(x0))))) 543.84/242.03 down(f(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) 543.84/242.03 down(g(g(g(f(x0))))) 543.84/242.03 down(g(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(x0)))))) 543.84/242.03 down(f(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(x0)))))) 543.84/242.03 down(g(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(x0))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(x0))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 f_flat(up(x0)) 543.84/242.03 g_flat(up(x0)) 543.84/242.03 543.84/242.03 We have to consider all minimal (P,Q,R)-chains. 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (903) DependencyGraphProof (EQUIVALENT) 543.84/242.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (904) 543.84/242.03 Obligation: 543.84/242.03 Q DP problem: 543.84/242.03 The TRS P consists of the following rules: 543.84/242.03 543.84/242.03 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.03 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.03 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.03 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.03 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.03 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.03 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.03 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.03 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))) 543.84/242.03 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.03 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.03 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.03 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.03 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.03 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.03 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))) 543.84/242.03 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.03 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.03 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.03 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.03 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.03 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.03 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.03 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.03 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.03 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.03 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.03 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.03 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.03 543.84/242.03 The TRS R consists of the following rules: 543.84/242.03 543.84/242.03 down(a) -> up(f(a)) 543.84/242.03 down(b) -> up(g(b)) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.03 down(f(a)) -> f_flat(down(a)) 543.84/242.03 down(f(b)) -> f_flat(down(b)) 543.84/242.03 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.03 down(f(c)) -> f_flat(down(c)) 543.84/242.03 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.03 down(g(a)) -> g_flat(down(a)) 543.84/242.03 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.03 down(g(b)) -> g_flat(down(b)) 543.84/242.03 down(g(c)) -> g_flat(down(c)) 543.84/242.03 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.03 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.03 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.03 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.03 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.03 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.03 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.03 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.03 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.03 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.03 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.03 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.03 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.03 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.03 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.03 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.03 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.03 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.03 543.84/242.03 The set Q consists of the following terms: 543.84/242.03 543.84/242.03 down(a) 543.84/242.03 down(b) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.03 down(f(a)) 543.84/242.03 down(f(b)) 543.84/242.03 down(f(g(x0))) 543.84/242.03 down(f(c)) 543.84/242.03 down(f(fresh_constant)) 543.84/242.03 down(g(a)) 543.84/242.03 down(g(f(x0))) 543.84/242.03 down(g(b)) 543.84/242.03 down(g(c)) 543.84/242.03 down(g(fresh_constant)) 543.84/242.03 down(f(f(a))) 543.84/242.03 down(f(f(b))) 543.84/242.03 down(f(f(g(x0)))) 543.84/242.03 down(f(f(c))) 543.84/242.03 down(f(f(fresh_constant))) 543.84/242.03 down(g(g(a))) 543.84/242.03 down(g(g(f(x0)))) 543.84/242.03 down(g(g(b))) 543.84/242.03 down(g(g(c))) 543.84/242.03 down(g(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) 543.84/242.03 down(f(f(f(g(x0))))) 543.84/242.03 down(f(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) 543.84/242.03 down(g(g(g(f(x0))))) 543.84/242.03 down(g(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(x0)))))) 543.84/242.03 down(f(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(x0)))))) 543.84/242.03 down(g(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(x0))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(x0))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 f_flat(up(x0)) 543.84/242.03 g_flat(up(x0)) 543.84/242.03 543.84/242.03 We have to consider all minimal (P,Q,R)-chains. 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (905) TransformationProof (EQUIVALENT) 543.84/242.03 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.03 543.84/242.03 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a)))))))))) 543.84/242.03 543.84/242.03 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (906) 543.84/242.03 Obligation: 543.84/242.03 Q DP problem: 543.84/242.03 The TRS P consists of the following rules: 543.84/242.03 543.84/242.03 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.03 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.03 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.03 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.03 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.03 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.03 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.03 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.03 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.03 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.03 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.03 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.03 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.03 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.03 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.03 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))) 543.84/242.03 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.03 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.03 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.03 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.03 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.03 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.03 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.03 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.03 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.03 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.03 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.03 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.03 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.03 543.84/242.03 The TRS R consists of the following rules: 543.84/242.03 543.84/242.03 down(a) -> up(f(a)) 543.84/242.03 down(b) -> up(g(b)) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.03 down(f(a)) -> f_flat(down(a)) 543.84/242.03 down(f(b)) -> f_flat(down(b)) 543.84/242.03 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.03 down(f(c)) -> f_flat(down(c)) 543.84/242.03 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.03 down(g(a)) -> g_flat(down(a)) 543.84/242.03 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.03 down(g(b)) -> g_flat(down(b)) 543.84/242.03 down(g(c)) -> g_flat(down(c)) 543.84/242.03 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.03 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.03 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.03 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.03 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.03 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.03 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.03 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.03 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.03 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.03 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.03 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.03 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.03 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.03 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.03 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.03 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.03 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.03 543.84/242.03 The set Q consists of the following terms: 543.84/242.03 543.84/242.03 down(a) 543.84/242.03 down(b) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.03 down(f(a)) 543.84/242.03 down(f(b)) 543.84/242.03 down(f(g(x0))) 543.84/242.03 down(f(c)) 543.84/242.03 down(f(fresh_constant)) 543.84/242.03 down(g(a)) 543.84/242.03 down(g(f(x0))) 543.84/242.03 down(g(b)) 543.84/242.03 down(g(c)) 543.84/242.03 down(g(fresh_constant)) 543.84/242.03 down(f(f(a))) 543.84/242.03 down(f(f(b))) 543.84/242.03 down(f(f(g(x0)))) 543.84/242.03 down(f(f(c))) 543.84/242.03 down(f(f(fresh_constant))) 543.84/242.03 down(g(g(a))) 543.84/242.03 down(g(g(f(x0)))) 543.84/242.03 down(g(g(b))) 543.84/242.03 down(g(g(c))) 543.84/242.03 down(g(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) 543.84/242.03 down(f(f(f(g(x0))))) 543.84/242.03 down(f(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) 543.84/242.03 down(g(g(g(f(x0))))) 543.84/242.03 down(g(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(x0)))))) 543.84/242.03 down(f(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(x0)))))) 543.84/242.03 down(g(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(x0))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(x0))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 f_flat(up(x0)) 543.84/242.03 g_flat(up(x0)) 543.84/242.03 543.84/242.03 We have to consider all minimal (P,Q,R)-chains. 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (907) TransformationProof (EQUIVALENT) 543.84/242.03 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.03 543.84/242.03 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b)))))))))) 543.84/242.03 543.84/242.03 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (908) 543.84/242.03 Obligation: 543.84/242.03 Q DP problem: 543.84/242.03 The TRS P consists of the following rules: 543.84/242.03 543.84/242.03 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.03 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.03 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.03 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.03 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.03 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.03 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.03 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.03 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.03 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.03 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.03 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.03 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.03 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.03 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.03 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.03 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.03 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.03 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.03 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.03 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.03 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.03 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.03 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.03 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.03 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.03 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.03 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.03 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.03 543.84/242.03 The TRS R consists of the following rules: 543.84/242.03 543.84/242.03 down(a) -> up(f(a)) 543.84/242.03 down(b) -> up(g(b)) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.03 down(f(a)) -> f_flat(down(a)) 543.84/242.03 down(f(b)) -> f_flat(down(b)) 543.84/242.03 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.03 down(f(c)) -> f_flat(down(c)) 543.84/242.03 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.03 down(g(a)) -> g_flat(down(a)) 543.84/242.03 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.03 down(g(b)) -> g_flat(down(b)) 543.84/242.03 down(g(c)) -> g_flat(down(c)) 543.84/242.03 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.03 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.03 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.03 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.03 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.03 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.03 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.03 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.03 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.03 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.03 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.03 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.03 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.03 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.03 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.03 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.03 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.03 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.03 543.84/242.03 The set Q consists of the following terms: 543.84/242.03 543.84/242.03 down(a) 543.84/242.03 down(b) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.03 down(f(a)) 543.84/242.03 down(f(b)) 543.84/242.03 down(f(g(x0))) 543.84/242.03 down(f(c)) 543.84/242.03 down(f(fresh_constant)) 543.84/242.03 down(g(a)) 543.84/242.03 down(g(f(x0))) 543.84/242.03 down(g(b)) 543.84/242.03 down(g(c)) 543.84/242.03 down(g(fresh_constant)) 543.84/242.03 down(f(f(a))) 543.84/242.03 down(f(f(b))) 543.84/242.03 down(f(f(g(x0)))) 543.84/242.03 down(f(f(c))) 543.84/242.03 down(f(f(fresh_constant))) 543.84/242.03 down(g(g(a))) 543.84/242.03 down(g(g(f(x0)))) 543.84/242.03 down(g(g(b))) 543.84/242.03 down(g(g(c))) 543.84/242.03 down(g(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) 543.84/242.03 down(f(f(f(g(x0))))) 543.84/242.03 down(f(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) 543.84/242.03 down(g(g(g(f(x0))))) 543.84/242.03 down(g(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(x0)))))) 543.84/242.03 down(f(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(x0)))))) 543.84/242.03 down(g(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(x0))))))) 543.84/242.03 down(f(f(f(f(f(c)))))) 543.84/242.03 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.03 down(g(g(g(g(g(a)))))) 543.84/242.03 down(g(g(g(g(g(f(x0))))))) 543.84/242.03 down(g(g(g(g(g(b)))))) 543.84/242.03 down(g(g(g(g(g(c)))))) 543.84/242.03 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.03 down(f(f(f(f(f(f(a))))))) 543.84/242.03 down(f(f(f(f(f(f(b))))))) 543.84/242.03 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.03 down(f(f(f(f(f(f(c))))))) 543.84/242.03 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.03 down(g(g(g(g(g(g(a))))))) 543.84/242.03 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.03 down(g(g(g(g(g(g(b))))))) 543.84/242.03 down(g(g(g(g(g(g(c))))))) 543.84/242.03 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.03 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.03 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.03 f_flat(up(x0)) 543.84/242.03 g_flat(up(x0)) 543.84/242.03 543.84/242.03 We have to consider all minimal (P,Q,R)-chains. 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (909) TransformationProof (EQUIVALENT) 543.84/242.03 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.03 543.84/242.03 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.84/242.03 543.84/242.03 543.84/242.03 ---------------------------------------- 543.84/242.03 543.84/242.03 (910) 543.84/242.03 Obligation: 543.84/242.03 Q DP problem: 543.84/242.03 The TRS P consists of the following rules: 543.84/242.03 543.84/242.03 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.03 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.03 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.03 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.03 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.03 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.03 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.03 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.03 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.03 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.03 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.03 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.03 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.03 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.03 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.03 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.03 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.03 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.03 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.03 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.03 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.03 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.03 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.03 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.03 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.03 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.03 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.03 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.03 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.03 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.03 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.03 543.84/242.03 The TRS R consists of the following rules: 543.84/242.03 543.84/242.03 down(a) -> up(f(a)) 543.84/242.03 down(b) -> up(g(b)) 543.84/242.03 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.03 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.03 down(f(a)) -> f_flat(down(a)) 543.84/242.03 down(f(b)) -> f_flat(down(b)) 543.84/242.03 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.03 down(f(c)) -> f_flat(down(c)) 543.84/242.03 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.03 down(g(a)) -> g_flat(down(a)) 543.84/242.03 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.03 down(g(b)) -> g_flat(down(b)) 543.84/242.03 down(g(c)) -> g_flat(down(c)) 543.84/242.03 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.03 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.03 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.03 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.03 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.03 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.03 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.03 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.03 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.03 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.03 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.03 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.03 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.03 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.03 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.03 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.03 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.03 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.03 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.03 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.03 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.03 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.03 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.03 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.03 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.03 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.03 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.03 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.03 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.03 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.03 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.03 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.03 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.03 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.04 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.04 543.84/242.04 The set Q consists of the following terms: 543.84/242.04 543.84/242.04 down(a) 543.84/242.04 down(b) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.04 down(f(a)) 543.84/242.04 down(f(b)) 543.84/242.04 down(f(g(x0))) 543.84/242.04 down(f(c)) 543.84/242.04 down(f(fresh_constant)) 543.84/242.04 down(g(a)) 543.84/242.04 down(g(f(x0))) 543.84/242.04 down(g(b)) 543.84/242.04 down(g(c)) 543.84/242.04 down(g(fresh_constant)) 543.84/242.04 down(f(f(a))) 543.84/242.04 down(f(f(b))) 543.84/242.04 down(f(f(g(x0)))) 543.84/242.04 down(f(f(c))) 543.84/242.04 down(f(f(fresh_constant))) 543.84/242.04 down(g(g(a))) 543.84/242.04 down(g(g(f(x0)))) 543.84/242.04 down(g(g(b))) 543.84/242.04 down(g(g(c))) 543.84/242.04 down(g(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) 543.84/242.04 down(f(f(f(g(x0))))) 543.84/242.04 down(f(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) 543.84/242.04 down(g(g(g(f(x0))))) 543.84/242.04 down(g(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(x0)))))) 543.84/242.04 down(f(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(x0)))))) 543.84/242.04 down(g(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(x0))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(x0))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 f_flat(up(x0)) 543.84/242.04 g_flat(up(x0)) 543.84/242.04 543.84/242.04 We have to consider all minimal (P,Q,R)-chains. 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (911) TransformationProof (EQUIVALENT) 543.84/242.04 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.04 543.84/242.04 (TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))),TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.84/242.04 543.84/242.04 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (912) 543.84/242.04 Obligation: 543.84/242.04 Q DP problem: 543.84/242.04 The TRS P consists of the following rules: 543.84/242.04 543.84/242.04 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.04 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.04 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.04 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.04 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.04 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.04 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.04 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.04 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.04 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.04 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.04 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.04 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.04 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.04 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.04 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.04 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.04 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.04 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.04 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.04 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.04 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.04 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.04 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.04 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.04 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.04 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.04 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.04 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.04 543.84/242.04 The TRS R consists of the following rules: 543.84/242.04 543.84/242.04 down(a) -> up(f(a)) 543.84/242.04 down(b) -> up(g(b)) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.04 down(f(a)) -> f_flat(down(a)) 543.84/242.04 down(f(b)) -> f_flat(down(b)) 543.84/242.04 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.04 down(f(c)) -> f_flat(down(c)) 543.84/242.04 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.04 down(g(a)) -> g_flat(down(a)) 543.84/242.04 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.04 down(g(b)) -> g_flat(down(b)) 543.84/242.04 down(g(c)) -> g_flat(down(c)) 543.84/242.04 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.04 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.04 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.04 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.04 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.04 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.04 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.04 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.04 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.04 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.04 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.04 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.04 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.04 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.04 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.04 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.04 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.04 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.04 543.84/242.04 The set Q consists of the following terms: 543.84/242.04 543.84/242.04 down(a) 543.84/242.04 down(b) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.04 down(f(a)) 543.84/242.04 down(f(b)) 543.84/242.04 down(f(g(x0))) 543.84/242.04 down(f(c)) 543.84/242.04 down(f(fresh_constant)) 543.84/242.04 down(g(a)) 543.84/242.04 down(g(f(x0))) 543.84/242.04 down(g(b)) 543.84/242.04 down(g(c)) 543.84/242.04 down(g(fresh_constant)) 543.84/242.04 down(f(f(a))) 543.84/242.04 down(f(f(b))) 543.84/242.04 down(f(f(g(x0)))) 543.84/242.04 down(f(f(c))) 543.84/242.04 down(f(f(fresh_constant))) 543.84/242.04 down(g(g(a))) 543.84/242.04 down(g(g(f(x0)))) 543.84/242.04 down(g(g(b))) 543.84/242.04 down(g(g(c))) 543.84/242.04 down(g(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) 543.84/242.04 down(f(f(f(g(x0))))) 543.84/242.04 down(f(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) 543.84/242.04 down(g(g(g(f(x0))))) 543.84/242.04 down(g(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(x0)))))) 543.84/242.04 down(f(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(x0)))))) 543.84/242.04 down(g(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(x0))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(x0))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 f_flat(up(x0)) 543.84/242.04 g_flat(up(x0)) 543.84/242.04 543.84/242.04 We have to consider all minimal (P,Q,R)-chains. 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (913) TransformationProof (EQUIVALENT) 543.84/242.04 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.04 543.84/242.04 (TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))),TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.84/242.04 543.84/242.04 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (914) 543.84/242.04 Obligation: 543.84/242.04 Q DP problem: 543.84/242.04 The TRS P consists of the following rules: 543.84/242.04 543.84/242.04 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.04 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.04 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.04 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.04 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.04 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.04 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.04 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.04 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.04 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.04 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.04 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.04 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.04 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.04 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.04 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.04 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.04 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.04 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.04 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.04 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.04 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.04 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.04 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.04 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.04 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.04 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.04 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.04 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.04 543.84/242.04 The TRS R consists of the following rules: 543.84/242.04 543.84/242.04 down(a) -> up(f(a)) 543.84/242.04 down(b) -> up(g(b)) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.04 down(f(a)) -> f_flat(down(a)) 543.84/242.04 down(f(b)) -> f_flat(down(b)) 543.84/242.04 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.04 down(f(c)) -> f_flat(down(c)) 543.84/242.04 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.04 down(g(a)) -> g_flat(down(a)) 543.84/242.04 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.04 down(g(b)) -> g_flat(down(b)) 543.84/242.04 down(g(c)) -> g_flat(down(c)) 543.84/242.04 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.04 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.04 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.04 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.04 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.04 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.04 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.04 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.04 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.04 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.04 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.04 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.04 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.04 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.04 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.04 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.04 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.04 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.04 543.84/242.04 The set Q consists of the following terms: 543.84/242.04 543.84/242.04 down(a) 543.84/242.04 down(b) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.04 down(f(a)) 543.84/242.04 down(f(b)) 543.84/242.04 down(f(g(x0))) 543.84/242.04 down(f(c)) 543.84/242.04 down(f(fresh_constant)) 543.84/242.04 down(g(a)) 543.84/242.04 down(g(f(x0))) 543.84/242.04 down(g(b)) 543.84/242.04 down(g(c)) 543.84/242.04 down(g(fresh_constant)) 543.84/242.04 down(f(f(a))) 543.84/242.04 down(f(f(b))) 543.84/242.04 down(f(f(g(x0)))) 543.84/242.04 down(f(f(c))) 543.84/242.04 down(f(f(fresh_constant))) 543.84/242.04 down(g(g(a))) 543.84/242.04 down(g(g(f(x0)))) 543.84/242.04 down(g(g(b))) 543.84/242.04 down(g(g(c))) 543.84/242.04 down(g(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) 543.84/242.04 down(f(f(f(g(x0))))) 543.84/242.04 down(f(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) 543.84/242.04 down(g(g(g(f(x0))))) 543.84/242.04 down(g(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(x0)))))) 543.84/242.04 down(f(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(x0)))))) 543.84/242.04 down(g(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(x0))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(x0))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 f_flat(up(x0)) 543.84/242.04 g_flat(up(x0)) 543.84/242.04 543.84/242.04 We have to consider all minimal (P,Q,R)-chains. 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (915) TransformationProof (EQUIVALENT) 543.84/242.04 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.04 543.84/242.04 (TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))),TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.84/242.04 543.84/242.04 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (916) 543.84/242.04 Obligation: 543.84/242.04 Q DP problem: 543.84/242.04 The TRS P consists of the following rules: 543.84/242.04 543.84/242.04 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.04 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.04 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.04 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.04 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.04 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.04 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.04 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.04 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.04 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.04 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.04 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.04 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.04 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.04 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.04 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.04 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.04 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.04 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.04 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.04 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.04 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.04 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.04 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.04 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.04 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.04 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.04 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.04 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.04 543.84/242.04 The TRS R consists of the following rules: 543.84/242.04 543.84/242.04 down(a) -> up(f(a)) 543.84/242.04 down(b) -> up(g(b)) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.04 down(f(a)) -> f_flat(down(a)) 543.84/242.04 down(f(b)) -> f_flat(down(b)) 543.84/242.04 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.04 down(f(c)) -> f_flat(down(c)) 543.84/242.04 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.04 down(g(a)) -> g_flat(down(a)) 543.84/242.04 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.04 down(g(b)) -> g_flat(down(b)) 543.84/242.04 down(g(c)) -> g_flat(down(c)) 543.84/242.04 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.04 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.04 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.04 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.04 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.04 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.04 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.04 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.04 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.04 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.04 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.04 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.04 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.04 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.04 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.04 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.04 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.04 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.04 543.84/242.04 The set Q consists of the following terms: 543.84/242.04 543.84/242.04 down(a) 543.84/242.04 down(b) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.04 down(f(a)) 543.84/242.04 down(f(b)) 543.84/242.04 down(f(g(x0))) 543.84/242.04 down(f(c)) 543.84/242.04 down(f(fresh_constant)) 543.84/242.04 down(g(a)) 543.84/242.04 down(g(f(x0))) 543.84/242.04 down(g(b)) 543.84/242.04 down(g(c)) 543.84/242.04 down(g(fresh_constant)) 543.84/242.04 down(f(f(a))) 543.84/242.04 down(f(f(b))) 543.84/242.04 down(f(f(g(x0)))) 543.84/242.04 down(f(f(c))) 543.84/242.04 down(f(f(fresh_constant))) 543.84/242.04 down(g(g(a))) 543.84/242.04 down(g(g(f(x0)))) 543.84/242.04 down(g(g(b))) 543.84/242.04 down(g(g(c))) 543.84/242.04 down(g(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) 543.84/242.04 down(f(f(f(g(x0))))) 543.84/242.04 down(f(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) 543.84/242.04 down(g(g(g(f(x0))))) 543.84/242.04 down(g(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(x0)))))) 543.84/242.04 down(f(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(x0)))))) 543.84/242.04 down(g(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(x0))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(x0))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 f_flat(up(x0)) 543.84/242.04 g_flat(up(x0)) 543.84/242.04 543.84/242.04 We have to consider all minimal (P,Q,R)-chains. 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (917) TransformationProof (EQUIVALENT) 543.84/242.04 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(a))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.04 543.84/242.04 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a)))))))))))) 543.84/242.04 543.84/242.04 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (918) 543.84/242.04 Obligation: 543.84/242.04 Q DP problem: 543.84/242.04 The TRS P consists of the following rules: 543.84/242.04 543.84/242.04 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.04 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.04 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.04 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.04 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.04 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.04 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.04 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.04 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.04 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.04 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.04 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.04 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.04 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.04 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.04 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.04 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.04 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.04 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.04 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.04 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.04 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.04 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.04 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.04 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.04 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.04 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.04 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.04 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.04 543.84/242.04 The TRS R consists of the following rules: 543.84/242.04 543.84/242.04 down(a) -> up(f(a)) 543.84/242.04 down(b) -> up(g(b)) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.04 down(f(a)) -> f_flat(down(a)) 543.84/242.04 down(f(b)) -> f_flat(down(b)) 543.84/242.04 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.04 down(f(c)) -> f_flat(down(c)) 543.84/242.04 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.04 down(g(a)) -> g_flat(down(a)) 543.84/242.04 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.04 down(g(b)) -> g_flat(down(b)) 543.84/242.04 down(g(c)) -> g_flat(down(c)) 543.84/242.04 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.04 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.04 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.04 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.04 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.04 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.04 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.04 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.04 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.04 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.04 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.04 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.04 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.04 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.04 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.04 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.04 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.04 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.04 543.84/242.04 The set Q consists of the following terms: 543.84/242.04 543.84/242.04 down(a) 543.84/242.04 down(b) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.04 down(f(a)) 543.84/242.04 down(f(b)) 543.84/242.04 down(f(g(x0))) 543.84/242.04 down(f(c)) 543.84/242.04 down(f(fresh_constant)) 543.84/242.04 down(g(a)) 543.84/242.04 down(g(f(x0))) 543.84/242.04 down(g(b)) 543.84/242.04 down(g(c)) 543.84/242.04 down(g(fresh_constant)) 543.84/242.04 down(f(f(a))) 543.84/242.04 down(f(f(b))) 543.84/242.04 down(f(f(g(x0)))) 543.84/242.04 down(f(f(c))) 543.84/242.04 down(f(f(fresh_constant))) 543.84/242.04 down(g(g(a))) 543.84/242.04 down(g(g(f(x0)))) 543.84/242.04 down(g(g(b))) 543.84/242.04 down(g(g(c))) 543.84/242.04 down(g(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) 543.84/242.04 down(f(f(f(g(x0))))) 543.84/242.04 down(f(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) 543.84/242.04 down(g(g(g(f(x0))))) 543.84/242.04 down(g(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(x0)))))) 543.84/242.04 down(f(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(x0)))))) 543.84/242.04 down(g(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(x0))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(x0))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 f_flat(up(x0)) 543.84/242.04 g_flat(up(x0)) 543.84/242.04 543.84/242.04 We have to consider all minimal (P,Q,R)-chains. 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (919) TransformationProof (EQUIVALENT) 543.84/242.04 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(b))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.04 543.84/242.04 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b)))))))))))) 543.84/242.04 543.84/242.04 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (920) 543.84/242.04 Obligation: 543.84/242.04 Q DP problem: 543.84/242.04 The TRS P consists of the following rules: 543.84/242.04 543.84/242.04 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.04 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.04 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.04 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.04 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.04 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.04 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.04 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.04 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.04 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.04 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.04 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.04 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.04 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.04 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.04 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.04 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.04 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.04 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.04 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.04 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.04 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.04 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.04 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.04 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.04 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.04 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.04 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.04 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.04 543.84/242.04 The TRS R consists of the following rules: 543.84/242.04 543.84/242.04 down(a) -> up(f(a)) 543.84/242.04 down(b) -> up(g(b)) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.04 down(f(a)) -> f_flat(down(a)) 543.84/242.04 down(f(b)) -> f_flat(down(b)) 543.84/242.04 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.04 down(f(c)) -> f_flat(down(c)) 543.84/242.04 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.04 down(g(a)) -> g_flat(down(a)) 543.84/242.04 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.04 down(g(b)) -> g_flat(down(b)) 543.84/242.04 down(g(c)) -> g_flat(down(c)) 543.84/242.04 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.04 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.04 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.04 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.04 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.04 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.04 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.04 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.04 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.04 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.04 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.04 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.04 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.04 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.04 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.04 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.04 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.04 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.04 543.84/242.04 The set Q consists of the following terms: 543.84/242.04 543.84/242.04 down(a) 543.84/242.04 down(b) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.04 down(f(a)) 543.84/242.04 down(f(b)) 543.84/242.04 down(f(g(x0))) 543.84/242.04 down(f(c)) 543.84/242.04 down(f(fresh_constant)) 543.84/242.04 down(g(a)) 543.84/242.04 down(g(f(x0))) 543.84/242.04 down(g(b)) 543.84/242.04 down(g(c)) 543.84/242.04 down(g(fresh_constant)) 543.84/242.04 down(f(f(a))) 543.84/242.04 down(f(f(b))) 543.84/242.04 down(f(f(g(x0)))) 543.84/242.04 down(f(f(c))) 543.84/242.04 down(f(f(fresh_constant))) 543.84/242.04 down(g(g(a))) 543.84/242.04 down(g(g(f(x0)))) 543.84/242.04 down(g(g(b))) 543.84/242.04 down(g(g(c))) 543.84/242.04 down(g(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) 543.84/242.04 down(f(f(f(g(x0))))) 543.84/242.04 down(f(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) 543.84/242.04 down(g(g(g(f(x0))))) 543.84/242.04 down(g(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(x0)))))) 543.84/242.04 down(f(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(x0)))))) 543.84/242.04 down(g(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(x0))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(x0))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 f_flat(up(x0)) 543.84/242.04 g_flat(up(x0)) 543.84/242.04 543.84/242.04 We have to consider all minimal (P,Q,R)-chains. 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (921) TransformationProof (EQUIVALENT) 543.84/242.04 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(g(x0)))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.04 543.84/242.04 (TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0))))))))))))) 543.84/242.04 543.84/242.04 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (922) 543.84/242.04 Obligation: 543.84/242.04 Q DP problem: 543.84/242.04 The TRS P consists of the following rules: 543.84/242.04 543.84/242.04 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.04 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.04 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.04 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.04 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.04 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.04 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.04 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.04 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.04 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.04 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.04 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.04 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.04 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.04 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.04 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.04 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.04 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.04 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.04 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.04 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.04 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.04 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.04 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.04 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.04 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.04 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.04 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.04 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.04 543.84/242.04 The TRS R consists of the following rules: 543.84/242.04 543.84/242.04 down(a) -> up(f(a)) 543.84/242.04 down(b) -> up(g(b)) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.04 down(f(a)) -> f_flat(down(a)) 543.84/242.04 down(f(b)) -> f_flat(down(b)) 543.84/242.04 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.04 down(f(c)) -> f_flat(down(c)) 543.84/242.04 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.04 down(g(a)) -> g_flat(down(a)) 543.84/242.04 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.04 down(g(b)) -> g_flat(down(b)) 543.84/242.04 down(g(c)) -> g_flat(down(c)) 543.84/242.04 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.04 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.04 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.04 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.04 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.04 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.04 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.04 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.04 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.04 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.04 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.04 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.04 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.04 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.04 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.04 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.04 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.04 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.04 543.84/242.04 The set Q consists of the following terms: 543.84/242.04 543.84/242.04 down(a) 543.84/242.04 down(b) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.04 down(f(a)) 543.84/242.04 down(f(b)) 543.84/242.04 down(f(g(x0))) 543.84/242.04 down(f(c)) 543.84/242.04 down(f(fresh_constant)) 543.84/242.04 down(g(a)) 543.84/242.04 down(g(f(x0))) 543.84/242.04 down(g(b)) 543.84/242.04 down(g(c)) 543.84/242.04 down(g(fresh_constant)) 543.84/242.04 down(f(f(a))) 543.84/242.04 down(f(f(b))) 543.84/242.04 down(f(f(g(x0)))) 543.84/242.04 down(f(f(c))) 543.84/242.04 down(f(f(fresh_constant))) 543.84/242.04 down(g(g(a))) 543.84/242.04 down(g(g(f(x0)))) 543.84/242.04 down(g(g(b))) 543.84/242.04 down(g(g(c))) 543.84/242.04 down(g(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) 543.84/242.04 down(f(f(f(g(x0))))) 543.84/242.04 down(f(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) 543.84/242.04 down(g(g(g(f(x0))))) 543.84/242.04 down(g(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(x0)))))) 543.84/242.04 down(f(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(x0)))))) 543.84/242.04 down(g(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(x0))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(x0))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 f_flat(up(x0)) 543.84/242.04 g_flat(up(x0)) 543.84/242.04 543.84/242.04 We have to consider all minimal (P,Q,R)-chains. 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (923) TransformationProof (EQUIVALENT) 543.84/242.04 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.04 543.84/242.04 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.84/242.04 543.84/242.04 543.84/242.04 ---------------------------------------- 543.84/242.04 543.84/242.04 (924) 543.84/242.04 Obligation: 543.84/242.04 Q DP problem: 543.84/242.04 The TRS P consists of the following rules: 543.84/242.04 543.84/242.04 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.04 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.04 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.04 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.04 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.04 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.04 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.04 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.04 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.04 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.04 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.04 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.04 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.04 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.04 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.04 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.04 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.04 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.04 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.04 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.04 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.04 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.04 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.04 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.04 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.04 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.04 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.04 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.04 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.04 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.04 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.04 543.84/242.04 The TRS R consists of the following rules: 543.84/242.04 543.84/242.04 down(a) -> up(f(a)) 543.84/242.04 down(b) -> up(g(b)) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.04 down(f(a)) -> f_flat(down(a)) 543.84/242.04 down(f(b)) -> f_flat(down(b)) 543.84/242.04 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.04 down(f(c)) -> f_flat(down(c)) 543.84/242.04 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.04 down(g(a)) -> g_flat(down(a)) 543.84/242.04 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.04 down(g(b)) -> g_flat(down(b)) 543.84/242.04 down(g(c)) -> g_flat(down(c)) 543.84/242.04 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.04 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.04 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.04 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.04 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.04 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.04 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.04 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.04 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.04 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.04 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.04 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.04 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.04 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.04 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.04 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.04 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.04 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.04 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.04 543.84/242.04 The set Q consists of the following terms: 543.84/242.04 543.84/242.04 down(a) 543.84/242.04 down(b) 543.84/242.04 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.04 down(f(a)) 543.84/242.04 down(f(b)) 543.84/242.04 down(f(g(x0))) 543.84/242.04 down(f(c)) 543.84/242.04 down(f(fresh_constant)) 543.84/242.04 down(g(a)) 543.84/242.04 down(g(f(x0))) 543.84/242.04 down(g(b)) 543.84/242.04 down(g(c)) 543.84/242.04 down(g(fresh_constant)) 543.84/242.04 down(f(f(a))) 543.84/242.04 down(f(f(b))) 543.84/242.04 down(f(f(g(x0)))) 543.84/242.04 down(f(f(c))) 543.84/242.04 down(f(f(fresh_constant))) 543.84/242.04 down(g(g(a))) 543.84/242.04 down(g(g(f(x0)))) 543.84/242.04 down(g(g(b))) 543.84/242.04 down(g(g(c))) 543.84/242.04 down(g(g(fresh_constant))) 543.84/242.04 down(f(f(f(a)))) 543.84/242.04 down(f(f(f(b)))) 543.84/242.04 down(f(f(f(g(x0))))) 543.84/242.04 down(f(f(f(c)))) 543.84/242.04 down(f(f(f(fresh_constant)))) 543.84/242.04 down(g(g(g(a)))) 543.84/242.04 down(g(g(g(f(x0))))) 543.84/242.04 down(g(g(g(b)))) 543.84/242.04 down(g(g(g(c)))) 543.84/242.04 down(g(g(g(fresh_constant)))) 543.84/242.04 down(f(f(f(f(a))))) 543.84/242.04 down(f(f(f(f(b))))) 543.84/242.04 down(f(f(f(f(g(x0)))))) 543.84/242.04 down(f(f(f(f(c))))) 543.84/242.04 down(f(f(f(f(fresh_constant))))) 543.84/242.04 down(g(g(g(g(a))))) 543.84/242.04 down(g(g(g(g(f(x0)))))) 543.84/242.04 down(g(g(g(g(b))))) 543.84/242.04 down(g(g(g(g(c))))) 543.84/242.04 down(g(g(g(g(fresh_constant))))) 543.84/242.04 down(f(f(f(f(f(a)))))) 543.84/242.04 down(f(f(f(f(f(b)))))) 543.84/242.04 down(f(f(f(f(f(g(x0))))))) 543.84/242.04 down(f(f(f(f(f(c)))))) 543.84/242.04 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.04 down(g(g(g(g(g(a)))))) 543.84/242.04 down(g(g(g(g(g(f(x0))))))) 543.84/242.04 down(g(g(g(g(g(b)))))) 543.84/242.04 down(g(g(g(g(g(c)))))) 543.84/242.04 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.04 down(f(f(f(f(f(f(a))))))) 543.84/242.04 down(f(f(f(f(f(f(b))))))) 543.84/242.04 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.04 down(f(f(f(f(f(f(c))))))) 543.84/242.04 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.04 down(g(g(g(g(g(g(a))))))) 543.84/242.04 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.04 down(g(g(g(g(g(g(b))))))) 543.84/242.04 down(g(g(g(g(g(g(c))))))) 543.84/242.04 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.04 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.04 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.04 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.04 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 f_flat(up(x0)) 543.84/242.05 g_flat(up(x0)) 543.84/242.05 543.84/242.05 We have to consider all minimal (P,Q,R)-chains. 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (925) TransformationProof (EQUIVALENT) 543.84/242.05 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.05 543.84/242.05 (TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))),TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.84/242.05 543.84/242.05 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (926) 543.84/242.05 Obligation: 543.84/242.05 Q DP problem: 543.84/242.05 The TRS P consists of the following rules: 543.84/242.05 543.84/242.05 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.05 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.05 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.05 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.05 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.05 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.05 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.05 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.05 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.05 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.05 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.05 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.05 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.05 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.05 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.05 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.05 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.05 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.05 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.05 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.05 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.05 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.05 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.05 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.05 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.05 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.05 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.05 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.05 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.05 543.84/242.05 The TRS R consists of the following rules: 543.84/242.05 543.84/242.05 down(a) -> up(f(a)) 543.84/242.05 down(b) -> up(g(b)) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.05 down(f(a)) -> f_flat(down(a)) 543.84/242.05 down(f(b)) -> f_flat(down(b)) 543.84/242.05 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.05 down(f(c)) -> f_flat(down(c)) 543.84/242.05 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.05 down(g(a)) -> g_flat(down(a)) 543.84/242.05 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.05 down(g(b)) -> g_flat(down(b)) 543.84/242.05 down(g(c)) -> g_flat(down(c)) 543.84/242.05 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.05 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.05 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.05 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.05 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.05 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.05 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.05 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.05 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.05 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.05 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.05 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.05 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.05 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.05 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.05 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.05 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.05 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.05 543.84/242.05 The set Q consists of the following terms: 543.84/242.05 543.84/242.05 down(a) 543.84/242.05 down(b) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.05 down(f(a)) 543.84/242.05 down(f(b)) 543.84/242.05 down(f(g(x0))) 543.84/242.05 down(f(c)) 543.84/242.05 down(f(fresh_constant)) 543.84/242.05 down(g(a)) 543.84/242.05 down(g(f(x0))) 543.84/242.05 down(g(b)) 543.84/242.05 down(g(c)) 543.84/242.05 down(g(fresh_constant)) 543.84/242.05 down(f(f(a))) 543.84/242.05 down(f(f(b))) 543.84/242.05 down(f(f(g(x0)))) 543.84/242.05 down(f(f(c))) 543.84/242.05 down(f(f(fresh_constant))) 543.84/242.05 down(g(g(a))) 543.84/242.05 down(g(g(f(x0)))) 543.84/242.05 down(g(g(b))) 543.84/242.05 down(g(g(c))) 543.84/242.05 down(g(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) 543.84/242.05 down(f(f(f(g(x0))))) 543.84/242.05 down(f(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) 543.84/242.05 down(g(g(g(f(x0))))) 543.84/242.05 down(g(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(x0)))))) 543.84/242.05 down(f(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(x0)))))) 543.84/242.05 down(g(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(x0))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(x0))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 f_flat(up(x0)) 543.84/242.05 g_flat(up(x0)) 543.84/242.05 543.84/242.05 We have to consider all minimal (P,Q,R)-chains. 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (927) TransformationProof (EQUIVALENT) 543.84/242.05 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.05 543.84/242.05 (TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))),TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.84/242.05 543.84/242.05 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (928) 543.84/242.05 Obligation: 543.84/242.05 Q DP problem: 543.84/242.05 The TRS P consists of the following rules: 543.84/242.05 543.84/242.05 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.05 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.05 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.05 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.05 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.05 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.05 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.05 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.05 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.05 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.05 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.05 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.05 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.05 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.05 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.05 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.05 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.05 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.05 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.05 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.05 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.05 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.05 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.05 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.05 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.05 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.05 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.05 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.05 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.05 543.84/242.05 The TRS R consists of the following rules: 543.84/242.05 543.84/242.05 down(a) -> up(f(a)) 543.84/242.05 down(b) -> up(g(b)) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.05 down(f(a)) -> f_flat(down(a)) 543.84/242.05 down(f(b)) -> f_flat(down(b)) 543.84/242.05 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.05 down(f(c)) -> f_flat(down(c)) 543.84/242.05 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.05 down(g(a)) -> g_flat(down(a)) 543.84/242.05 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.05 down(g(b)) -> g_flat(down(b)) 543.84/242.05 down(g(c)) -> g_flat(down(c)) 543.84/242.05 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.05 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.05 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.05 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.05 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.05 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.05 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.05 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.05 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.05 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.05 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.05 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.05 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.05 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.05 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.05 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.05 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.05 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.05 543.84/242.05 The set Q consists of the following terms: 543.84/242.05 543.84/242.05 down(a) 543.84/242.05 down(b) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.05 down(f(a)) 543.84/242.05 down(f(b)) 543.84/242.05 down(f(g(x0))) 543.84/242.05 down(f(c)) 543.84/242.05 down(f(fresh_constant)) 543.84/242.05 down(g(a)) 543.84/242.05 down(g(f(x0))) 543.84/242.05 down(g(b)) 543.84/242.05 down(g(c)) 543.84/242.05 down(g(fresh_constant)) 543.84/242.05 down(f(f(a))) 543.84/242.05 down(f(f(b))) 543.84/242.05 down(f(f(g(x0)))) 543.84/242.05 down(f(f(c))) 543.84/242.05 down(f(f(fresh_constant))) 543.84/242.05 down(g(g(a))) 543.84/242.05 down(g(g(f(x0)))) 543.84/242.05 down(g(g(b))) 543.84/242.05 down(g(g(c))) 543.84/242.05 down(g(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) 543.84/242.05 down(f(f(f(g(x0))))) 543.84/242.05 down(f(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) 543.84/242.05 down(g(g(g(f(x0))))) 543.84/242.05 down(g(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(x0)))))) 543.84/242.05 down(f(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(x0)))))) 543.84/242.05 down(g(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(x0))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(x0))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 f_flat(up(x0)) 543.84/242.05 g_flat(up(x0)) 543.84/242.05 543.84/242.05 We have to consider all minimal (P,Q,R)-chains. 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (929) TransformationProof (EQUIVALENT) 543.84/242.05 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(a))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.05 543.84/242.05 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a)))))))))))) 543.84/242.05 543.84/242.05 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (930) 543.84/242.05 Obligation: 543.84/242.05 Q DP problem: 543.84/242.05 The TRS P consists of the following rules: 543.84/242.05 543.84/242.05 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.05 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.05 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.05 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.05 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.05 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.05 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.05 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.05 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.05 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.05 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.05 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.05 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.05 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.05 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.05 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.05 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.05 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.05 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.05 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.05 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.05 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.05 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.05 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.05 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.05 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.05 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.05 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.05 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.84/242.05 543.84/242.05 The TRS R consists of the following rules: 543.84/242.05 543.84/242.05 down(a) -> up(f(a)) 543.84/242.05 down(b) -> up(g(b)) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.05 down(f(a)) -> f_flat(down(a)) 543.84/242.05 down(f(b)) -> f_flat(down(b)) 543.84/242.05 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.05 down(f(c)) -> f_flat(down(c)) 543.84/242.05 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.05 down(g(a)) -> g_flat(down(a)) 543.84/242.05 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.05 down(g(b)) -> g_flat(down(b)) 543.84/242.05 down(g(c)) -> g_flat(down(c)) 543.84/242.05 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.05 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.05 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.05 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.05 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.05 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.05 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.05 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.05 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.05 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.05 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.05 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.05 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.05 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.05 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.05 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.05 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.05 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.05 543.84/242.05 The set Q consists of the following terms: 543.84/242.05 543.84/242.05 down(a) 543.84/242.05 down(b) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.05 down(f(a)) 543.84/242.05 down(f(b)) 543.84/242.05 down(f(g(x0))) 543.84/242.05 down(f(c)) 543.84/242.05 down(f(fresh_constant)) 543.84/242.05 down(g(a)) 543.84/242.05 down(g(f(x0))) 543.84/242.05 down(g(b)) 543.84/242.05 down(g(c)) 543.84/242.05 down(g(fresh_constant)) 543.84/242.05 down(f(f(a))) 543.84/242.05 down(f(f(b))) 543.84/242.05 down(f(f(g(x0)))) 543.84/242.05 down(f(f(c))) 543.84/242.05 down(f(f(fresh_constant))) 543.84/242.05 down(g(g(a))) 543.84/242.05 down(g(g(f(x0)))) 543.84/242.05 down(g(g(b))) 543.84/242.05 down(g(g(c))) 543.84/242.05 down(g(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) 543.84/242.05 down(f(f(f(g(x0))))) 543.84/242.05 down(f(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) 543.84/242.05 down(g(g(g(f(x0))))) 543.84/242.05 down(g(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(x0)))))) 543.84/242.05 down(f(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(x0)))))) 543.84/242.05 down(g(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(x0))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(x0))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 f_flat(up(x0)) 543.84/242.05 g_flat(up(x0)) 543.84/242.05 543.84/242.05 We have to consider all minimal (P,Q,R)-chains. 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (931) TransformationProof (EQUIVALENT) 543.84/242.05 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(f(x0)))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.05 543.84/242.05 (TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0))))))))))))) 543.84/242.05 543.84/242.05 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (932) 543.84/242.05 Obligation: 543.84/242.05 Q DP problem: 543.84/242.05 The TRS P consists of the following rules: 543.84/242.05 543.84/242.05 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.05 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.05 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.05 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.05 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.05 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.05 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.05 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.05 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.05 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.05 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.05 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.05 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.05 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.05 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.05 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.05 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.05 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.05 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.05 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.05 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.05 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.05 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.05 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.05 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.05 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.05 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.05 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.05 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.84/242.05 543.84/242.05 The TRS R consists of the following rules: 543.84/242.05 543.84/242.05 down(a) -> up(f(a)) 543.84/242.05 down(b) -> up(g(b)) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.05 down(f(a)) -> f_flat(down(a)) 543.84/242.05 down(f(b)) -> f_flat(down(b)) 543.84/242.05 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.05 down(f(c)) -> f_flat(down(c)) 543.84/242.05 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.05 down(g(a)) -> g_flat(down(a)) 543.84/242.05 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.05 down(g(b)) -> g_flat(down(b)) 543.84/242.05 down(g(c)) -> g_flat(down(c)) 543.84/242.05 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.05 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.05 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.05 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.05 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.05 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.05 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.05 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.05 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.05 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.05 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.05 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.05 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.05 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.05 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.05 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.05 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.05 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.05 543.84/242.05 The set Q consists of the following terms: 543.84/242.05 543.84/242.05 down(a) 543.84/242.05 down(b) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.05 down(f(a)) 543.84/242.05 down(f(b)) 543.84/242.05 down(f(g(x0))) 543.84/242.05 down(f(c)) 543.84/242.05 down(f(fresh_constant)) 543.84/242.05 down(g(a)) 543.84/242.05 down(g(f(x0))) 543.84/242.05 down(g(b)) 543.84/242.05 down(g(c)) 543.84/242.05 down(g(fresh_constant)) 543.84/242.05 down(f(f(a))) 543.84/242.05 down(f(f(b))) 543.84/242.05 down(f(f(g(x0)))) 543.84/242.05 down(f(f(c))) 543.84/242.05 down(f(f(fresh_constant))) 543.84/242.05 down(g(g(a))) 543.84/242.05 down(g(g(f(x0)))) 543.84/242.05 down(g(g(b))) 543.84/242.05 down(g(g(c))) 543.84/242.05 down(g(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) 543.84/242.05 down(f(f(f(g(x0))))) 543.84/242.05 down(f(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) 543.84/242.05 down(g(g(g(f(x0))))) 543.84/242.05 down(g(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(x0)))))) 543.84/242.05 down(f(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(x0)))))) 543.84/242.05 down(g(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(x0))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(x0))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 f_flat(up(x0)) 543.84/242.05 g_flat(up(x0)) 543.84/242.05 543.84/242.05 We have to consider all minimal (P,Q,R)-chains. 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (933) TransformationProof (EQUIVALENT) 543.84/242.05 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(c))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.05 543.84/242.05 (TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c)))))))))))) 543.84/242.05 543.84/242.05 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (934) 543.84/242.05 Obligation: 543.84/242.05 Q DP problem: 543.84/242.05 The TRS P consists of the following rules: 543.84/242.05 543.84/242.05 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.05 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.05 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.05 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.05 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.05 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.05 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.05 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.05 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.05 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.05 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.05 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.05 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.05 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.05 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.05 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.05 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.05 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.05 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.05 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.05 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.05 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.05 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) 543.84/242.05 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.05 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.05 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.05 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.05 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.05 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.84/242.05 543.84/242.05 The TRS R consists of the following rules: 543.84/242.05 543.84/242.05 down(a) -> up(f(a)) 543.84/242.05 down(b) -> up(g(b)) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.05 down(f(a)) -> f_flat(down(a)) 543.84/242.05 down(f(b)) -> f_flat(down(b)) 543.84/242.05 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.05 down(f(c)) -> f_flat(down(c)) 543.84/242.05 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.05 down(g(a)) -> g_flat(down(a)) 543.84/242.05 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.05 down(g(b)) -> g_flat(down(b)) 543.84/242.05 down(g(c)) -> g_flat(down(c)) 543.84/242.05 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.05 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.05 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.05 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.05 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.05 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.05 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.05 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.05 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.05 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.05 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.05 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.05 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.05 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.05 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.05 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.05 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.05 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.05 543.84/242.05 The set Q consists of the following terms: 543.84/242.05 543.84/242.05 down(a) 543.84/242.05 down(b) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.05 down(f(a)) 543.84/242.05 down(f(b)) 543.84/242.05 down(f(g(x0))) 543.84/242.05 down(f(c)) 543.84/242.05 down(f(fresh_constant)) 543.84/242.05 down(g(a)) 543.84/242.05 down(g(f(x0))) 543.84/242.05 down(g(b)) 543.84/242.05 down(g(c)) 543.84/242.05 down(g(fresh_constant)) 543.84/242.05 down(f(f(a))) 543.84/242.05 down(f(f(b))) 543.84/242.05 down(f(f(g(x0)))) 543.84/242.05 down(f(f(c))) 543.84/242.05 down(f(f(fresh_constant))) 543.84/242.05 down(g(g(a))) 543.84/242.05 down(g(g(f(x0)))) 543.84/242.05 down(g(g(b))) 543.84/242.05 down(g(g(c))) 543.84/242.05 down(g(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) 543.84/242.05 down(f(f(f(g(x0))))) 543.84/242.05 down(f(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) 543.84/242.05 down(g(g(g(f(x0))))) 543.84/242.05 down(g(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(x0)))))) 543.84/242.05 down(f(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(x0)))))) 543.84/242.05 down(g(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(x0))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(x0))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 f_flat(up(x0)) 543.84/242.05 g_flat(up(x0)) 543.84/242.05 543.84/242.05 We have to consider all minimal (P,Q,R)-chains. 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (935) TransformationProof (EQUIVALENT) 543.84/242.05 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(f(fresh_constant))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.05 543.84/242.05 (TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant)))))))))))) 543.84/242.05 543.84/242.05 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (936) 543.84/242.05 Obligation: 543.84/242.05 Q DP problem: 543.84/242.05 The TRS P consists of the following rules: 543.84/242.05 543.84/242.05 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.05 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.05 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.05 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.05 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.05 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.05 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.05 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.05 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.05 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.05 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.05 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.05 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.05 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.05 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.05 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.05 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.05 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.05 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.05 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.05 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.05 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.05 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.05 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.05 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) 543.84/242.05 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.05 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.05 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.05 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.84/242.05 543.84/242.05 The TRS R consists of the following rules: 543.84/242.05 543.84/242.05 down(a) -> up(f(a)) 543.84/242.05 down(b) -> up(g(b)) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.05 down(f(a)) -> f_flat(down(a)) 543.84/242.05 down(f(b)) -> f_flat(down(b)) 543.84/242.05 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.05 down(f(c)) -> f_flat(down(c)) 543.84/242.05 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.05 down(g(a)) -> g_flat(down(a)) 543.84/242.05 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.05 down(g(b)) -> g_flat(down(b)) 543.84/242.05 down(g(c)) -> g_flat(down(c)) 543.84/242.05 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.05 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.05 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.05 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.05 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.05 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.05 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.05 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.05 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.05 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.05 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.05 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.05 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.05 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.05 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.05 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.05 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.05 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.05 543.84/242.05 The set Q consists of the following terms: 543.84/242.05 543.84/242.05 down(a) 543.84/242.05 down(b) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.05 down(f(a)) 543.84/242.05 down(f(b)) 543.84/242.05 down(f(g(x0))) 543.84/242.05 down(f(c)) 543.84/242.05 down(f(fresh_constant)) 543.84/242.05 down(g(a)) 543.84/242.05 down(g(f(x0))) 543.84/242.05 down(g(b)) 543.84/242.05 down(g(c)) 543.84/242.05 down(g(fresh_constant)) 543.84/242.05 down(f(f(a))) 543.84/242.05 down(f(f(b))) 543.84/242.05 down(f(f(g(x0)))) 543.84/242.05 down(f(f(c))) 543.84/242.05 down(f(f(fresh_constant))) 543.84/242.05 down(g(g(a))) 543.84/242.05 down(g(g(f(x0)))) 543.84/242.05 down(g(g(b))) 543.84/242.05 down(g(g(c))) 543.84/242.05 down(g(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) 543.84/242.05 down(f(f(f(g(x0))))) 543.84/242.05 down(f(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) 543.84/242.05 down(g(g(g(f(x0))))) 543.84/242.05 down(g(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(x0)))))) 543.84/242.05 down(f(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(x0)))))) 543.84/242.05 down(g(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(x0))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(x0))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 f_flat(up(x0)) 543.84/242.05 g_flat(up(x0)) 543.84/242.05 543.84/242.05 We have to consider all minimal (P,Q,R)-chains. 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (937) TransformationProof (EQUIVALENT) 543.84/242.05 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(f_flat(up(f(f(g(b))))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.84/242.05 543.84/242.05 (TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))),TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b)))))))) 543.84/242.05 543.84/242.05 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (938) 543.84/242.05 Obligation: 543.84/242.05 Q DP problem: 543.84/242.05 The TRS P consists of the following rules: 543.84/242.05 543.84/242.05 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.05 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.05 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.05 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.05 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.05 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.05 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.05 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.05 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.05 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.05 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.05 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.05 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.05 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.05 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.05 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.05 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.05 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.05 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.05 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.05 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.05 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.05 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.05 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.05 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.05 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.05 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.05 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.84/242.05 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.84/242.05 543.84/242.05 The TRS R consists of the following rules: 543.84/242.05 543.84/242.05 down(a) -> up(f(a)) 543.84/242.05 down(b) -> up(g(b)) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.05 down(f(a)) -> f_flat(down(a)) 543.84/242.05 down(f(b)) -> f_flat(down(b)) 543.84/242.05 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.05 down(f(c)) -> f_flat(down(c)) 543.84/242.05 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.05 down(g(a)) -> g_flat(down(a)) 543.84/242.05 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.05 down(g(b)) -> g_flat(down(b)) 543.84/242.05 down(g(c)) -> g_flat(down(c)) 543.84/242.05 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.05 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.05 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.05 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.05 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.05 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.05 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.05 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.05 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.05 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.05 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.05 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.05 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.05 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.05 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.05 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.05 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.05 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.05 543.84/242.05 The set Q consists of the following terms: 543.84/242.05 543.84/242.05 down(a) 543.84/242.05 down(b) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.05 down(f(a)) 543.84/242.05 down(f(b)) 543.84/242.05 down(f(g(x0))) 543.84/242.05 down(f(c)) 543.84/242.05 down(f(fresh_constant)) 543.84/242.05 down(g(a)) 543.84/242.05 down(g(f(x0))) 543.84/242.05 down(g(b)) 543.84/242.05 down(g(c)) 543.84/242.05 down(g(fresh_constant)) 543.84/242.05 down(f(f(a))) 543.84/242.05 down(f(f(b))) 543.84/242.05 down(f(f(g(x0)))) 543.84/242.05 down(f(f(c))) 543.84/242.05 down(f(f(fresh_constant))) 543.84/242.05 down(g(g(a))) 543.84/242.05 down(g(g(f(x0)))) 543.84/242.05 down(g(g(b))) 543.84/242.05 down(g(g(c))) 543.84/242.05 down(g(g(fresh_constant))) 543.84/242.05 down(f(f(f(a)))) 543.84/242.05 down(f(f(f(b)))) 543.84/242.05 down(f(f(f(g(x0))))) 543.84/242.05 down(f(f(f(c)))) 543.84/242.05 down(f(f(f(fresh_constant)))) 543.84/242.05 down(g(g(g(a)))) 543.84/242.05 down(g(g(g(f(x0))))) 543.84/242.05 down(g(g(g(b)))) 543.84/242.05 down(g(g(g(c)))) 543.84/242.05 down(g(g(g(fresh_constant)))) 543.84/242.05 down(f(f(f(f(a))))) 543.84/242.05 down(f(f(f(f(b))))) 543.84/242.05 down(f(f(f(f(g(x0)))))) 543.84/242.05 down(f(f(f(f(c))))) 543.84/242.05 down(f(f(f(f(fresh_constant))))) 543.84/242.05 down(g(g(g(g(a))))) 543.84/242.05 down(g(g(g(g(f(x0)))))) 543.84/242.05 down(g(g(g(g(b))))) 543.84/242.05 down(g(g(g(g(c))))) 543.84/242.05 down(g(g(g(g(fresh_constant))))) 543.84/242.05 down(f(f(f(f(f(a)))))) 543.84/242.05 down(f(f(f(f(f(b)))))) 543.84/242.05 down(f(f(f(f(f(g(x0))))))) 543.84/242.05 down(f(f(f(f(f(c)))))) 543.84/242.05 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.05 down(g(g(g(g(g(a)))))) 543.84/242.05 down(g(g(g(g(g(f(x0))))))) 543.84/242.05 down(g(g(g(g(g(b)))))) 543.84/242.05 down(g(g(g(g(g(c)))))) 543.84/242.05 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.05 down(f(f(f(f(f(f(a))))))) 543.84/242.05 down(f(f(f(f(f(f(b))))))) 543.84/242.05 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.05 down(f(f(f(f(f(f(c))))))) 543.84/242.05 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.05 down(g(g(g(g(g(g(a))))))) 543.84/242.05 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.05 down(g(g(g(g(g(g(b))))))) 543.84/242.05 down(g(g(g(g(g(g(c))))))) 543.84/242.05 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.05 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.05 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.05 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.05 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.05 f_flat(up(x0)) 543.84/242.05 g_flat(up(x0)) 543.84/242.05 543.84/242.05 We have to consider all minimal (P,Q,R)-chains. 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (939) TransformationProof (EQUIVALENT) 543.84/242.05 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.05 543.84/242.05 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.84/242.05 543.84/242.05 543.84/242.05 ---------------------------------------- 543.84/242.05 543.84/242.05 (940) 543.84/242.05 Obligation: 543.84/242.05 Q DP problem: 543.84/242.05 The TRS P consists of the following rules: 543.84/242.05 543.84/242.05 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.05 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.05 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.05 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.05 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.05 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.05 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.05 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.05 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.05 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.05 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.05 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.05 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.05 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.05 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.05 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.05 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.05 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.05 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.05 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.05 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.05 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.05 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.05 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.05 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.05 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.05 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.05 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.05 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.84/242.06 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.84/242.06 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.84/242.06 543.84/242.06 The TRS R consists of the following rules: 543.84/242.06 543.84/242.06 down(a) -> up(f(a)) 543.84/242.06 down(b) -> up(g(b)) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.06 down(f(a)) -> f_flat(down(a)) 543.84/242.06 down(f(b)) -> f_flat(down(b)) 543.84/242.06 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.06 down(f(c)) -> f_flat(down(c)) 543.84/242.06 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.06 down(g(a)) -> g_flat(down(a)) 543.84/242.06 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.06 down(g(b)) -> g_flat(down(b)) 543.84/242.06 down(g(c)) -> g_flat(down(c)) 543.84/242.06 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.06 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.06 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.06 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.06 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.06 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.06 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.06 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.06 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.06 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.06 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.06 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.06 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.06 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.06 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.06 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.06 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.06 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.06 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.06 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.06 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.06 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.06 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.06 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.06 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.06 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.06 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.06 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.06 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.06 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.06 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.06 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.06 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.06 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.06 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.06 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.06 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.06 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.06 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.06 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.06 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.06 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.06 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.06 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.06 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.06 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.06 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.06 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.06 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.06 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.06 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.06 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.06 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.06 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.06 543.84/242.06 The set Q consists of the following terms: 543.84/242.06 543.84/242.06 down(a) 543.84/242.06 down(b) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.06 down(f(a)) 543.84/242.06 down(f(b)) 543.84/242.06 down(f(g(x0))) 543.84/242.06 down(f(c)) 543.84/242.06 down(f(fresh_constant)) 543.84/242.06 down(g(a)) 543.84/242.06 down(g(f(x0))) 543.84/242.06 down(g(b)) 543.84/242.06 down(g(c)) 543.84/242.06 down(g(fresh_constant)) 543.84/242.06 down(f(f(a))) 543.84/242.06 down(f(f(b))) 543.84/242.06 down(f(f(g(x0)))) 543.84/242.06 down(f(f(c))) 543.84/242.06 down(f(f(fresh_constant))) 543.84/242.06 down(g(g(a))) 543.84/242.06 down(g(g(f(x0)))) 543.84/242.06 down(g(g(b))) 543.84/242.06 down(g(g(c))) 543.84/242.06 down(g(g(fresh_constant))) 543.84/242.06 down(f(f(f(a)))) 543.84/242.06 down(f(f(f(b)))) 543.84/242.06 down(f(f(f(g(x0))))) 543.84/242.06 down(f(f(f(c)))) 543.84/242.06 down(f(f(f(fresh_constant)))) 543.84/242.06 down(g(g(g(a)))) 543.84/242.06 down(g(g(g(f(x0))))) 543.84/242.06 down(g(g(g(b)))) 543.84/242.06 down(g(g(g(c)))) 543.84/242.06 down(g(g(g(fresh_constant)))) 543.84/242.06 down(f(f(f(f(a))))) 543.84/242.06 down(f(f(f(f(b))))) 543.84/242.06 down(f(f(f(f(g(x0)))))) 543.84/242.06 down(f(f(f(f(c))))) 543.84/242.06 down(f(f(f(f(fresh_constant))))) 543.84/242.06 down(g(g(g(g(a))))) 543.84/242.06 down(g(g(g(g(f(x0)))))) 543.84/242.06 down(g(g(g(g(b))))) 543.84/242.06 down(g(g(g(g(c))))) 543.84/242.06 down(g(g(g(g(fresh_constant))))) 543.84/242.06 down(f(f(f(f(f(a)))))) 543.84/242.06 down(f(f(f(f(f(b)))))) 543.84/242.06 down(f(f(f(f(f(g(x0))))))) 543.84/242.06 down(f(f(f(f(f(c)))))) 543.84/242.06 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.06 down(g(g(g(g(g(a)))))) 543.84/242.06 down(g(g(g(g(g(f(x0))))))) 543.84/242.06 down(g(g(g(g(g(b)))))) 543.84/242.06 down(g(g(g(g(g(c)))))) 543.84/242.06 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.06 down(f(f(f(f(f(f(a))))))) 543.84/242.06 down(f(f(f(f(f(f(b))))))) 543.84/242.06 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.06 down(f(f(f(f(f(f(c))))))) 543.84/242.06 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.06 down(g(g(g(g(g(g(a))))))) 543.84/242.06 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.06 down(g(g(g(g(g(g(b))))))) 543.84/242.06 down(g(g(g(g(g(g(c))))))) 543.84/242.06 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.06 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.06 f_flat(up(x0)) 543.84/242.06 g_flat(up(x0)) 543.84/242.06 543.84/242.06 We have to consider all minimal (P,Q,R)-chains. 543.84/242.06 ---------------------------------------- 543.84/242.06 543.84/242.06 (941) TransformationProof (EQUIVALENT) 543.84/242.06 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.06 543.84/242.06 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.84/242.06 543.84/242.06 543.84/242.06 ---------------------------------------- 543.84/242.06 543.84/242.06 (942) 543.84/242.06 Obligation: 543.84/242.06 Q DP problem: 543.84/242.06 The TRS P consists of the following rules: 543.84/242.06 543.84/242.06 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.06 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.06 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.06 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.06 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.06 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.06 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.06 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.06 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.06 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.06 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.06 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.06 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.06 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.06 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.06 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.06 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.06 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.06 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.06 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.06 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.06 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.06 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.06 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.06 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.06 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.06 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.06 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.84/242.06 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.84/242.06 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.84/242.06 543.84/242.06 The TRS R consists of the following rules: 543.84/242.06 543.84/242.06 down(a) -> up(f(a)) 543.84/242.06 down(b) -> up(g(b)) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.06 down(f(a)) -> f_flat(down(a)) 543.84/242.06 down(f(b)) -> f_flat(down(b)) 543.84/242.06 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.06 down(f(c)) -> f_flat(down(c)) 543.84/242.06 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.06 down(g(a)) -> g_flat(down(a)) 543.84/242.06 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.06 down(g(b)) -> g_flat(down(b)) 543.84/242.06 down(g(c)) -> g_flat(down(c)) 543.84/242.06 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.06 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.06 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.06 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.06 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.06 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.06 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.06 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.06 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.06 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.06 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.06 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.06 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.06 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.06 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.06 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.06 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.06 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.06 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.06 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.06 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.06 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.06 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.06 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.06 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.06 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.06 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.06 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.06 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.06 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.06 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.06 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.06 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.06 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.06 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.06 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.06 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.06 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.06 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.06 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.06 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.06 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.06 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.06 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.06 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.06 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.06 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.06 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.06 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.06 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.06 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.06 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.06 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.06 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.06 543.84/242.06 The set Q consists of the following terms: 543.84/242.06 543.84/242.06 down(a) 543.84/242.06 down(b) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.06 down(f(a)) 543.84/242.06 down(f(b)) 543.84/242.06 down(f(g(x0))) 543.84/242.06 down(f(c)) 543.84/242.06 down(f(fresh_constant)) 543.84/242.06 down(g(a)) 543.84/242.06 down(g(f(x0))) 543.84/242.06 down(g(b)) 543.84/242.06 down(g(c)) 543.84/242.06 down(g(fresh_constant)) 543.84/242.06 down(f(f(a))) 543.84/242.06 down(f(f(b))) 543.84/242.06 down(f(f(g(x0)))) 543.84/242.06 down(f(f(c))) 543.84/242.06 down(f(f(fresh_constant))) 543.84/242.06 down(g(g(a))) 543.84/242.06 down(g(g(f(x0)))) 543.84/242.06 down(g(g(b))) 543.84/242.06 down(g(g(c))) 543.84/242.06 down(g(g(fresh_constant))) 543.84/242.06 down(f(f(f(a)))) 543.84/242.06 down(f(f(f(b)))) 543.84/242.06 down(f(f(f(g(x0))))) 543.84/242.06 down(f(f(f(c)))) 543.84/242.06 down(f(f(f(fresh_constant)))) 543.84/242.06 down(g(g(g(a)))) 543.84/242.06 down(g(g(g(f(x0))))) 543.84/242.06 down(g(g(g(b)))) 543.84/242.06 down(g(g(g(c)))) 543.84/242.06 down(g(g(g(fresh_constant)))) 543.84/242.06 down(f(f(f(f(a))))) 543.84/242.06 down(f(f(f(f(b))))) 543.84/242.06 down(f(f(f(f(g(x0)))))) 543.84/242.06 down(f(f(f(f(c))))) 543.84/242.06 down(f(f(f(f(fresh_constant))))) 543.84/242.06 down(g(g(g(g(a))))) 543.84/242.06 down(g(g(g(g(f(x0)))))) 543.84/242.06 down(g(g(g(g(b))))) 543.84/242.06 down(g(g(g(g(c))))) 543.84/242.06 down(g(g(g(g(fresh_constant))))) 543.84/242.06 down(f(f(f(f(f(a)))))) 543.84/242.06 down(f(f(f(f(f(b)))))) 543.84/242.06 down(f(f(f(f(f(g(x0))))))) 543.84/242.06 down(f(f(f(f(f(c)))))) 543.84/242.06 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.06 down(g(g(g(g(g(a)))))) 543.84/242.06 down(g(g(g(g(g(f(x0))))))) 543.84/242.06 down(g(g(g(g(g(b)))))) 543.84/242.06 down(g(g(g(g(g(c)))))) 543.84/242.06 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.06 down(f(f(f(f(f(f(a))))))) 543.84/242.06 down(f(f(f(f(f(f(b))))))) 543.84/242.06 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.06 down(f(f(f(f(f(f(c))))))) 543.84/242.06 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.06 down(g(g(g(g(g(g(a))))))) 543.84/242.06 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.06 down(g(g(g(g(g(g(b))))))) 543.84/242.06 down(g(g(g(g(g(g(c))))))) 543.84/242.06 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.06 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.06 f_flat(up(x0)) 543.84/242.06 g_flat(up(x0)) 543.84/242.06 543.84/242.06 We have to consider all minimal (P,Q,R)-chains. 543.84/242.06 ---------------------------------------- 543.84/242.06 543.84/242.06 (943) TransformationProof (EQUIVALENT) 543.84/242.06 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.06 543.84/242.06 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.84/242.06 543.84/242.06 543.84/242.06 ---------------------------------------- 543.84/242.06 543.84/242.06 (944) 543.84/242.06 Obligation: 543.84/242.06 Q DP problem: 543.84/242.06 The TRS P consists of the following rules: 543.84/242.06 543.84/242.06 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.06 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.06 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.06 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.06 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.06 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.06 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.06 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.06 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.06 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.06 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.06 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.06 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.06 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.06 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.06 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.06 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.06 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.06 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.06 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.06 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.06 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.06 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.06 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.06 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.06 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.06 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.06 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.84/242.06 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.84/242.06 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.84/242.06 543.84/242.06 The TRS R consists of the following rules: 543.84/242.06 543.84/242.06 down(a) -> up(f(a)) 543.84/242.06 down(b) -> up(g(b)) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.84/242.06 down(f(a)) -> f_flat(down(a)) 543.84/242.06 down(f(b)) -> f_flat(down(b)) 543.84/242.06 down(f(g(y4))) -> f_flat(down(g(y4))) 543.84/242.06 down(f(c)) -> f_flat(down(c)) 543.84/242.06 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.84/242.06 down(g(a)) -> g_flat(down(a)) 543.84/242.06 down(g(f(y6))) -> g_flat(down(f(y6))) 543.84/242.06 down(g(b)) -> g_flat(down(b)) 543.84/242.06 down(g(c)) -> g_flat(down(c)) 543.84/242.06 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.84/242.06 down(f(f(a))) -> f_flat(down(f(a))) 543.84/242.06 down(f(f(b))) -> f_flat(down(f(b))) 543.84/242.06 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.84/242.06 down(f(f(c))) -> f_flat(down(f(c))) 543.84/242.06 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.84/242.06 down(g(g(a))) -> g_flat(down(g(a))) 543.84/242.06 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.84/242.06 down(g(g(b))) -> g_flat(down(g(b))) 543.84/242.06 down(g(g(c))) -> g_flat(down(g(c))) 543.84/242.06 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.84/242.06 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.84/242.06 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.84/242.06 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.84/242.06 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.84/242.06 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.84/242.06 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.84/242.06 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.84/242.06 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.84/242.06 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.84/242.06 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.84/242.06 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.84/242.06 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.84/242.06 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.84/242.06 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.84/242.06 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.84/242.06 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.84/242.06 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.84/242.06 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.84/242.06 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.84/242.06 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.84/242.06 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.84/242.06 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.84/242.06 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.84/242.06 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.84/242.06 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.84/242.06 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.84/242.06 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.84/242.06 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.84/242.06 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.84/242.06 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.84/242.06 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.84/242.06 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.84/242.06 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.84/242.06 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.84/242.06 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.84/242.06 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.84/242.06 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.84/242.06 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.84/242.06 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.84/242.06 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.84/242.06 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.06 g_flat(up(x_1)) -> up(g(x_1)) 543.84/242.06 f_flat(up(x_1)) -> up(f(x_1)) 543.84/242.06 543.84/242.06 The set Q consists of the following terms: 543.84/242.06 543.84/242.06 down(a) 543.84/242.06 down(b) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.84/242.06 down(f(a)) 543.84/242.06 down(f(b)) 543.84/242.06 down(f(g(x0))) 543.84/242.06 down(f(c)) 543.84/242.06 down(f(fresh_constant)) 543.84/242.06 down(g(a)) 543.84/242.06 down(g(f(x0))) 543.84/242.06 down(g(b)) 543.84/242.06 down(g(c)) 543.84/242.06 down(g(fresh_constant)) 543.84/242.06 down(f(f(a))) 543.84/242.06 down(f(f(b))) 543.84/242.06 down(f(f(g(x0)))) 543.84/242.06 down(f(f(c))) 543.84/242.06 down(f(f(fresh_constant))) 543.84/242.06 down(g(g(a))) 543.84/242.06 down(g(g(f(x0)))) 543.84/242.06 down(g(g(b))) 543.84/242.06 down(g(g(c))) 543.84/242.06 down(g(g(fresh_constant))) 543.84/242.06 down(f(f(f(a)))) 543.84/242.06 down(f(f(f(b)))) 543.84/242.06 down(f(f(f(g(x0))))) 543.84/242.06 down(f(f(f(c)))) 543.84/242.06 down(f(f(f(fresh_constant)))) 543.84/242.06 down(g(g(g(a)))) 543.84/242.06 down(g(g(g(f(x0))))) 543.84/242.06 down(g(g(g(b)))) 543.84/242.06 down(g(g(g(c)))) 543.84/242.06 down(g(g(g(fresh_constant)))) 543.84/242.06 down(f(f(f(f(a))))) 543.84/242.06 down(f(f(f(f(b))))) 543.84/242.06 down(f(f(f(f(g(x0)))))) 543.84/242.06 down(f(f(f(f(c))))) 543.84/242.06 down(f(f(f(f(fresh_constant))))) 543.84/242.06 down(g(g(g(g(a))))) 543.84/242.06 down(g(g(g(g(f(x0)))))) 543.84/242.06 down(g(g(g(g(b))))) 543.84/242.06 down(g(g(g(g(c))))) 543.84/242.06 down(g(g(g(g(fresh_constant))))) 543.84/242.06 down(f(f(f(f(f(a)))))) 543.84/242.06 down(f(f(f(f(f(b)))))) 543.84/242.06 down(f(f(f(f(f(g(x0))))))) 543.84/242.06 down(f(f(f(f(f(c)))))) 543.84/242.06 down(f(f(f(f(f(fresh_constant)))))) 543.84/242.06 down(g(g(g(g(g(a)))))) 543.84/242.06 down(g(g(g(g(g(f(x0))))))) 543.84/242.06 down(g(g(g(g(g(b)))))) 543.84/242.06 down(g(g(g(g(g(c)))))) 543.84/242.06 down(g(g(g(g(g(fresh_constant)))))) 543.84/242.06 down(f(f(f(f(f(f(a))))))) 543.84/242.06 down(f(f(f(f(f(f(b))))))) 543.84/242.06 down(f(f(f(f(f(f(g(x0)))))))) 543.84/242.06 down(f(f(f(f(f(f(c))))))) 543.84/242.06 down(f(f(f(f(f(f(fresh_constant))))))) 543.84/242.06 down(g(g(g(g(g(g(a))))))) 543.84/242.06 down(g(g(g(g(g(g(f(x0)))))))) 543.84/242.06 down(g(g(g(g(g(g(b))))))) 543.84/242.06 down(g(g(g(g(g(g(c))))))) 543.84/242.06 down(g(g(g(g(g(g(fresh_constant))))))) 543.84/242.06 down(f(f(f(f(f(f(f(a)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(b)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(g(x0))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(c)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(a)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(f(x0))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(b)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(c)))))))) 543.84/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(a))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(b))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(c))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(a))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(b))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(c))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.84/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.84/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.84/242.06 f_flat(up(x0)) 543.84/242.06 g_flat(up(x0)) 543.84/242.06 543.84/242.06 We have to consider all minimal (P,Q,R)-chains. 543.84/242.06 ---------------------------------------- 543.84/242.06 543.84/242.06 (945) TransformationProof (EQUIVALENT) 543.84/242.06 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.84/242.06 543.84/242.06 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.84/242.06 543.84/242.06 543.84/242.06 ---------------------------------------- 543.84/242.06 543.84/242.06 (946) 543.84/242.06 Obligation: 543.84/242.06 Q DP problem: 543.84/242.06 The TRS P consists of the following rules: 543.84/242.06 543.84/242.06 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.84/242.06 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.84/242.06 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.84/242.06 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.84/242.06 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.84/242.06 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.84/242.06 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.84/242.06 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.84/242.06 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.84/242.06 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.84/242.06 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.84/242.06 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.84/242.06 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.84/242.06 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.84/242.06 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.84/242.06 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.84/242.06 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.84/242.06 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.84/242.06 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.84/242.06 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.84/242.06 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.84/242.06 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.84/242.06 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.84/242.06 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.84/242.06 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.84/242.06 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.84/242.06 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.84/242.06 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.84/242.06 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.84/242.06 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.84/242.06 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.84/242.06 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.06 543.93/242.06 The TRS R consists of the following rules: 543.93/242.06 543.93/242.06 down(a) -> up(f(a)) 543.93/242.06 down(b) -> up(g(b)) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.06 down(f(a)) -> f_flat(down(a)) 543.93/242.06 down(f(b)) -> f_flat(down(b)) 543.93/242.06 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.06 down(f(c)) -> f_flat(down(c)) 543.93/242.06 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.06 down(g(a)) -> g_flat(down(a)) 543.93/242.06 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.06 down(g(b)) -> g_flat(down(b)) 543.93/242.06 down(g(c)) -> g_flat(down(c)) 543.93/242.06 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.06 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.06 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.06 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.06 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.06 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.06 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.06 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.06 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.06 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.06 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.06 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.06 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.06 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.06 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.06 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.06 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.06 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.06 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.06 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.06 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.06 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.06 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.06 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.06 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.06 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.06 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.06 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.06 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.06 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.06 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.06 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.06 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.06 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.06 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.06 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.06 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.06 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.06 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.06 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.06 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.06 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.06 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.06 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.06 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.06 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.06 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.06 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.06 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.06 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.06 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.06 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.06 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.06 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.06 543.93/242.06 The set Q consists of the following terms: 543.93/242.06 543.93/242.06 down(a) 543.93/242.06 down(b) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.06 down(f(a)) 543.93/242.06 down(f(b)) 543.93/242.06 down(f(g(x0))) 543.93/242.06 down(f(c)) 543.93/242.06 down(f(fresh_constant)) 543.93/242.06 down(g(a)) 543.93/242.06 down(g(f(x0))) 543.93/242.06 down(g(b)) 543.93/242.06 down(g(c)) 543.93/242.06 down(g(fresh_constant)) 543.93/242.06 down(f(f(a))) 543.93/242.06 down(f(f(b))) 543.93/242.06 down(f(f(g(x0)))) 543.93/242.06 down(f(f(c))) 543.93/242.06 down(f(f(fresh_constant))) 543.93/242.06 down(g(g(a))) 543.93/242.06 down(g(g(f(x0)))) 543.93/242.06 down(g(g(b))) 543.93/242.06 down(g(g(c))) 543.93/242.06 down(g(g(fresh_constant))) 543.93/242.06 down(f(f(f(a)))) 543.93/242.06 down(f(f(f(b)))) 543.93/242.06 down(f(f(f(g(x0))))) 543.93/242.06 down(f(f(f(c)))) 543.93/242.06 down(f(f(f(fresh_constant)))) 543.93/242.06 down(g(g(g(a)))) 543.93/242.06 down(g(g(g(f(x0))))) 543.93/242.06 down(g(g(g(b)))) 543.93/242.06 down(g(g(g(c)))) 543.93/242.06 down(g(g(g(fresh_constant)))) 543.93/242.06 down(f(f(f(f(a))))) 543.93/242.06 down(f(f(f(f(b))))) 543.93/242.06 down(f(f(f(f(g(x0)))))) 543.93/242.06 down(f(f(f(f(c))))) 543.93/242.06 down(f(f(f(f(fresh_constant))))) 543.93/242.06 down(g(g(g(g(a))))) 543.93/242.06 down(g(g(g(g(f(x0)))))) 543.93/242.06 down(g(g(g(g(b))))) 543.93/242.06 down(g(g(g(g(c))))) 543.93/242.06 down(g(g(g(g(fresh_constant))))) 543.93/242.06 down(f(f(f(f(f(a)))))) 543.93/242.06 down(f(f(f(f(f(b)))))) 543.93/242.06 down(f(f(f(f(f(g(x0))))))) 543.93/242.06 down(f(f(f(f(f(c)))))) 543.93/242.06 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.06 down(g(g(g(g(g(a)))))) 543.93/242.06 down(g(g(g(g(g(f(x0))))))) 543.93/242.06 down(g(g(g(g(g(b)))))) 543.93/242.06 down(g(g(g(g(g(c)))))) 543.93/242.06 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.06 down(f(f(f(f(f(f(a))))))) 543.93/242.06 down(f(f(f(f(f(f(b))))))) 543.93/242.06 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.06 down(f(f(f(f(f(f(c))))))) 543.93/242.06 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.06 down(g(g(g(g(g(g(a))))))) 543.93/242.06 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.06 down(g(g(g(g(g(g(b))))))) 543.93/242.06 down(g(g(g(g(g(g(c))))))) 543.93/242.06 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.06 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.06 f_flat(up(x0)) 543.93/242.06 g_flat(up(x0)) 543.93/242.06 543.93/242.06 We have to consider all minimal (P,Q,R)-chains. 543.93/242.06 ---------------------------------------- 543.93/242.06 543.93/242.06 (947) TransformationProof (EQUIVALENT) 543.93/242.06 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(b))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.06 543.93/242.06 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b)))))))))))) 543.93/242.06 543.93/242.06 543.93/242.06 ---------------------------------------- 543.93/242.06 543.93/242.06 (948) 543.93/242.06 Obligation: 543.93/242.06 Q DP problem: 543.93/242.06 The TRS P consists of the following rules: 543.93/242.06 543.93/242.06 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.06 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.06 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.06 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.06 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.06 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.06 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.06 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.06 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.06 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.06 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.06 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.06 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.06 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.06 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.06 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.06 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.06 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.06 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.06 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.06 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.06 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.06 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.06 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.06 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.93/242.06 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.06 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.93/242.06 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.06 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.06 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.06 543.93/242.06 The TRS R consists of the following rules: 543.93/242.06 543.93/242.06 down(a) -> up(f(a)) 543.93/242.06 down(b) -> up(g(b)) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.06 down(f(a)) -> f_flat(down(a)) 543.93/242.06 down(f(b)) -> f_flat(down(b)) 543.93/242.06 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.06 down(f(c)) -> f_flat(down(c)) 543.93/242.06 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.06 down(g(a)) -> g_flat(down(a)) 543.93/242.06 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.06 down(g(b)) -> g_flat(down(b)) 543.93/242.06 down(g(c)) -> g_flat(down(c)) 543.93/242.06 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.06 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.06 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.06 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.06 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.06 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.06 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.06 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.06 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.06 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.06 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.06 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.06 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.06 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.06 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.06 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.06 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.06 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.06 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.06 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.06 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.06 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.06 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.06 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.06 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.06 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.06 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.06 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.06 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.06 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.06 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.06 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.06 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.06 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.06 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.06 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.06 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.06 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.06 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.06 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.06 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.06 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.06 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.06 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.06 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.06 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.06 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.06 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.06 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.06 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.06 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.06 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.06 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.06 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.06 543.93/242.06 The set Q consists of the following terms: 543.93/242.06 543.93/242.06 down(a) 543.93/242.06 down(b) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.06 down(f(a)) 543.93/242.06 down(f(b)) 543.93/242.06 down(f(g(x0))) 543.93/242.06 down(f(c)) 543.93/242.06 down(f(fresh_constant)) 543.93/242.06 down(g(a)) 543.93/242.06 down(g(f(x0))) 543.93/242.06 down(g(b)) 543.93/242.06 down(g(c)) 543.93/242.06 down(g(fresh_constant)) 543.93/242.06 down(f(f(a))) 543.93/242.06 down(f(f(b))) 543.93/242.06 down(f(f(g(x0)))) 543.93/242.06 down(f(f(c))) 543.93/242.06 down(f(f(fresh_constant))) 543.93/242.06 down(g(g(a))) 543.93/242.06 down(g(g(f(x0)))) 543.93/242.06 down(g(g(b))) 543.93/242.06 down(g(g(c))) 543.93/242.06 down(g(g(fresh_constant))) 543.93/242.06 down(f(f(f(a)))) 543.93/242.06 down(f(f(f(b)))) 543.93/242.06 down(f(f(f(g(x0))))) 543.93/242.06 down(f(f(f(c)))) 543.93/242.06 down(f(f(f(fresh_constant)))) 543.93/242.06 down(g(g(g(a)))) 543.93/242.06 down(g(g(g(f(x0))))) 543.93/242.06 down(g(g(g(b)))) 543.93/242.06 down(g(g(g(c)))) 543.93/242.06 down(g(g(g(fresh_constant)))) 543.93/242.06 down(f(f(f(f(a))))) 543.93/242.06 down(f(f(f(f(b))))) 543.93/242.06 down(f(f(f(f(g(x0)))))) 543.93/242.06 down(f(f(f(f(c))))) 543.93/242.06 down(f(f(f(f(fresh_constant))))) 543.93/242.06 down(g(g(g(g(a))))) 543.93/242.06 down(g(g(g(g(f(x0)))))) 543.93/242.06 down(g(g(g(g(b))))) 543.93/242.06 down(g(g(g(g(c))))) 543.93/242.06 down(g(g(g(g(fresh_constant))))) 543.93/242.06 down(f(f(f(f(f(a)))))) 543.93/242.06 down(f(f(f(f(f(b)))))) 543.93/242.06 down(f(f(f(f(f(g(x0))))))) 543.93/242.06 down(f(f(f(f(f(c)))))) 543.93/242.06 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.06 down(g(g(g(g(g(a)))))) 543.93/242.06 down(g(g(g(g(g(f(x0))))))) 543.93/242.06 down(g(g(g(g(g(b)))))) 543.93/242.06 down(g(g(g(g(g(c)))))) 543.93/242.06 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.06 down(f(f(f(f(f(f(a))))))) 543.93/242.06 down(f(f(f(f(f(f(b))))))) 543.93/242.06 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.06 down(f(f(f(f(f(f(c))))))) 543.93/242.06 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.06 down(g(g(g(g(g(g(a))))))) 543.93/242.06 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.06 down(g(g(g(g(g(g(b))))))) 543.93/242.06 down(g(g(g(g(g(g(c))))))) 543.93/242.06 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.06 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.06 f_flat(up(x0)) 543.93/242.06 g_flat(up(x0)) 543.93/242.06 543.93/242.06 We have to consider all minimal (P,Q,R)-chains. 543.93/242.06 ---------------------------------------- 543.93/242.06 543.93/242.06 (949) TransformationProof (EQUIVALENT) 543.93/242.06 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(c))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.06 543.93/242.06 (TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c)))))))))))) 543.93/242.06 543.93/242.06 543.93/242.06 ---------------------------------------- 543.93/242.06 543.93/242.06 (950) 543.93/242.06 Obligation: 543.93/242.06 Q DP problem: 543.93/242.06 The TRS P consists of the following rules: 543.93/242.06 543.93/242.06 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.06 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.06 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.06 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.06 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.06 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.06 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.06 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.06 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.06 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.06 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.06 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.06 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.06 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.06 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.06 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.06 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.06 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.06 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.06 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.06 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.06 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.06 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.06 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.06 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) 543.93/242.06 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.06 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.93/242.06 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.06 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.06 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.06 543.93/242.06 The TRS R consists of the following rules: 543.93/242.06 543.93/242.06 down(a) -> up(f(a)) 543.93/242.06 down(b) -> up(g(b)) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.06 down(f(a)) -> f_flat(down(a)) 543.93/242.06 down(f(b)) -> f_flat(down(b)) 543.93/242.06 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.06 down(f(c)) -> f_flat(down(c)) 543.93/242.06 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.06 down(g(a)) -> g_flat(down(a)) 543.93/242.06 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.06 down(g(b)) -> g_flat(down(b)) 543.93/242.06 down(g(c)) -> g_flat(down(c)) 543.93/242.06 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.06 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.06 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.06 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.06 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.06 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.06 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.06 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.06 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.06 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.06 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.06 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.06 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.06 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.06 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.06 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.06 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.06 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.06 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.06 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.06 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.06 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.06 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.06 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.06 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.06 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.06 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.06 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.06 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.06 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.06 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.06 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.06 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.06 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.06 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.06 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.06 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.06 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.06 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.06 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.06 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.06 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.06 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.06 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.06 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.06 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.06 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.06 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.06 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.06 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.06 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.06 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.06 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.06 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.06 543.93/242.06 The set Q consists of the following terms: 543.93/242.06 543.93/242.06 down(a) 543.93/242.06 down(b) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.06 down(f(a)) 543.93/242.06 down(f(b)) 543.93/242.06 down(f(g(x0))) 543.93/242.06 down(f(c)) 543.93/242.06 down(f(fresh_constant)) 543.93/242.06 down(g(a)) 543.93/242.06 down(g(f(x0))) 543.93/242.06 down(g(b)) 543.93/242.06 down(g(c)) 543.93/242.06 down(g(fresh_constant)) 543.93/242.06 down(f(f(a))) 543.93/242.06 down(f(f(b))) 543.93/242.06 down(f(f(g(x0)))) 543.93/242.06 down(f(f(c))) 543.93/242.06 down(f(f(fresh_constant))) 543.93/242.06 down(g(g(a))) 543.93/242.06 down(g(g(f(x0)))) 543.93/242.06 down(g(g(b))) 543.93/242.06 down(g(g(c))) 543.93/242.06 down(g(g(fresh_constant))) 543.93/242.06 down(f(f(f(a)))) 543.93/242.06 down(f(f(f(b)))) 543.93/242.06 down(f(f(f(g(x0))))) 543.93/242.06 down(f(f(f(c)))) 543.93/242.06 down(f(f(f(fresh_constant)))) 543.93/242.06 down(g(g(g(a)))) 543.93/242.06 down(g(g(g(f(x0))))) 543.93/242.06 down(g(g(g(b)))) 543.93/242.06 down(g(g(g(c)))) 543.93/242.06 down(g(g(g(fresh_constant)))) 543.93/242.06 down(f(f(f(f(a))))) 543.93/242.06 down(f(f(f(f(b))))) 543.93/242.06 down(f(f(f(f(g(x0)))))) 543.93/242.06 down(f(f(f(f(c))))) 543.93/242.06 down(f(f(f(f(fresh_constant))))) 543.93/242.06 down(g(g(g(g(a))))) 543.93/242.06 down(g(g(g(g(f(x0)))))) 543.93/242.06 down(g(g(g(g(b))))) 543.93/242.06 down(g(g(g(g(c))))) 543.93/242.06 down(g(g(g(g(fresh_constant))))) 543.93/242.06 down(f(f(f(f(f(a)))))) 543.93/242.06 down(f(f(f(f(f(b)))))) 543.93/242.06 down(f(f(f(f(f(g(x0))))))) 543.93/242.06 down(f(f(f(f(f(c)))))) 543.93/242.06 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.06 down(g(g(g(g(g(a)))))) 543.93/242.06 down(g(g(g(g(g(f(x0))))))) 543.93/242.06 down(g(g(g(g(g(b)))))) 543.93/242.06 down(g(g(g(g(g(c)))))) 543.93/242.06 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.06 down(f(f(f(f(f(f(a))))))) 543.93/242.06 down(f(f(f(f(f(f(b))))))) 543.93/242.06 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.06 down(f(f(f(f(f(f(c))))))) 543.93/242.06 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.06 down(g(g(g(g(g(g(a))))))) 543.93/242.06 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.06 down(g(g(g(g(g(g(b))))))) 543.93/242.06 down(g(g(g(g(g(g(c))))))) 543.93/242.06 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.06 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.06 f_flat(up(x0)) 543.93/242.06 g_flat(up(x0)) 543.93/242.06 543.93/242.06 We have to consider all minimal (P,Q,R)-chains. 543.93/242.06 ---------------------------------------- 543.93/242.06 543.93/242.06 (951) TransformationProof (EQUIVALENT) 543.93/242.06 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(g(fresh_constant))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.06 543.93/242.06 (TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant)))))))))))) 543.93/242.06 543.93/242.06 543.93/242.06 ---------------------------------------- 543.93/242.06 543.93/242.06 (952) 543.93/242.06 Obligation: 543.93/242.06 Q DP problem: 543.93/242.06 The TRS P consists of the following rules: 543.93/242.06 543.93/242.06 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.06 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.06 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.06 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.06 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.06 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.06 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.06 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.06 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.06 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.06 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.06 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.06 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.06 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.06 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.06 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.06 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.06 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.06 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.06 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.06 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.06 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.06 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.06 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.06 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.06 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.06 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) 543.93/242.06 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.06 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.06 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.06 543.93/242.06 The TRS R consists of the following rules: 543.93/242.06 543.93/242.06 down(a) -> up(f(a)) 543.93/242.06 down(b) -> up(g(b)) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.06 down(f(a)) -> f_flat(down(a)) 543.93/242.06 down(f(b)) -> f_flat(down(b)) 543.93/242.06 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.06 down(f(c)) -> f_flat(down(c)) 543.93/242.06 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.06 down(g(a)) -> g_flat(down(a)) 543.93/242.06 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.06 down(g(b)) -> g_flat(down(b)) 543.93/242.06 down(g(c)) -> g_flat(down(c)) 543.93/242.06 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.06 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.06 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.06 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.06 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.06 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.06 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.06 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.06 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.06 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.06 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.06 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.06 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.06 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.06 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.06 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.06 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.06 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.06 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.06 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.06 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.06 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.06 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.06 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.06 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.06 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.06 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.06 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.06 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.06 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.06 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.06 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.06 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.06 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.06 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.06 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.06 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.06 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.06 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.06 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.06 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.06 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.06 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.06 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.06 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.06 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.06 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.06 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.06 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.06 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.06 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.06 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.06 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.06 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.06 543.93/242.06 The set Q consists of the following terms: 543.93/242.06 543.93/242.06 down(a) 543.93/242.06 down(b) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.06 down(f(a)) 543.93/242.06 down(f(b)) 543.93/242.06 down(f(g(x0))) 543.93/242.06 down(f(c)) 543.93/242.06 down(f(fresh_constant)) 543.93/242.06 down(g(a)) 543.93/242.06 down(g(f(x0))) 543.93/242.06 down(g(b)) 543.93/242.06 down(g(c)) 543.93/242.06 down(g(fresh_constant)) 543.93/242.06 down(f(f(a))) 543.93/242.06 down(f(f(b))) 543.93/242.06 down(f(f(g(x0)))) 543.93/242.06 down(f(f(c))) 543.93/242.06 down(f(f(fresh_constant))) 543.93/242.06 down(g(g(a))) 543.93/242.06 down(g(g(f(x0)))) 543.93/242.06 down(g(g(b))) 543.93/242.06 down(g(g(c))) 543.93/242.06 down(g(g(fresh_constant))) 543.93/242.06 down(f(f(f(a)))) 543.93/242.06 down(f(f(f(b)))) 543.93/242.06 down(f(f(f(g(x0))))) 543.93/242.06 down(f(f(f(c)))) 543.93/242.06 down(f(f(f(fresh_constant)))) 543.93/242.06 down(g(g(g(a)))) 543.93/242.06 down(g(g(g(f(x0))))) 543.93/242.06 down(g(g(g(b)))) 543.93/242.06 down(g(g(g(c)))) 543.93/242.06 down(g(g(g(fresh_constant)))) 543.93/242.06 down(f(f(f(f(a))))) 543.93/242.06 down(f(f(f(f(b))))) 543.93/242.06 down(f(f(f(f(g(x0)))))) 543.93/242.06 down(f(f(f(f(c))))) 543.93/242.06 down(f(f(f(f(fresh_constant))))) 543.93/242.06 down(g(g(g(g(a))))) 543.93/242.06 down(g(g(g(g(f(x0)))))) 543.93/242.06 down(g(g(g(g(b))))) 543.93/242.06 down(g(g(g(g(c))))) 543.93/242.06 down(g(g(g(g(fresh_constant))))) 543.93/242.06 down(f(f(f(f(f(a)))))) 543.93/242.06 down(f(f(f(f(f(b)))))) 543.93/242.06 down(f(f(f(f(f(g(x0))))))) 543.93/242.06 down(f(f(f(f(f(c)))))) 543.93/242.06 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.06 down(g(g(g(g(g(a)))))) 543.93/242.06 down(g(g(g(g(g(f(x0))))))) 543.93/242.06 down(g(g(g(g(g(b)))))) 543.93/242.06 down(g(g(g(g(g(c)))))) 543.93/242.06 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.06 down(f(f(f(f(f(f(a))))))) 543.93/242.06 down(f(f(f(f(f(f(b))))))) 543.93/242.06 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.06 down(f(f(f(f(f(f(c))))))) 543.93/242.06 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.06 down(g(g(g(g(g(g(a))))))) 543.93/242.06 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.06 down(g(g(g(g(g(g(b))))))) 543.93/242.06 down(g(g(g(g(g(g(c))))))) 543.93/242.06 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.06 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.06 f_flat(up(x0)) 543.93/242.06 g_flat(up(x0)) 543.93/242.06 543.93/242.06 We have to consider all minimal (P,Q,R)-chains. 543.93/242.06 ---------------------------------------- 543.93/242.06 543.93/242.06 (953) TransformationProof (EQUIVALENT) 543.93/242.06 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(g_flat(up(g(g(f(a))))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.93/242.06 543.93/242.06 (TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))),TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a)))))))) 543.93/242.06 543.93/242.06 543.93/242.06 ---------------------------------------- 543.93/242.06 543.93/242.06 (954) 543.93/242.06 Obligation: 543.93/242.06 Q DP problem: 543.93/242.06 The TRS P consists of the following rules: 543.93/242.06 543.93/242.06 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.06 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.06 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.06 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.06 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.06 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.06 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.06 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.06 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.06 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.06 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.06 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.06 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.06 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.06 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.06 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.06 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.06 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.06 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.06 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.06 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.06 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.06 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.06 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.06 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.06 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.06 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.06 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.06 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.06 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.06 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.06 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.06 543.93/242.06 The TRS R consists of the following rules: 543.93/242.06 543.93/242.06 down(a) -> up(f(a)) 543.93/242.06 down(b) -> up(g(b)) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.06 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.06 down(f(a)) -> f_flat(down(a)) 543.93/242.06 down(f(b)) -> f_flat(down(b)) 543.93/242.06 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.06 down(f(c)) -> f_flat(down(c)) 543.93/242.06 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.06 down(g(a)) -> g_flat(down(a)) 543.93/242.06 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.06 down(g(b)) -> g_flat(down(b)) 543.93/242.06 down(g(c)) -> g_flat(down(c)) 543.93/242.06 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.06 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.06 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.06 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.06 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.06 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.06 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.06 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.06 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.06 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.06 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.06 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.06 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.06 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.06 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.06 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.06 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.06 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.06 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.06 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.06 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.06 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.06 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.06 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.06 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.06 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.06 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.06 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.06 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.06 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.06 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.06 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.06 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.06 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.06 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.06 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.06 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.06 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.06 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.06 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.06 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.06 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.06 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.06 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.06 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.06 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.06 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.06 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.06 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.06 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.06 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.06 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.06 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.06 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.06 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.07 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.07 543.93/242.07 The set Q consists of the following terms: 543.93/242.07 543.93/242.07 down(a) 543.93/242.07 down(b) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.07 down(f(a)) 543.93/242.07 down(f(b)) 543.93/242.07 down(f(g(x0))) 543.93/242.07 down(f(c)) 543.93/242.07 down(f(fresh_constant)) 543.93/242.07 down(g(a)) 543.93/242.07 down(g(f(x0))) 543.93/242.07 down(g(b)) 543.93/242.07 down(g(c)) 543.93/242.07 down(g(fresh_constant)) 543.93/242.07 down(f(f(a))) 543.93/242.07 down(f(f(b))) 543.93/242.07 down(f(f(g(x0)))) 543.93/242.07 down(f(f(c))) 543.93/242.07 down(f(f(fresh_constant))) 543.93/242.07 down(g(g(a))) 543.93/242.07 down(g(g(f(x0)))) 543.93/242.07 down(g(g(b))) 543.93/242.07 down(g(g(c))) 543.93/242.07 down(g(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) 543.93/242.07 down(f(f(f(g(x0))))) 543.93/242.07 down(f(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) 543.93/242.07 down(g(g(g(f(x0))))) 543.93/242.07 down(g(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(x0)))))) 543.93/242.07 down(f(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(x0)))))) 543.93/242.07 down(g(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(x0))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(x0))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 f_flat(up(x0)) 543.93/242.07 g_flat(up(x0)) 543.93/242.07 543.93/242.07 We have to consider all minimal (P,Q,R)-chains. 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (955) TransformationProof (EQUIVALENT) 543.93/242.07 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.07 543.93/242.07 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 543.93/242.07 543.93/242.07 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (956) 543.93/242.07 Obligation: 543.93/242.07 Q DP problem: 543.93/242.07 The TRS P consists of the following rules: 543.93/242.07 543.93/242.07 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.07 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.07 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.07 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.07 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.07 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.07 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.07 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.07 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.07 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.07 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.07 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.07 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.07 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.07 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.07 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.07 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.07 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.07 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.07 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.07 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.07 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.07 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.07 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.07 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.07 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.07 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.07 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.07 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.07 543.93/242.07 The TRS R consists of the following rules: 543.93/242.07 543.93/242.07 down(a) -> up(f(a)) 543.93/242.07 down(b) -> up(g(b)) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.07 down(f(a)) -> f_flat(down(a)) 543.93/242.07 down(f(b)) -> f_flat(down(b)) 543.93/242.07 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.07 down(f(c)) -> f_flat(down(c)) 543.93/242.07 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.07 down(g(a)) -> g_flat(down(a)) 543.93/242.07 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.07 down(g(b)) -> g_flat(down(b)) 543.93/242.07 down(g(c)) -> g_flat(down(c)) 543.93/242.07 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.07 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.07 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.07 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.07 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.07 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.07 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.07 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.07 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.07 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.07 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.07 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.07 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.07 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.07 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.07 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.07 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.07 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.07 543.93/242.07 The set Q consists of the following terms: 543.93/242.07 543.93/242.07 down(a) 543.93/242.07 down(b) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.07 down(f(a)) 543.93/242.07 down(f(b)) 543.93/242.07 down(f(g(x0))) 543.93/242.07 down(f(c)) 543.93/242.07 down(f(fresh_constant)) 543.93/242.07 down(g(a)) 543.93/242.07 down(g(f(x0))) 543.93/242.07 down(g(b)) 543.93/242.07 down(g(c)) 543.93/242.07 down(g(fresh_constant)) 543.93/242.07 down(f(f(a))) 543.93/242.07 down(f(f(b))) 543.93/242.07 down(f(f(g(x0)))) 543.93/242.07 down(f(f(c))) 543.93/242.07 down(f(f(fresh_constant))) 543.93/242.07 down(g(g(a))) 543.93/242.07 down(g(g(f(x0)))) 543.93/242.07 down(g(g(b))) 543.93/242.07 down(g(g(c))) 543.93/242.07 down(g(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) 543.93/242.07 down(f(f(f(g(x0))))) 543.93/242.07 down(f(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) 543.93/242.07 down(g(g(g(f(x0))))) 543.93/242.07 down(g(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(x0)))))) 543.93/242.07 down(f(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(x0)))))) 543.93/242.07 down(g(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(x0))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(x0))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 f_flat(up(x0)) 543.93/242.07 g_flat(up(x0)) 543.93/242.07 543.93/242.07 We have to consider all minimal (P,Q,R)-chains. 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (957) TransformationProof (EQUIVALENT) 543.93/242.07 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.07 543.93/242.07 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 543.93/242.07 543.93/242.07 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (958) 543.93/242.07 Obligation: 543.93/242.07 Q DP problem: 543.93/242.07 The TRS P consists of the following rules: 543.93/242.07 543.93/242.07 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.07 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.07 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.07 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.07 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.07 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.07 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.07 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.07 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.07 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.07 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.07 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.07 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.07 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.07 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.07 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.07 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.07 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.07 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.07 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.07 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.07 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.07 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.07 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.07 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.07 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.07 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.07 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.07 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.93/242.07 543.93/242.07 The TRS R consists of the following rules: 543.93/242.07 543.93/242.07 down(a) -> up(f(a)) 543.93/242.07 down(b) -> up(g(b)) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.07 down(f(a)) -> f_flat(down(a)) 543.93/242.07 down(f(b)) -> f_flat(down(b)) 543.93/242.07 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.07 down(f(c)) -> f_flat(down(c)) 543.93/242.07 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.07 down(g(a)) -> g_flat(down(a)) 543.93/242.07 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.07 down(g(b)) -> g_flat(down(b)) 543.93/242.07 down(g(c)) -> g_flat(down(c)) 543.93/242.07 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.07 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.07 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.07 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.07 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.07 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.07 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.07 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.07 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.07 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.07 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.07 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.07 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.07 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.07 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.07 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.07 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.07 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.07 543.93/242.07 The set Q consists of the following terms: 543.93/242.07 543.93/242.07 down(a) 543.93/242.07 down(b) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.07 down(f(a)) 543.93/242.07 down(f(b)) 543.93/242.07 down(f(g(x0))) 543.93/242.07 down(f(c)) 543.93/242.07 down(f(fresh_constant)) 543.93/242.07 down(g(a)) 543.93/242.07 down(g(f(x0))) 543.93/242.07 down(g(b)) 543.93/242.07 down(g(c)) 543.93/242.07 down(g(fresh_constant)) 543.93/242.07 down(f(f(a))) 543.93/242.07 down(f(f(b))) 543.93/242.07 down(f(f(g(x0)))) 543.93/242.07 down(f(f(c))) 543.93/242.07 down(f(f(fresh_constant))) 543.93/242.07 down(g(g(a))) 543.93/242.07 down(g(g(f(x0)))) 543.93/242.07 down(g(g(b))) 543.93/242.07 down(g(g(c))) 543.93/242.07 down(g(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) 543.93/242.07 down(f(f(f(g(x0))))) 543.93/242.07 down(f(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) 543.93/242.07 down(g(g(g(f(x0))))) 543.93/242.07 down(g(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(x0)))))) 543.93/242.07 down(f(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(x0)))))) 543.93/242.07 down(g(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(x0))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(x0))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 f_flat(up(x0)) 543.93/242.07 g_flat(up(x0)) 543.93/242.07 543.93/242.07 We have to consider all minimal (P,Q,R)-chains. 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (959) TransformationProof (EQUIVALENT) 543.93/242.07 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.07 543.93/242.07 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 543.93/242.07 543.93/242.07 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (960) 543.93/242.07 Obligation: 543.93/242.07 Q DP problem: 543.93/242.07 The TRS P consists of the following rules: 543.93/242.07 543.93/242.07 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.07 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.07 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.07 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.07 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.07 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.07 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.07 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.07 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.07 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.07 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.07 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.07 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.07 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.07 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.07 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.07 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.07 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.07 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.07 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.07 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.07 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.07 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.07 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.07 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.07 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.07 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.07 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.07 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.93/242.07 543.93/242.07 The TRS R consists of the following rules: 543.93/242.07 543.93/242.07 down(a) -> up(f(a)) 543.93/242.07 down(b) -> up(g(b)) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.07 down(f(a)) -> f_flat(down(a)) 543.93/242.07 down(f(b)) -> f_flat(down(b)) 543.93/242.07 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.07 down(f(c)) -> f_flat(down(c)) 543.93/242.07 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.07 down(g(a)) -> g_flat(down(a)) 543.93/242.07 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.07 down(g(b)) -> g_flat(down(b)) 543.93/242.07 down(g(c)) -> g_flat(down(c)) 543.93/242.07 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.07 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.07 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.07 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.07 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.07 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.07 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.07 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.07 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.07 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.07 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.07 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.07 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.07 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.07 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.07 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.07 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.07 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.07 543.93/242.07 The set Q consists of the following terms: 543.93/242.07 543.93/242.07 down(a) 543.93/242.07 down(b) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.07 down(f(a)) 543.93/242.07 down(f(b)) 543.93/242.07 down(f(g(x0))) 543.93/242.07 down(f(c)) 543.93/242.07 down(f(fresh_constant)) 543.93/242.07 down(g(a)) 543.93/242.07 down(g(f(x0))) 543.93/242.07 down(g(b)) 543.93/242.07 down(g(c)) 543.93/242.07 down(g(fresh_constant)) 543.93/242.07 down(f(f(a))) 543.93/242.07 down(f(f(b))) 543.93/242.07 down(f(f(g(x0)))) 543.93/242.07 down(f(f(c))) 543.93/242.07 down(f(f(fresh_constant))) 543.93/242.07 down(g(g(a))) 543.93/242.07 down(g(g(f(x0)))) 543.93/242.07 down(g(g(b))) 543.93/242.07 down(g(g(c))) 543.93/242.07 down(g(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) 543.93/242.07 down(f(f(f(g(x0))))) 543.93/242.07 down(f(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) 543.93/242.07 down(g(g(g(f(x0))))) 543.93/242.07 down(g(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(x0)))))) 543.93/242.07 down(f(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(x0)))))) 543.93/242.07 down(g(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(x0))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(x0))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 f_flat(up(x0)) 543.93/242.07 g_flat(up(x0)) 543.93/242.07 543.93/242.07 We have to consider all minimal (P,Q,R)-chains. 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (961) TransformationProof (EQUIVALENT) 543.93/242.07 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.07 543.93/242.07 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 543.93/242.07 543.93/242.07 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (962) 543.93/242.07 Obligation: 543.93/242.07 Q DP problem: 543.93/242.07 The TRS P consists of the following rules: 543.93/242.07 543.93/242.07 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.07 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.07 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.07 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.07 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.07 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.07 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.07 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.07 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.07 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.07 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.07 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.07 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.07 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.07 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.07 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.07 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.07 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.07 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.07 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.07 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.07 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.07 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.07 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.07 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.07 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.07 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.07 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.07 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.93/242.07 543.93/242.07 The TRS R consists of the following rules: 543.93/242.07 543.93/242.07 down(a) -> up(f(a)) 543.93/242.07 down(b) -> up(g(b)) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.07 down(f(a)) -> f_flat(down(a)) 543.93/242.07 down(f(b)) -> f_flat(down(b)) 543.93/242.07 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.07 down(f(c)) -> f_flat(down(c)) 543.93/242.07 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.07 down(g(a)) -> g_flat(down(a)) 543.93/242.07 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.07 down(g(b)) -> g_flat(down(b)) 543.93/242.07 down(g(c)) -> g_flat(down(c)) 543.93/242.07 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.07 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.07 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.07 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.07 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.07 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.07 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.07 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.07 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.07 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.07 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.07 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.07 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.07 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.07 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.07 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.07 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.07 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.07 543.93/242.07 The set Q consists of the following terms: 543.93/242.07 543.93/242.07 down(a) 543.93/242.07 down(b) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.07 down(f(a)) 543.93/242.07 down(f(b)) 543.93/242.07 down(f(g(x0))) 543.93/242.07 down(f(c)) 543.93/242.07 down(f(fresh_constant)) 543.93/242.07 down(g(a)) 543.93/242.07 down(g(f(x0))) 543.93/242.07 down(g(b)) 543.93/242.07 down(g(c)) 543.93/242.07 down(g(fresh_constant)) 543.93/242.07 down(f(f(a))) 543.93/242.07 down(f(f(b))) 543.93/242.07 down(f(f(g(x0)))) 543.93/242.07 down(f(f(c))) 543.93/242.07 down(f(f(fresh_constant))) 543.93/242.07 down(g(g(a))) 543.93/242.07 down(g(g(f(x0)))) 543.93/242.07 down(g(g(b))) 543.93/242.07 down(g(g(c))) 543.93/242.07 down(g(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) 543.93/242.07 down(f(f(f(g(x0))))) 543.93/242.07 down(f(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) 543.93/242.07 down(g(g(g(f(x0))))) 543.93/242.07 down(g(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(x0)))))) 543.93/242.07 down(f(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(x0)))))) 543.93/242.07 down(g(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(x0))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(x0))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 f_flat(up(x0)) 543.93/242.07 g_flat(up(x0)) 543.93/242.07 543.93/242.07 We have to consider all minimal (P,Q,R)-chains. 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (963) TransformationProof (EQUIVALENT) 543.93/242.07 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.07 543.93/242.07 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 543.93/242.07 543.93/242.07 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (964) 543.93/242.07 Obligation: 543.93/242.07 Q DP problem: 543.93/242.07 The TRS P consists of the following rules: 543.93/242.07 543.93/242.07 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.07 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.07 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.07 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.07 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.07 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.07 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.07 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.07 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.07 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.07 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.07 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.07 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.07 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.07 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.07 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.07 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.07 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.07 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.07 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.07 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.07 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.07 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.07 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.07 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.07 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.07 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.07 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.07 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.93/242.07 543.93/242.07 The TRS R consists of the following rules: 543.93/242.07 543.93/242.07 down(a) -> up(f(a)) 543.93/242.07 down(b) -> up(g(b)) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.07 down(f(a)) -> f_flat(down(a)) 543.93/242.07 down(f(b)) -> f_flat(down(b)) 543.93/242.07 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.07 down(f(c)) -> f_flat(down(c)) 543.93/242.07 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.07 down(g(a)) -> g_flat(down(a)) 543.93/242.07 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.07 down(g(b)) -> g_flat(down(b)) 543.93/242.07 down(g(c)) -> g_flat(down(c)) 543.93/242.07 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.07 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.07 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.07 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.07 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.07 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.07 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.07 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.07 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.07 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.07 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.07 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.07 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.07 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.07 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.07 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.07 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.07 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.07 543.93/242.07 The set Q consists of the following terms: 543.93/242.07 543.93/242.07 down(a) 543.93/242.07 down(b) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.07 down(f(a)) 543.93/242.07 down(f(b)) 543.93/242.07 down(f(g(x0))) 543.93/242.07 down(f(c)) 543.93/242.07 down(f(fresh_constant)) 543.93/242.07 down(g(a)) 543.93/242.07 down(g(f(x0))) 543.93/242.07 down(g(b)) 543.93/242.07 down(g(c)) 543.93/242.07 down(g(fresh_constant)) 543.93/242.07 down(f(f(a))) 543.93/242.07 down(f(f(b))) 543.93/242.07 down(f(f(g(x0)))) 543.93/242.07 down(f(f(c))) 543.93/242.07 down(f(f(fresh_constant))) 543.93/242.07 down(g(g(a))) 543.93/242.07 down(g(g(f(x0)))) 543.93/242.07 down(g(g(b))) 543.93/242.07 down(g(g(c))) 543.93/242.07 down(g(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) 543.93/242.07 down(f(f(f(g(x0))))) 543.93/242.07 down(f(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) 543.93/242.07 down(g(g(g(f(x0))))) 543.93/242.07 down(g(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(x0)))))) 543.93/242.07 down(f(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(x0)))))) 543.93/242.07 down(g(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(x0))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(x0))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 f_flat(up(x0)) 543.93/242.07 g_flat(up(x0)) 543.93/242.07 543.93/242.07 We have to consider all minimal (P,Q,R)-chains. 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (965) TransformationProof (EQUIVALENT) 543.93/242.07 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.07 543.93/242.07 (TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))),TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 543.93/242.07 543.93/242.07 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (966) 543.93/242.07 Obligation: 543.93/242.07 Q DP problem: 543.93/242.07 The TRS P consists of the following rules: 543.93/242.07 543.93/242.07 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.07 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.07 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.07 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.07 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.07 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.07 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.07 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.07 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.07 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.07 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.07 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.07 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.07 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.07 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.07 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.07 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.07 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.07 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.07 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.07 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.07 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.07 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.07 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.07 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.07 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.07 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.07 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.07 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.93/242.07 543.93/242.07 The TRS R consists of the following rules: 543.93/242.07 543.93/242.07 down(a) -> up(f(a)) 543.93/242.07 down(b) -> up(g(b)) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.07 down(f(a)) -> f_flat(down(a)) 543.93/242.07 down(f(b)) -> f_flat(down(b)) 543.93/242.07 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.07 down(f(c)) -> f_flat(down(c)) 543.93/242.07 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.07 down(g(a)) -> g_flat(down(a)) 543.93/242.07 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.07 down(g(b)) -> g_flat(down(b)) 543.93/242.07 down(g(c)) -> g_flat(down(c)) 543.93/242.07 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.07 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.07 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.07 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.07 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.07 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.07 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.07 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.07 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.07 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.07 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.07 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.07 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.07 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.07 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.07 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.07 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.07 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.07 543.93/242.07 The set Q consists of the following terms: 543.93/242.07 543.93/242.07 down(a) 543.93/242.07 down(b) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.07 down(f(a)) 543.93/242.07 down(f(b)) 543.93/242.07 down(f(g(x0))) 543.93/242.07 down(f(c)) 543.93/242.07 down(f(fresh_constant)) 543.93/242.07 down(g(a)) 543.93/242.07 down(g(f(x0))) 543.93/242.07 down(g(b)) 543.93/242.07 down(g(c)) 543.93/242.07 down(g(fresh_constant)) 543.93/242.07 down(f(f(a))) 543.93/242.07 down(f(f(b))) 543.93/242.07 down(f(f(g(x0)))) 543.93/242.07 down(f(f(c))) 543.93/242.07 down(f(f(fresh_constant))) 543.93/242.07 down(g(g(a))) 543.93/242.07 down(g(g(f(x0)))) 543.93/242.07 down(g(g(b))) 543.93/242.07 down(g(g(c))) 543.93/242.07 down(g(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) 543.93/242.07 down(f(f(f(g(x0))))) 543.93/242.07 down(f(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) 543.93/242.07 down(g(g(g(f(x0))))) 543.93/242.07 down(g(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(x0)))))) 543.93/242.07 down(f(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(x0)))))) 543.93/242.07 down(g(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(x0))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(x0))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 f_flat(up(x0)) 543.93/242.07 g_flat(up(x0)) 543.93/242.07 543.93/242.07 We have to consider all minimal (P,Q,R)-chains. 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (967) TransformationProof (EQUIVALENT) 543.93/242.07 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.07 543.93/242.07 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 543.93/242.07 543.93/242.07 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (968) 543.93/242.07 Obligation: 543.93/242.07 Q DP problem: 543.93/242.07 The TRS P consists of the following rules: 543.93/242.07 543.93/242.07 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.07 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.07 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.07 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.07 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.07 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.07 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.07 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.07 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.07 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.07 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.07 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.07 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.07 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.07 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.07 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.07 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.07 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.07 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.07 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.07 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.07 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.07 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.07 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.07 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.07 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.07 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.07 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.07 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.93/242.07 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.93/242.07 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.93/242.07 543.93/242.07 The TRS R consists of the following rules: 543.93/242.07 543.93/242.07 down(a) -> up(f(a)) 543.93/242.07 down(b) -> up(g(b)) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.07 down(f(a)) -> f_flat(down(a)) 543.93/242.07 down(f(b)) -> f_flat(down(b)) 543.93/242.07 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.07 down(f(c)) -> f_flat(down(c)) 543.93/242.07 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.07 down(g(a)) -> g_flat(down(a)) 543.93/242.07 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.07 down(g(b)) -> g_flat(down(b)) 543.93/242.07 down(g(c)) -> g_flat(down(c)) 543.93/242.07 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.07 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.07 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.07 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.07 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.07 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.07 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.07 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.07 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.07 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.07 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.07 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.07 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.07 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.07 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.07 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.07 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.07 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.07 543.93/242.07 The set Q consists of the following terms: 543.93/242.07 543.93/242.07 down(a) 543.93/242.07 down(b) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.07 down(f(a)) 543.93/242.07 down(f(b)) 543.93/242.07 down(f(g(x0))) 543.93/242.07 down(f(c)) 543.93/242.07 down(f(fresh_constant)) 543.93/242.07 down(g(a)) 543.93/242.07 down(g(f(x0))) 543.93/242.07 down(g(b)) 543.93/242.07 down(g(c)) 543.93/242.07 down(g(fresh_constant)) 543.93/242.07 down(f(f(a))) 543.93/242.07 down(f(f(b))) 543.93/242.07 down(f(f(g(x0)))) 543.93/242.07 down(f(f(c))) 543.93/242.07 down(f(f(fresh_constant))) 543.93/242.07 down(g(g(a))) 543.93/242.07 down(g(g(f(x0)))) 543.93/242.07 down(g(g(b))) 543.93/242.07 down(g(g(c))) 543.93/242.07 down(g(g(fresh_constant))) 543.93/242.07 down(f(f(f(a)))) 543.93/242.07 down(f(f(f(b)))) 543.93/242.07 down(f(f(f(g(x0))))) 543.93/242.07 down(f(f(f(c)))) 543.93/242.07 down(f(f(f(fresh_constant)))) 543.93/242.07 down(g(g(g(a)))) 543.93/242.07 down(g(g(g(f(x0))))) 543.93/242.07 down(g(g(g(b)))) 543.93/242.07 down(g(g(g(c)))) 543.93/242.07 down(g(g(g(fresh_constant)))) 543.93/242.07 down(f(f(f(f(a))))) 543.93/242.07 down(f(f(f(f(b))))) 543.93/242.07 down(f(f(f(f(g(x0)))))) 543.93/242.07 down(f(f(f(f(c))))) 543.93/242.07 down(f(f(f(f(fresh_constant))))) 543.93/242.07 down(g(g(g(g(a))))) 543.93/242.07 down(g(g(g(g(f(x0)))))) 543.93/242.07 down(g(g(g(g(b))))) 543.93/242.07 down(g(g(g(g(c))))) 543.93/242.07 down(g(g(g(g(fresh_constant))))) 543.93/242.07 down(f(f(f(f(f(a)))))) 543.93/242.07 down(f(f(f(f(f(b)))))) 543.93/242.07 down(f(f(f(f(f(g(x0))))))) 543.93/242.07 down(f(f(f(f(f(c)))))) 543.93/242.07 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.07 down(g(g(g(g(g(a)))))) 543.93/242.07 down(g(g(g(g(g(f(x0))))))) 543.93/242.07 down(g(g(g(g(g(b)))))) 543.93/242.07 down(g(g(g(g(g(c)))))) 543.93/242.07 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.07 down(f(f(f(f(f(f(a))))))) 543.93/242.07 down(f(f(f(f(f(f(b))))))) 543.93/242.07 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.07 down(f(f(f(f(f(f(c))))))) 543.93/242.07 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.07 down(g(g(g(g(g(g(a))))))) 543.93/242.07 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.07 down(g(g(g(g(g(g(b))))))) 543.93/242.07 down(g(g(g(g(g(g(c))))))) 543.93/242.07 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.07 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.07 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.07 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.07 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.07 f_flat(up(x0)) 543.93/242.07 g_flat(up(x0)) 543.93/242.07 543.93/242.07 We have to consider all minimal (P,Q,R)-chains. 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (969) TransformationProof (EQUIVALENT) 543.93/242.07 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(a))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.93/242.07 543.93/242.07 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(up(f(f(f(f(f(f(a))))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(up(f(f(f(f(f(f(a)))))))))) 543.93/242.07 543.93/242.07 543.93/242.07 ---------------------------------------- 543.93/242.07 543.93/242.07 (970) 543.93/242.07 Obligation: 543.93/242.07 Q DP problem: 543.93/242.07 The TRS P consists of the following rules: 543.93/242.07 543.93/242.07 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.07 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.08 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.08 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.08 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.08 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.08 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.08 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.08 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.08 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.08 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.08 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.08 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.08 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.08 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.08 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.08 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.08 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.08 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.08 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.08 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.08 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.08 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.08 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.08 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.08 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.08 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.08 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.08 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.08 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(up(f(f(f(f(f(f(a))))))))) 543.93/242.08 543.93/242.08 The TRS R consists of the following rules: 543.93/242.08 543.93/242.08 down(a) -> up(f(a)) 543.93/242.08 down(b) -> up(g(b)) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.08 down(f(a)) -> f_flat(down(a)) 543.93/242.08 down(f(b)) -> f_flat(down(b)) 543.93/242.08 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.08 down(f(c)) -> f_flat(down(c)) 543.93/242.08 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.08 down(g(a)) -> g_flat(down(a)) 543.93/242.08 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.08 down(g(b)) -> g_flat(down(b)) 543.93/242.08 down(g(c)) -> g_flat(down(c)) 543.93/242.08 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.08 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.08 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.08 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.08 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.08 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.08 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.08 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.08 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.08 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.08 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.08 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.08 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.08 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.08 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.08 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.08 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.08 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.08 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.08 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.08 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.08 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.08 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.08 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.08 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.08 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.08 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.08 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.08 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.08 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.08 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.08 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.08 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.08 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.08 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.08 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.08 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.08 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.08 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.08 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.08 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.08 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.08 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.08 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.08 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.08 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.08 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.08 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.08 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.08 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.08 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.08 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.08 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.08 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.08 543.93/242.08 The set Q consists of the following terms: 543.93/242.08 543.93/242.08 down(a) 543.93/242.08 down(b) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.08 down(f(a)) 543.93/242.08 down(f(b)) 543.93/242.08 down(f(g(x0))) 543.93/242.08 down(f(c)) 543.93/242.08 down(f(fresh_constant)) 543.93/242.08 down(g(a)) 543.93/242.08 down(g(f(x0))) 543.93/242.08 down(g(b)) 543.93/242.08 down(g(c)) 543.93/242.08 down(g(fresh_constant)) 543.93/242.08 down(f(f(a))) 543.93/242.08 down(f(f(b))) 543.93/242.08 down(f(f(g(x0)))) 543.93/242.08 down(f(f(c))) 543.93/242.08 down(f(f(fresh_constant))) 543.93/242.08 down(g(g(a))) 543.93/242.08 down(g(g(f(x0)))) 543.93/242.08 down(g(g(b))) 543.93/242.08 down(g(g(c))) 543.93/242.08 down(g(g(fresh_constant))) 543.93/242.08 down(f(f(f(a)))) 543.93/242.08 down(f(f(f(b)))) 543.93/242.08 down(f(f(f(g(x0))))) 543.93/242.08 down(f(f(f(c)))) 543.93/242.08 down(f(f(f(fresh_constant)))) 543.93/242.08 down(g(g(g(a)))) 543.93/242.08 down(g(g(g(f(x0))))) 543.93/242.08 down(g(g(g(b)))) 543.93/242.08 down(g(g(g(c)))) 543.93/242.08 down(g(g(g(fresh_constant)))) 543.93/242.08 down(f(f(f(f(a))))) 543.93/242.08 down(f(f(f(f(b))))) 543.93/242.08 down(f(f(f(f(g(x0)))))) 543.93/242.08 down(f(f(f(f(c))))) 543.93/242.08 down(f(f(f(f(fresh_constant))))) 543.93/242.08 down(g(g(g(g(a))))) 543.93/242.08 down(g(g(g(g(f(x0)))))) 543.93/242.08 down(g(g(g(g(b))))) 543.93/242.08 down(g(g(g(g(c))))) 543.93/242.08 down(g(g(g(g(fresh_constant))))) 543.93/242.08 down(f(f(f(f(f(a)))))) 543.93/242.08 down(f(f(f(f(f(b)))))) 543.93/242.08 down(f(f(f(f(f(g(x0))))))) 543.93/242.08 down(f(f(f(f(f(c)))))) 543.93/242.08 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.08 down(g(g(g(g(g(a)))))) 543.93/242.08 down(g(g(g(g(g(f(x0))))))) 543.93/242.08 down(g(g(g(g(g(b)))))) 543.93/242.08 down(g(g(g(g(g(c)))))) 543.93/242.08 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.08 down(f(f(f(f(f(f(a))))))) 543.93/242.08 down(f(f(f(f(f(f(b))))))) 543.93/242.08 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.08 down(f(f(f(f(f(f(c))))))) 543.93/242.08 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.08 down(g(g(g(g(g(g(a))))))) 543.93/242.08 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.08 down(g(g(g(g(g(g(b))))))) 543.93/242.08 down(g(g(g(g(g(g(c))))))) 543.93/242.08 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.08 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.08 f_flat(up(x0)) 543.93/242.08 g_flat(up(x0)) 543.93/242.08 543.93/242.08 We have to consider all minimal (P,Q,R)-chains. 543.93/242.08 ---------------------------------------- 543.93/242.08 543.93/242.08 (971) TransformationProof (EQUIVALENT) 543.93/242.08 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(b))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 543.93/242.08 543.93/242.08 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(up(g(g(g(g(g(g(b))))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(up(g(g(g(g(g(g(b)))))))))) 543.93/242.08 543.93/242.08 543.93/242.08 ---------------------------------------- 543.93/242.08 543.93/242.08 (972) 543.93/242.08 Obligation: 543.93/242.08 Q DP problem: 543.93/242.08 The TRS P consists of the following rules: 543.93/242.08 543.93/242.08 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.08 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.08 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.08 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.08 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.08 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.08 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.08 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.08 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.08 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.08 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.08 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.08 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.08 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.08 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.08 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.08 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.08 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.08 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.08 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.08 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.08 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.08 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.08 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.08 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.08 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.08 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.08 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.08 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.08 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(up(f(f(f(f(f(f(a))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(up(g(g(g(g(g(g(b))))))))) 543.93/242.08 543.93/242.08 The TRS R consists of the following rules: 543.93/242.08 543.93/242.08 down(a) -> up(f(a)) 543.93/242.08 down(b) -> up(g(b)) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.08 down(f(a)) -> f_flat(down(a)) 543.93/242.08 down(f(b)) -> f_flat(down(b)) 543.93/242.08 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.08 down(f(c)) -> f_flat(down(c)) 543.93/242.08 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.08 down(g(a)) -> g_flat(down(a)) 543.93/242.08 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.08 down(g(b)) -> g_flat(down(b)) 543.93/242.08 down(g(c)) -> g_flat(down(c)) 543.93/242.08 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.08 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.08 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.08 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.08 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.08 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.08 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.08 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.08 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.08 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.08 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.08 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.08 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.08 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.08 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.08 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.08 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.08 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.08 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.08 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.08 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.08 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.08 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.08 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.08 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.08 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.08 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.08 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.08 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.08 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.08 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.08 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.08 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.08 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.08 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.08 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.08 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.08 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.08 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.08 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.08 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.08 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.08 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.08 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.08 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.08 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.08 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.08 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.08 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.08 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.08 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.08 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.08 g_flat(up(x_1)) -> up(g(x_1)) 543.93/242.08 f_flat(up(x_1)) -> up(f(x_1)) 543.93/242.08 543.93/242.08 The set Q consists of the following terms: 543.93/242.08 543.93/242.08 down(a) 543.93/242.08 down(b) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.93/242.08 down(f(a)) 543.93/242.08 down(f(b)) 543.93/242.08 down(f(g(x0))) 543.93/242.08 down(f(c)) 543.93/242.08 down(f(fresh_constant)) 543.93/242.08 down(g(a)) 543.93/242.08 down(g(f(x0))) 543.93/242.08 down(g(b)) 543.93/242.08 down(g(c)) 543.93/242.08 down(g(fresh_constant)) 543.93/242.08 down(f(f(a))) 543.93/242.08 down(f(f(b))) 543.93/242.08 down(f(f(g(x0)))) 543.93/242.08 down(f(f(c))) 543.93/242.08 down(f(f(fresh_constant))) 543.93/242.08 down(g(g(a))) 543.93/242.08 down(g(g(f(x0)))) 543.93/242.08 down(g(g(b))) 543.93/242.08 down(g(g(c))) 543.93/242.08 down(g(g(fresh_constant))) 543.93/242.08 down(f(f(f(a)))) 543.93/242.08 down(f(f(f(b)))) 543.93/242.08 down(f(f(f(g(x0))))) 543.93/242.08 down(f(f(f(c)))) 543.93/242.08 down(f(f(f(fresh_constant)))) 543.93/242.08 down(g(g(g(a)))) 543.93/242.08 down(g(g(g(f(x0))))) 543.93/242.08 down(g(g(g(b)))) 543.93/242.08 down(g(g(g(c)))) 543.93/242.08 down(g(g(g(fresh_constant)))) 543.93/242.08 down(f(f(f(f(a))))) 543.93/242.08 down(f(f(f(f(b))))) 543.93/242.08 down(f(f(f(f(g(x0)))))) 543.93/242.08 down(f(f(f(f(c))))) 543.93/242.08 down(f(f(f(f(fresh_constant))))) 543.93/242.08 down(g(g(g(g(a))))) 543.93/242.08 down(g(g(g(g(f(x0)))))) 543.93/242.08 down(g(g(g(g(b))))) 543.93/242.08 down(g(g(g(g(c))))) 543.93/242.08 down(g(g(g(g(fresh_constant))))) 543.93/242.08 down(f(f(f(f(f(a)))))) 543.93/242.08 down(f(f(f(f(f(b)))))) 543.93/242.08 down(f(f(f(f(f(g(x0))))))) 543.93/242.08 down(f(f(f(f(f(c)))))) 543.93/242.08 down(f(f(f(f(f(fresh_constant)))))) 543.93/242.08 down(g(g(g(g(g(a)))))) 543.93/242.08 down(g(g(g(g(g(f(x0))))))) 543.93/242.08 down(g(g(g(g(g(b)))))) 543.93/242.08 down(g(g(g(g(g(c)))))) 543.93/242.08 down(g(g(g(g(g(fresh_constant)))))) 543.93/242.08 down(f(f(f(f(f(f(a))))))) 543.93/242.08 down(f(f(f(f(f(f(b))))))) 543.93/242.08 down(f(f(f(f(f(f(g(x0)))))))) 543.93/242.08 down(f(f(f(f(f(f(c))))))) 543.93/242.08 down(f(f(f(f(f(f(fresh_constant))))))) 543.93/242.08 down(g(g(g(g(g(g(a))))))) 543.93/242.08 down(g(g(g(g(g(g(f(x0)))))))) 543.93/242.08 down(g(g(g(g(g(g(b))))))) 543.93/242.08 down(g(g(g(g(g(g(c))))))) 543.93/242.08 down(g(g(g(g(g(g(fresh_constant))))))) 543.93/242.08 down(f(f(f(f(f(f(f(a)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(b)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(g(x0))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(c)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(a)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(f(x0))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(b)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(c)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(a))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(b))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(c))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(a))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(b))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(c))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.93/242.08 f_flat(up(x0)) 543.93/242.08 g_flat(up(x0)) 543.93/242.08 543.93/242.08 We have to consider all minimal (P,Q,R)-chains. 543.93/242.08 ---------------------------------------- 543.93/242.08 543.93/242.08 (973) TransformationProof (EQUIVALENT) 543.93/242.08 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.93/242.08 543.93/242.08 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 543.93/242.08 543.93/242.08 543.93/242.08 ---------------------------------------- 543.93/242.08 543.93/242.08 (974) 543.93/242.08 Obligation: 543.93/242.08 Q DP problem: 543.93/242.08 The TRS P consists of the following rules: 543.93/242.08 543.93/242.08 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.93/242.08 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.93/242.08 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.93/242.08 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.93/242.08 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.93/242.08 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.93/242.08 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.93/242.08 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.93/242.08 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.93/242.08 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.93/242.08 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.93/242.08 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.93/242.08 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.93/242.08 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.93/242.08 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.93/242.08 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.93/242.08 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.93/242.08 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.93/242.08 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.93/242.08 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.93/242.08 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.93/242.08 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.93/242.08 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.93/242.08 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.93/242.08 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.93/242.08 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.93/242.08 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.93/242.08 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.93/242.08 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.93/242.08 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.93/242.08 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(up(f(f(f(f(f(f(a))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(up(g(g(g(g(g(g(b))))))))) 543.93/242.08 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.93/242.08 543.93/242.08 The TRS R consists of the following rules: 543.93/242.08 543.93/242.08 down(a) -> up(f(a)) 543.93/242.08 down(b) -> up(g(b)) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.93/242.08 down(f(a)) -> f_flat(down(a)) 543.93/242.08 down(f(b)) -> f_flat(down(b)) 543.93/242.08 down(f(g(y4))) -> f_flat(down(g(y4))) 543.93/242.08 down(f(c)) -> f_flat(down(c)) 543.93/242.08 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.93/242.08 down(g(a)) -> g_flat(down(a)) 543.93/242.08 down(g(f(y6))) -> g_flat(down(f(y6))) 543.93/242.08 down(g(b)) -> g_flat(down(b)) 543.93/242.08 down(g(c)) -> g_flat(down(c)) 543.93/242.08 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.93/242.08 down(f(f(a))) -> f_flat(down(f(a))) 543.93/242.08 down(f(f(b))) -> f_flat(down(f(b))) 543.93/242.08 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.93/242.08 down(f(f(c))) -> f_flat(down(f(c))) 543.93/242.08 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.93/242.08 down(g(g(a))) -> g_flat(down(g(a))) 543.93/242.08 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.93/242.08 down(g(g(b))) -> g_flat(down(g(b))) 543.93/242.08 down(g(g(c))) -> g_flat(down(g(c))) 543.93/242.08 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.93/242.08 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.93/242.08 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.93/242.08 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.93/242.08 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.93/242.08 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.93/242.08 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.93/242.08 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.93/242.08 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.93/242.08 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.93/242.08 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.93/242.08 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.93/242.08 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.93/242.08 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.93/242.08 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.93/242.08 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.93/242.08 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.93/242.08 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.93/242.08 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.93/242.08 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.93/242.08 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.93/242.08 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.93/242.08 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.93/242.08 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.93/242.08 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.93/242.08 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.93/242.08 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.93/242.08 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.93/242.08 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.93/242.08 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.93/242.08 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.93/242.08 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.93/242.08 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.93/242.08 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.93/242.08 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.93/242.08 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.93/242.08 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.93/242.08 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.93/242.08 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.93/242.08 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.93/242.08 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.93/242.08 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.93/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.93/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.93/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.08 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.08 543.95/242.08 The set Q consists of the following terms: 543.95/242.08 543.95/242.08 down(a) 543.95/242.08 down(b) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.08 down(f(a)) 543.95/242.08 down(f(b)) 543.95/242.08 down(f(g(x0))) 543.95/242.08 down(f(c)) 543.95/242.08 down(f(fresh_constant)) 543.95/242.08 down(g(a)) 543.95/242.08 down(g(f(x0))) 543.95/242.08 down(g(b)) 543.95/242.08 down(g(c)) 543.95/242.08 down(g(fresh_constant)) 543.95/242.08 down(f(f(a))) 543.95/242.08 down(f(f(b))) 543.95/242.08 down(f(f(g(x0)))) 543.95/242.08 down(f(f(c))) 543.95/242.08 down(f(f(fresh_constant))) 543.95/242.08 down(g(g(a))) 543.95/242.08 down(g(g(f(x0)))) 543.95/242.08 down(g(g(b))) 543.95/242.08 down(g(g(c))) 543.95/242.08 down(g(g(fresh_constant))) 543.95/242.08 down(f(f(f(a)))) 543.95/242.08 down(f(f(f(b)))) 543.95/242.08 down(f(f(f(g(x0))))) 543.95/242.08 down(f(f(f(c)))) 543.95/242.08 down(f(f(f(fresh_constant)))) 543.95/242.08 down(g(g(g(a)))) 543.95/242.08 down(g(g(g(f(x0))))) 543.95/242.08 down(g(g(g(b)))) 543.95/242.08 down(g(g(g(c)))) 543.95/242.08 down(g(g(g(fresh_constant)))) 543.95/242.08 down(f(f(f(f(a))))) 543.95/242.08 down(f(f(f(f(b))))) 543.95/242.08 down(f(f(f(f(g(x0)))))) 543.95/242.08 down(f(f(f(f(c))))) 543.95/242.08 down(f(f(f(f(fresh_constant))))) 543.95/242.08 down(g(g(g(g(a))))) 543.95/242.08 down(g(g(g(g(f(x0)))))) 543.95/242.08 down(g(g(g(g(b))))) 543.95/242.08 down(g(g(g(g(c))))) 543.95/242.08 down(g(g(g(g(fresh_constant))))) 543.95/242.08 down(f(f(f(f(f(a)))))) 543.95/242.08 down(f(f(f(f(f(b)))))) 543.95/242.08 down(f(f(f(f(f(g(x0))))))) 543.95/242.08 down(f(f(f(f(f(c)))))) 543.95/242.08 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.08 down(g(g(g(g(g(a)))))) 543.95/242.08 down(g(g(g(g(g(f(x0))))))) 543.95/242.08 down(g(g(g(g(g(b)))))) 543.95/242.08 down(g(g(g(g(g(c)))))) 543.95/242.08 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.08 down(f(f(f(f(f(f(a))))))) 543.95/242.08 down(f(f(f(f(f(f(b))))))) 543.95/242.08 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.08 down(f(f(f(f(f(f(c))))))) 543.95/242.08 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.08 down(g(g(g(g(g(g(a))))))) 543.95/242.08 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.08 down(g(g(g(g(g(g(b))))))) 543.95/242.08 down(g(g(g(g(g(g(c))))))) 543.95/242.08 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.08 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 f_flat(up(x0)) 543.95/242.08 g_flat(up(x0)) 543.95/242.08 543.95/242.08 We have to consider all minimal (P,Q,R)-chains. 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (975) TransformationProof (EQUIVALENT) 543.95/242.08 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.08 543.95/242.08 (TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))),TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 543.95/242.08 543.95/242.08 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (976) 543.95/242.08 Obligation: 543.95/242.08 Q DP problem: 543.95/242.08 The TRS P consists of the following rules: 543.95/242.08 543.95/242.08 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.08 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.08 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.08 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.08 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.08 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.08 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.08 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.08 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.08 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.08 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.08 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.08 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.08 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.08 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.08 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.08 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.08 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.08 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.08 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.08 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.08 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.08 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.08 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.08 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.08 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.08 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.08 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.08 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(up(f(f(f(f(f(f(a))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(up(g(g(g(g(g(g(b))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.08 543.95/242.08 The TRS R consists of the following rules: 543.95/242.08 543.95/242.08 down(a) -> up(f(a)) 543.95/242.08 down(b) -> up(g(b)) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.08 down(f(a)) -> f_flat(down(a)) 543.95/242.08 down(f(b)) -> f_flat(down(b)) 543.95/242.08 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.08 down(f(c)) -> f_flat(down(c)) 543.95/242.08 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.08 down(g(a)) -> g_flat(down(a)) 543.95/242.08 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.08 down(g(b)) -> g_flat(down(b)) 543.95/242.08 down(g(c)) -> g_flat(down(c)) 543.95/242.08 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.08 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.08 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.08 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.08 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.08 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.08 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.08 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.08 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.08 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.08 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.08 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.08 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.08 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.08 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.08 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.08 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.08 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.08 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.08 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.08 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.08 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.08 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.08 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.08 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.08 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.08 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.08 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.08 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.08 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.08 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.08 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.08 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.08 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.08 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.08 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.08 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.08 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.08 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.08 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.08 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.08 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.08 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.08 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.08 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.08 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.08 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.08 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.08 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.08 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.08 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.08 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.08 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.08 543.95/242.08 The set Q consists of the following terms: 543.95/242.08 543.95/242.08 down(a) 543.95/242.08 down(b) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.08 down(f(a)) 543.95/242.08 down(f(b)) 543.95/242.08 down(f(g(x0))) 543.95/242.08 down(f(c)) 543.95/242.08 down(f(fresh_constant)) 543.95/242.08 down(g(a)) 543.95/242.08 down(g(f(x0))) 543.95/242.08 down(g(b)) 543.95/242.08 down(g(c)) 543.95/242.08 down(g(fresh_constant)) 543.95/242.08 down(f(f(a))) 543.95/242.08 down(f(f(b))) 543.95/242.08 down(f(f(g(x0)))) 543.95/242.08 down(f(f(c))) 543.95/242.08 down(f(f(fresh_constant))) 543.95/242.08 down(g(g(a))) 543.95/242.08 down(g(g(f(x0)))) 543.95/242.08 down(g(g(b))) 543.95/242.08 down(g(g(c))) 543.95/242.08 down(g(g(fresh_constant))) 543.95/242.08 down(f(f(f(a)))) 543.95/242.08 down(f(f(f(b)))) 543.95/242.08 down(f(f(f(g(x0))))) 543.95/242.08 down(f(f(f(c)))) 543.95/242.08 down(f(f(f(fresh_constant)))) 543.95/242.08 down(g(g(g(a)))) 543.95/242.08 down(g(g(g(f(x0))))) 543.95/242.08 down(g(g(g(b)))) 543.95/242.08 down(g(g(g(c)))) 543.95/242.08 down(g(g(g(fresh_constant)))) 543.95/242.08 down(f(f(f(f(a))))) 543.95/242.08 down(f(f(f(f(b))))) 543.95/242.08 down(f(f(f(f(g(x0)))))) 543.95/242.08 down(f(f(f(f(c))))) 543.95/242.08 down(f(f(f(f(fresh_constant))))) 543.95/242.08 down(g(g(g(g(a))))) 543.95/242.08 down(g(g(g(g(f(x0)))))) 543.95/242.08 down(g(g(g(g(b))))) 543.95/242.08 down(g(g(g(g(c))))) 543.95/242.08 down(g(g(g(g(fresh_constant))))) 543.95/242.08 down(f(f(f(f(f(a)))))) 543.95/242.08 down(f(f(f(f(f(b)))))) 543.95/242.08 down(f(f(f(f(f(g(x0))))))) 543.95/242.08 down(f(f(f(f(f(c)))))) 543.95/242.08 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.08 down(g(g(g(g(g(a)))))) 543.95/242.08 down(g(g(g(g(g(f(x0))))))) 543.95/242.08 down(g(g(g(g(g(b)))))) 543.95/242.08 down(g(g(g(g(g(c)))))) 543.95/242.08 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.08 down(f(f(f(f(f(f(a))))))) 543.95/242.08 down(f(f(f(f(f(f(b))))))) 543.95/242.08 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.08 down(f(f(f(f(f(f(c))))))) 543.95/242.08 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.08 down(g(g(g(g(g(g(a))))))) 543.95/242.08 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.08 down(g(g(g(g(g(g(b))))))) 543.95/242.08 down(g(g(g(g(g(g(c))))))) 543.95/242.08 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.08 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 f_flat(up(x0)) 543.95/242.08 g_flat(up(x0)) 543.95/242.08 543.95/242.08 We have to consider all minimal (P,Q,R)-chains. 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (977) TransformationProof (EQUIVALENT) 543.95/242.08 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.08 543.95/242.08 (TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c)))))))))),TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c))))))))))) 543.95/242.08 543.95/242.08 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (978) 543.95/242.08 Obligation: 543.95/242.08 Q DP problem: 543.95/242.08 The TRS P consists of the following rules: 543.95/242.08 543.95/242.08 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.08 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.08 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.08 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.08 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.08 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.08 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.08 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.08 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.08 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.08 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.08 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.08 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.08 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.08 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.08 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.08 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.08 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.08 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.08 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.08 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.08 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.08 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.08 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.08 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.08 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.08 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.08 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.08 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(up(f(f(f(f(f(f(a))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(up(g(g(g(g(g(g(b))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(c)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c)))))))))) 543.95/242.08 543.95/242.08 The TRS R consists of the following rules: 543.95/242.08 543.95/242.08 down(a) -> up(f(a)) 543.95/242.08 down(b) -> up(g(b)) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.08 down(f(a)) -> f_flat(down(a)) 543.95/242.08 down(f(b)) -> f_flat(down(b)) 543.95/242.08 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.08 down(f(c)) -> f_flat(down(c)) 543.95/242.08 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.08 down(g(a)) -> g_flat(down(a)) 543.95/242.08 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.08 down(g(b)) -> g_flat(down(b)) 543.95/242.08 down(g(c)) -> g_flat(down(c)) 543.95/242.08 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.08 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.08 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.08 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.08 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.08 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.08 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.08 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.08 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.08 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.08 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.08 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.08 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.08 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.08 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.08 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.08 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.08 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.08 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.08 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.08 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.08 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.08 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.08 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.08 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.08 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.08 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.08 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.08 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.08 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.08 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.08 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.08 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.08 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.08 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.08 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.08 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.08 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.08 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.08 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.08 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.08 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.08 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.08 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.08 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.08 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.08 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.08 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.08 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.08 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.08 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.08 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.08 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.08 543.95/242.08 The set Q consists of the following terms: 543.95/242.08 543.95/242.08 down(a) 543.95/242.08 down(b) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.08 down(f(a)) 543.95/242.08 down(f(b)) 543.95/242.08 down(f(g(x0))) 543.95/242.08 down(f(c)) 543.95/242.08 down(f(fresh_constant)) 543.95/242.08 down(g(a)) 543.95/242.08 down(g(f(x0))) 543.95/242.08 down(g(b)) 543.95/242.08 down(g(c)) 543.95/242.08 down(g(fresh_constant)) 543.95/242.08 down(f(f(a))) 543.95/242.08 down(f(f(b))) 543.95/242.08 down(f(f(g(x0)))) 543.95/242.08 down(f(f(c))) 543.95/242.08 down(f(f(fresh_constant))) 543.95/242.08 down(g(g(a))) 543.95/242.08 down(g(g(f(x0)))) 543.95/242.08 down(g(g(b))) 543.95/242.08 down(g(g(c))) 543.95/242.08 down(g(g(fresh_constant))) 543.95/242.08 down(f(f(f(a)))) 543.95/242.08 down(f(f(f(b)))) 543.95/242.08 down(f(f(f(g(x0))))) 543.95/242.08 down(f(f(f(c)))) 543.95/242.08 down(f(f(f(fresh_constant)))) 543.95/242.08 down(g(g(g(a)))) 543.95/242.08 down(g(g(g(f(x0))))) 543.95/242.08 down(g(g(g(b)))) 543.95/242.08 down(g(g(g(c)))) 543.95/242.08 down(g(g(g(fresh_constant)))) 543.95/242.08 down(f(f(f(f(a))))) 543.95/242.08 down(f(f(f(f(b))))) 543.95/242.08 down(f(f(f(f(g(x0)))))) 543.95/242.08 down(f(f(f(f(c))))) 543.95/242.08 down(f(f(f(f(fresh_constant))))) 543.95/242.08 down(g(g(g(g(a))))) 543.95/242.08 down(g(g(g(g(f(x0)))))) 543.95/242.08 down(g(g(g(g(b))))) 543.95/242.08 down(g(g(g(g(c))))) 543.95/242.08 down(g(g(g(g(fresh_constant))))) 543.95/242.08 down(f(f(f(f(f(a)))))) 543.95/242.08 down(f(f(f(f(f(b)))))) 543.95/242.08 down(f(f(f(f(f(g(x0))))))) 543.95/242.08 down(f(f(f(f(f(c)))))) 543.95/242.08 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.08 down(g(g(g(g(g(a)))))) 543.95/242.08 down(g(g(g(g(g(f(x0))))))) 543.95/242.08 down(g(g(g(g(g(b)))))) 543.95/242.08 down(g(g(g(g(g(c)))))) 543.95/242.08 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.08 down(f(f(f(f(f(f(a))))))) 543.95/242.08 down(f(f(f(f(f(f(b))))))) 543.95/242.08 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.08 down(f(f(f(f(f(f(c))))))) 543.95/242.08 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.08 down(g(g(g(g(g(g(a))))))) 543.95/242.08 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.08 down(g(g(g(g(g(g(b))))))) 543.95/242.08 down(g(g(g(g(g(g(c))))))) 543.95/242.08 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.08 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 f_flat(up(x0)) 543.95/242.08 g_flat(up(x0)) 543.95/242.08 543.95/242.08 We have to consider all minimal (P,Q,R)-chains. 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (979) DependencyGraphProof (EQUIVALENT) 543.95/242.08 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (980) 543.95/242.08 Obligation: 543.95/242.08 Q DP problem: 543.95/242.08 The TRS P consists of the following rules: 543.95/242.08 543.95/242.08 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.08 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.08 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.08 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.08 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.08 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.08 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.08 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.08 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(up(f(f(f(f(f(f(a))))))))) 543.95/242.08 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.08 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.08 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.08 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.08 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.08 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.08 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(up(g(g(g(g(g(g(b))))))))) 543.95/242.08 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.08 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.08 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.08 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.08 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.08 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.08 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.08 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.08 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.08 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.08 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.08 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.08 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.08 543.95/242.08 The TRS R consists of the following rules: 543.95/242.08 543.95/242.08 down(a) -> up(f(a)) 543.95/242.08 down(b) -> up(g(b)) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.08 down(f(a)) -> f_flat(down(a)) 543.95/242.08 down(f(b)) -> f_flat(down(b)) 543.95/242.08 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.08 down(f(c)) -> f_flat(down(c)) 543.95/242.08 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.08 down(g(a)) -> g_flat(down(a)) 543.95/242.08 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.08 down(g(b)) -> g_flat(down(b)) 543.95/242.08 down(g(c)) -> g_flat(down(c)) 543.95/242.08 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.08 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.08 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.08 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.08 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.08 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.08 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.08 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.08 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.08 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.08 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.08 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.08 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.08 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.08 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.08 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.08 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.08 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.08 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.08 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.08 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.08 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.08 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.08 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.08 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.08 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.08 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.08 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.08 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.08 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.08 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.08 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.08 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.08 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.08 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.08 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.08 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.08 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.08 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.08 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.08 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.08 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.08 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.08 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.08 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.08 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.08 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.08 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.08 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.08 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.08 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.08 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.08 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.08 543.95/242.08 The set Q consists of the following terms: 543.95/242.08 543.95/242.08 down(a) 543.95/242.08 down(b) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.08 down(f(a)) 543.95/242.08 down(f(b)) 543.95/242.08 down(f(g(x0))) 543.95/242.08 down(f(c)) 543.95/242.08 down(f(fresh_constant)) 543.95/242.08 down(g(a)) 543.95/242.08 down(g(f(x0))) 543.95/242.08 down(g(b)) 543.95/242.08 down(g(c)) 543.95/242.08 down(g(fresh_constant)) 543.95/242.08 down(f(f(a))) 543.95/242.08 down(f(f(b))) 543.95/242.08 down(f(f(g(x0)))) 543.95/242.08 down(f(f(c))) 543.95/242.08 down(f(f(fresh_constant))) 543.95/242.08 down(g(g(a))) 543.95/242.08 down(g(g(f(x0)))) 543.95/242.08 down(g(g(b))) 543.95/242.08 down(g(g(c))) 543.95/242.08 down(g(g(fresh_constant))) 543.95/242.08 down(f(f(f(a)))) 543.95/242.08 down(f(f(f(b)))) 543.95/242.08 down(f(f(f(g(x0))))) 543.95/242.08 down(f(f(f(c)))) 543.95/242.08 down(f(f(f(fresh_constant)))) 543.95/242.08 down(g(g(g(a)))) 543.95/242.08 down(g(g(g(f(x0))))) 543.95/242.08 down(g(g(g(b)))) 543.95/242.08 down(g(g(g(c)))) 543.95/242.08 down(g(g(g(fresh_constant)))) 543.95/242.08 down(f(f(f(f(a))))) 543.95/242.08 down(f(f(f(f(b))))) 543.95/242.08 down(f(f(f(f(g(x0)))))) 543.95/242.08 down(f(f(f(f(c))))) 543.95/242.08 down(f(f(f(f(fresh_constant))))) 543.95/242.08 down(g(g(g(g(a))))) 543.95/242.08 down(g(g(g(g(f(x0)))))) 543.95/242.08 down(g(g(g(g(b))))) 543.95/242.08 down(g(g(g(g(c))))) 543.95/242.08 down(g(g(g(g(fresh_constant))))) 543.95/242.08 down(f(f(f(f(f(a)))))) 543.95/242.08 down(f(f(f(f(f(b)))))) 543.95/242.08 down(f(f(f(f(f(g(x0))))))) 543.95/242.08 down(f(f(f(f(f(c)))))) 543.95/242.08 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.08 down(g(g(g(g(g(a)))))) 543.95/242.08 down(g(g(g(g(g(f(x0))))))) 543.95/242.08 down(g(g(g(g(g(b)))))) 543.95/242.08 down(g(g(g(g(g(c)))))) 543.95/242.08 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.08 down(f(f(f(f(f(f(a))))))) 543.95/242.08 down(f(f(f(f(f(f(b))))))) 543.95/242.08 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.08 down(f(f(f(f(f(f(c))))))) 543.95/242.08 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.08 down(g(g(g(g(g(g(a))))))) 543.95/242.08 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.08 down(g(g(g(g(g(g(b))))))) 543.95/242.08 down(g(g(g(g(g(g(c))))))) 543.95/242.08 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.08 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 f_flat(up(x0)) 543.95/242.08 g_flat(up(x0)) 543.95/242.08 543.95/242.08 We have to consider all minimal (P,Q,R)-chains. 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (981) TransformationProof (EQUIVALENT) 543.95/242.08 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(f_flat(up(f(f(f(f(f(f(a))))))))) at position [0] we obtained the following new rules [LPAR04]: 543.95/242.08 543.95/242.08 (TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))),TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 543.95/242.08 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (982) 543.95/242.08 Obligation: 543.95/242.08 Q DP problem: 543.95/242.08 The TRS P consists of the following rules: 543.95/242.08 543.95/242.08 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.08 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.08 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.08 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.08 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.08 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.08 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.08 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.08 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.08 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.08 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.08 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.08 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.08 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.08 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.08 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(up(g(g(g(g(g(g(b))))))))) 543.95/242.08 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.08 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.08 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.08 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.08 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.08 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.08 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.08 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.08 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.08 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.08 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.08 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.08 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 543.95/242.08 The TRS R consists of the following rules: 543.95/242.08 543.95/242.08 down(a) -> up(f(a)) 543.95/242.08 down(b) -> up(g(b)) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.08 down(f(a)) -> f_flat(down(a)) 543.95/242.08 down(f(b)) -> f_flat(down(b)) 543.95/242.08 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.08 down(f(c)) -> f_flat(down(c)) 543.95/242.08 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.08 down(g(a)) -> g_flat(down(a)) 543.95/242.08 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.08 down(g(b)) -> g_flat(down(b)) 543.95/242.08 down(g(c)) -> g_flat(down(c)) 543.95/242.08 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.08 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.08 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.08 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.08 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.08 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.08 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.08 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.08 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.08 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.08 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.08 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.08 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.08 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.08 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.08 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.08 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.08 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.08 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.08 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.08 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.08 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.08 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.08 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.08 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.08 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.08 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.08 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.08 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.08 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.08 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.08 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.08 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.08 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.08 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.08 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.08 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.08 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.08 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.08 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.08 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.08 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.08 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.08 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.08 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.08 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.08 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.08 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.08 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.08 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.08 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.08 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.08 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.08 543.95/242.08 The set Q consists of the following terms: 543.95/242.08 543.95/242.08 down(a) 543.95/242.08 down(b) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.08 down(f(a)) 543.95/242.08 down(f(b)) 543.95/242.08 down(f(g(x0))) 543.95/242.08 down(f(c)) 543.95/242.08 down(f(fresh_constant)) 543.95/242.08 down(g(a)) 543.95/242.08 down(g(f(x0))) 543.95/242.08 down(g(b)) 543.95/242.08 down(g(c)) 543.95/242.08 down(g(fresh_constant)) 543.95/242.08 down(f(f(a))) 543.95/242.08 down(f(f(b))) 543.95/242.08 down(f(f(g(x0)))) 543.95/242.08 down(f(f(c))) 543.95/242.08 down(f(f(fresh_constant))) 543.95/242.08 down(g(g(a))) 543.95/242.08 down(g(g(f(x0)))) 543.95/242.08 down(g(g(b))) 543.95/242.08 down(g(g(c))) 543.95/242.08 down(g(g(fresh_constant))) 543.95/242.08 down(f(f(f(a)))) 543.95/242.08 down(f(f(f(b)))) 543.95/242.08 down(f(f(f(g(x0))))) 543.95/242.08 down(f(f(f(c)))) 543.95/242.08 down(f(f(f(fresh_constant)))) 543.95/242.08 down(g(g(g(a)))) 543.95/242.08 down(g(g(g(f(x0))))) 543.95/242.08 down(g(g(g(b)))) 543.95/242.08 down(g(g(g(c)))) 543.95/242.08 down(g(g(g(fresh_constant)))) 543.95/242.08 down(f(f(f(f(a))))) 543.95/242.08 down(f(f(f(f(b))))) 543.95/242.08 down(f(f(f(f(g(x0)))))) 543.95/242.08 down(f(f(f(f(c))))) 543.95/242.08 down(f(f(f(f(fresh_constant))))) 543.95/242.08 down(g(g(g(g(a))))) 543.95/242.08 down(g(g(g(g(f(x0)))))) 543.95/242.08 down(g(g(g(g(b))))) 543.95/242.08 down(g(g(g(g(c))))) 543.95/242.08 down(g(g(g(g(fresh_constant))))) 543.95/242.08 down(f(f(f(f(f(a)))))) 543.95/242.08 down(f(f(f(f(f(b)))))) 543.95/242.08 down(f(f(f(f(f(g(x0))))))) 543.95/242.08 down(f(f(f(f(f(c)))))) 543.95/242.08 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.08 down(g(g(g(g(g(a)))))) 543.95/242.08 down(g(g(g(g(g(f(x0))))))) 543.95/242.08 down(g(g(g(g(g(b)))))) 543.95/242.08 down(g(g(g(g(g(c)))))) 543.95/242.08 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.08 down(f(f(f(f(f(f(a))))))) 543.95/242.08 down(f(f(f(f(f(f(b))))))) 543.95/242.08 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.08 down(f(f(f(f(f(f(c))))))) 543.95/242.08 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.08 down(g(g(g(g(g(g(a))))))) 543.95/242.08 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.08 down(g(g(g(g(g(g(b))))))) 543.95/242.08 down(g(g(g(g(g(g(c))))))) 543.95/242.08 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.08 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.08 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.08 f_flat(up(x0)) 543.95/242.08 g_flat(up(x0)) 543.95/242.08 543.95/242.08 We have to consider all minimal (P,Q,R)-chains. 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (983) TransformationProof (EQUIVALENT) 543.95/242.08 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(g_flat(up(g(g(g(g(g(g(b))))))))) at position [0] we obtained the following new rules [LPAR04]: 543.95/242.08 543.95/242.08 (TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))),TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b)))))))))) 543.95/242.08 543.95/242.08 543.95/242.08 ---------------------------------------- 543.95/242.08 543.95/242.08 (984) 543.95/242.08 Obligation: 543.95/242.08 Q DP problem: 543.95/242.08 The TRS P consists of the following rules: 543.95/242.08 543.95/242.08 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.08 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.08 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.08 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.08 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.08 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.08 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.08 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.08 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.08 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.08 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.08 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.08 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.08 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.08 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.08 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.08 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.08 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.08 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.08 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.08 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.08 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.08 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.08 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.08 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.08 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.08 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.08 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.08 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.08 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.08 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.08 543.95/242.08 The TRS R consists of the following rules: 543.95/242.08 543.95/242.08 down(a) -> up(f(a)) 543.95/242.08 down(b) -> up(g(b)) 543.95/242.08 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.08 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.08 down(f(a)) -> f_flat(down(a)) 543.95/242.08 down(f(b)) -> f_flat(down(b)) 543.95/242.08 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.08 down(f(c)) -> f_flat(down(c)) 543.95/242.08 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.08 down(g(a)) -> g_flat(down(a)) 543.95/242.08 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.08 down(g(b)) -> g_flat(down(b)) 543.95/242.08 down(g(c)) -> g_flat(down(c)) 543.95/242.08 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.09 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.09 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.09 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.09 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.09 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.09 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.09 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.09 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.09 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.09 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.09 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.09 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.09 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.09 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.09 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.09 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.09 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.09 543.95/242.09 The set Q consists of the following terms: 543.95/242.09 543.95/242.09 down(a) 543.95/242.09 down(b) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.09 down(f(a)) 543.95/242.09 down(f(b)) 543.95/242.09 down(f(g(x0))) 543.95/242.09 down(f(c)) 543.95/242.09 down(f(fresh_constant)) 543.95/242.09 down(g(a)) 543.95/242.09 down(g(f(x0))) 543.95/242.09 down(g(b)) 543.95/242.09 down(g(c)) 543.95/242.09 down(g(fresh_constant)) 543.95/242.09 down(f(f(a))) 543.95/242.09 down(f(f(b))) 543.95/242.09 down(f(f(g(x0)))) 543.95/242.09 down(f(f(c))) 543.95/242.09 down(f(f(fresh_constant))) 543.95/242.09 down(g(g(a))) 543.95/242.09 down(g(g(f(x0)))) 543.95/242.09 down(g(g(b))) 543.95/242.09 down(g(g(c))) 543.95/242.09 down(g(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) 543.95/242.09 down(f(f(f(g(x0))))) 543.95/242.09 down(f(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) 543.95/242.09 down(g(g(g(f(x0))))) 543.95/242.09 down(g(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(x0)))))) 543.95/242.09 down(f(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(x0)))))) 543.95/242.09 down(g(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(x0))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(x0))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 f_flat(up(x0)) 543.95/242.09 g_flat(up(x0)) 543.95/242.09 543.95/242.09 We have to consider all minimal (P,Q,R)-chains. 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (985) TransformationProof (EQUIVALENT) 543.95/242.09 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.09 543.95/242.09 (TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant)))))))))),TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant))))))))))) 543.95/242.09 543.95/242.09 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (986) 543.95/242.09 Obligation: 543.95/242.09 Q DP problem: 543.95/242.09 The TRS P consists of the following rules: 543.95/242.09 543.95/242.09 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.09 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.09 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.09 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.09 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.09 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.09 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.09 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.09 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.09 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.09 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.09 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.09 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.09 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.09 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.09 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.09 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.09 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.09 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.09 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.09 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.09 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.09 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.09 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.09 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.09 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.09 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.09 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant)))))))))) 543.95/242.09 543.95/242.09 The TRS R consists of the following rules: 543.95/242.09 543.95/242.09 down(a) -> up(f(a)) 543.95/242.09 down(b) -> up(g(b)) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.09 down(f(a)) -> f_flat(down(a)) 543.95/242.09 down(f(b)) -> f_flat(down(b)) 543.95/242.09 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.09 down(f(c)) -> f_flat(down(c)) 543.95/242.09 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.09 down(g(a)) -> g_flat(down(a)) 543.95/242.09 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.09 down(g(b)) -> g_flat(down(b)) 543.95/242.09 down(g(c)) -> g_flat(down(c)) 543.95/242.09 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.09 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.09 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.09 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.09 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.09 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.09 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.09 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.09 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.09 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.09 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.09 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.09 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.09 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.09 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.09 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.09 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.09 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.09 543.95/242.09 The set Q consists of the following terms: 543.95/242.09 543.95/242.09 down(a) 543.95/242.09 down(b) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.09 down(f(a)) 543.95/242.09 down(f(b)) 543.95/242.09 down(f(g(x0))) 543.95/242.09 down(f(c)) 543.95/242.09 down(f(fresh_constant)) 543.95/242.09 down(g(a)) 543.95/242.09 down(g(f(x0))) 543.95/242.09 down(g(b)) 543.95/242.09 down(g(c)) 543.95/242.09 down(g(fresh_constant)) 543.95/242.09 down(f(f(a))) 543.95/242.09 down(f(f(b))) 543.95/242.09 down(f(f(g(x0)))) 543.95/242.09 down(f(f(c))) 543.95/242.09 down(f(f(fresh_constant))) 543.95/242.09 down(g(g(a))) 543.95/242.09 down(g(g(f(x0)))) 543.95/242.09 down(g(g(b))) 543.95/242.09 down(g(g(c))) 543.95/242.09 down(g(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) 543.95/242.09 down(f(f(f(g(x0))))) 543.95/242.09 down(f(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) 543.95/242.09 down(g(g(g(f(x0))))) 543.95/242.09 down(g(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(x0)))))) 543.95/242.09 down(f(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(x0)))))) 543.95/242.09 down(g(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(x0))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(x0))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 f_flat(up(x0)) 543.95/242.09 g_flat(up(x0)) 543.95/242.09 543.95/242.09 We have to consider all minimal (P,Q,R)-chains. 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (987) DependencyGraphProof (EQUIVALENT) 543.95/242.09 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (988) 543.95/242.09 Obligation: 543.95/242.09 Q DP problem: 543.95/242.09 The TRS P consists of the following rules: 543.95/242.09 543.95/242.09 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.09 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.09 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.09 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.09 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.09 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.09 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.09 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) 543.95/242.09 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.09 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.09 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.09 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.09 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.09 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.09 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.09 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.09 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.09 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.09 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.09 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.09 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.09 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.09 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.09 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.09 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.09 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.09 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.09 543.95/242.09 The TRS R consists of the following rules: 543.95/242.09 543.95/242.09 down(a) -> up(f(a)) 543.95/242.09 down(b) -> up(g(b)) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.09 down(f(a)) -> f_flat(down(a)) 543.95/242.09 down(f(b)) -> f_flat(down(b)) 543.95/242.09 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.09 down(f(c)) -> f_flat(down(c)) 543.95/242.09 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.09 down(g(a)) -> g_flat(down(a)) 543.95/242.09 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.09 down(g(b)) -> g_flat(down(b)) 543.95/242.09 down(g(c)) -> g_flat(down(c)) 543.95/242.09 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.09 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.09 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.09 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.09 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.09 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.09 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.09 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.09 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.09 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.09 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.09 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.09 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.09 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.09 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.09 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.09 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.09 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.09 543.95/242.09 The set Q consists of the following terms: 543.95/242.09 543.95/242.09 down(a) 543.95/242.09 down(b) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.09 down(f(a)) 543.95/242.09 down(f(b)) 543.95/242.09 down(f(g(x0))) 543.95/242.09 down(f(c)) 543.95/242.09 down(f(fresh_constant)) 543.95/242.09 down(g(a)) 543.95/242.09 down(g(f(x0))) 543.95/242.09 down(g(b)) 543.95/242.09 down(g(c)) 543.95/242.09 down(g(fresh_constant)) 543.95/242.09 down(f(f(a))) 543.95/242.09 down(f(f(b))) 543.95/242.09 down(f(f(g(x0)))) 543.95/242.09 down(f(f(c))) 543.95/242.09 down(f(f(fresh_constant))) 543.95/242.09 down(g(g(a))) 543.95/242.09 down(g(g(f(x0)))) 543.95/242.09 down(g(g(b))) 543.95/242.09 down(g(g(c))) 543.95/242.09 down(g(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) 543.95/242.09 down(f(f(f(g(x0))))) 543.95/242.09 down(f(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) 543.95/242.09 down(g(g(g(f(x0))))) 543.95/242.09 down(g(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(x0)))))) 543.95/242.09 down(f(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(x0)))))) 543.95/242.09 down(g(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(x0))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(x0))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 f_flat(up(x0)) 543.95/242.09 g_flat(up(x0)) 543.95/242.09 543.95/242.09 We have to consider all minimal (P,Q,R)-chains. 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (989) TransformationProof (EQUIVALENT) 543.95/242.09 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.09 543.95/242.09 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 543.95/242.09 543.95/242.09 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (990) 543.95/242.09 Obligation: 543.95/242.09 Q DP problem: 543.95/242.09 The TRS P consists of the following rules: 543.95/242.09 543.95/242.09 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.09 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.09 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.09 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.09 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.09 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.09 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.09 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.09 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.09 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.09 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.09 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.09 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.09 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.09 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.09 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.09 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.09 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.09 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.09 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.09 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.09 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.09 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.09 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.09 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.09 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) 543.95/242.09 543.95/242.09 The TRS R consists of the following rules: 543.95/242.09 543.95/242.09 down(a) -> up(f(a)) 543.95/242.09 down(b) -> up(g(b)) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.09 down(f(a)) -> f_flat(down(a)) 543.95/242.09 down(f(b)) -> f_flat(down(b)) 543.95/242.09 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.09 down(f(c)) -> f_flat(down(c)) 543.95/242.09 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.09 down(g(a)) -> g_flat(down(a)) 543.95/242.09 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.09 down(g(b)) -> g_flat(down(b)) 543.95/242.09 down(g(c)) -> g_flat(down(c)) 543.95/242.09 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.09 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.09 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.09 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.09 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.09 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.09 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.09 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.09 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.09 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.09 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.09 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.09 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.09 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.09 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.09 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.09 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.09 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.09 543.95/242.09 The set Q consists of the following terms: 543.95/242.09 543.95/242.09 down(a) 543.95/242.09 down(b) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.09 down(f(a)) 543.95/242.09 down(f(b)) 543.95/242.09 down(f(g(x0))) 543.95/242.09 down(f(c)) 543.95/242.09 down(f(fresh_constant)) 543.95/242.09 down(g(a)) 543.95/242.09 down(g(f(x0))) 543.95/242.09 down(g(b)) 543.95/242.09 down(g(c)) 543.95/242.09 down(g(fresh_constant)) 543.95/242.09 down(f(f(a))) 543.95/242.09 down(f(f(b))) 543.95/242.09 down(f(f(g(x0)))) 543.95/242.09 down(f(f(c))) 543.95/242.09 down(f(f(fresh_constant))) 543.95/242.09 down(g(g(a))) 543.95/242.09 down(g(g(f(x0)))) 543.95/242.09 down(g(g(b))) 543.95/242.09 down(g(g(c))) 543.95/242.09 down(g(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) 543.95/242.09 down(f(f(f(g(x0))))) 543.95/242.09 down(f(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) 543.95/242.09 down(g(g(g(f(x0))))) 543.95/242.09 down(g(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(x0)))))) 543.95/242.09 down(f(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(x0)))))) 543.95/242.09 down(g(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(x0))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(x0))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 f_flat(up(x0)) 543.95/242.09 g_flat(up(x0)) 543.95/242.09 543.95/242.09 We have to consider all minimal (P,Q,R)-chains. 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (991) TransformationProof (EQUIVALENT) 543.95/242.09 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.09 543.95/242.09 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 543.95/242.09 543.95/242.09 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (992) 543.95/242.09 Obligation: 543.95/242.09 Q DP problem: 543.95/242.09 The TRS P consists of the following rules: 543.95/242.09 543.95/242.09 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.09 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.09 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.09 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.09 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.09 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.09 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.09 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.09 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.09 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.09 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.09 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.09 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.09 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.09 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.09 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.09 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.09 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.09 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.09 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.09 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.09 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.09 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.09 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.09 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.09 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) 543.95/242.09 543.95/242.09 The TRS R consists of the following rules: 543.95/242.09 543.95/242.09 down(a) -> up(f(a)) 543.95/242.09 down(b) -> up(g(b)) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.09 down(f(a)) -> f_flat(down(a)) 543.95/242.09 down(f(b)) -> f_flat(down(b)) 543.95/242.09 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.09 down(f(c)) -> f_flat(down(c)) 543.95/242.09 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.09 down(g(a)) -> g_flat(down(a)) 543.95/242.09 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.09 down(g(b)) -> g_flat(down(b)) 543.95/242.09 down(g(c)) -> g_flat(down(c)) 543.95/242.09 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.09 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.09 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.09 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.09 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.09 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.09 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.09 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.09 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.09 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.09 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.09 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.09 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.09 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.09 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.09 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.09 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.09 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.09 543.95/242.09 The set Q consists of the following terms: 543.95/242.09 543.95/242.09 down(a) 543.95/242.09 down(b) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.09 down(f(a)) 543.95/242.09 down(f(b)) 543.95/242.09 down(f(g(x0))) 543.95/242.09 down(f(c)) 543.95/242.09 down(f(fresh_constant)) 543.95/242.09 down(g(a)) 543.95/242.09 down(g(f(x0))) 543.95/242.09 down(g(b)) 543.95/242.09 down(g(c)) 543.95/242.09 down(g(fresh_constant)) 543.95/242.09 down(f(f(a))) 543.95/242.09 down(f(f(b))) 543.95/242.09 down(f(f(g(x0)))) 543.95/242.09 down(f(f(c))) 543.95/242.09 down(f(f(fresh_constant))) 543.95/242.09 down(g(g(a))) 543.95/242.09 down(g(g(f(x0)))) 543.95/242.09 down(g(g(b))) 543.95/242.09 down(g(g(c))) 543.95/242.09 down(g(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) 543.95/242.09 down(f(f(f(g(x0))))) 543.95/242.09 down(f(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) 543.95/242.09 down(g(g(g(f(x0))))) 543.95/242.09 down(g(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(x0)))))) 543.95/242.09 down(f(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(x0)))))) 543.95/242.09 down(g(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(x0))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(x0))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 f_flat(up(x0)) 543.95/242.09 g_flat(up(x0)) 543.95/242.09 543.95/242.09 We have to consider all minimal (P,Q,R)-chains. 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (993) TransformationProof (EQUIVALENT) 543.95/242.09 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(a))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.09 543.95/242.09 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a)))))))))))) 543.95/242.09 543.95/242.09 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (994) 543.95/242.09 Obligation: 543.95/242.09 Q DP problem: 543.95/242.09 The TRS P consists of the following rules: 543.95/242.09 543.95/242.09 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.09 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.09 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.09 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.09 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.09 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.09 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.09 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.09 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.09 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.09 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.09 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.09 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.09 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.09 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.09 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.09 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.09 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.09 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.09 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.09 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.09 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.09 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.09 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.09 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.09 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.09 543.95/242.09 The TRS R consists of the following rules: 543.95/242.09 543.95/242.09 down(a) -> up(f(a)) 543.95/242.09 down(b) -> up(g(b)) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.09 down(f(a)) -> f_flat(down(a)) 543.95/242.09 down(f(b)) -> f_flat(down(b)) 543.95/242.09 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.09 down(f(c)) -> f_flat(down(c)) 543.95/242.09 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.09 down(g(a)) -> g_flat(down(a)) 543.95/242.09 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.09 down(g(b)) -> g_flat(down(b)) 543.95/242.09 down(g(c)) -> g_flat(down(c)) 543.95/242.09 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.09 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.09 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.09 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.09 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.09 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.09 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.09 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.09 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.09 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.09 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.09 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.09 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.09 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.09 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.09 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.09 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.09 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.09 543.95/242.09 The set Q consists of the following terms: 543.95/242.09 543.95/242.09 down(a) 543.95/242.09 down(b) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.09 down(f(a)) 543.95/242.09 down(f(b)) 543.95/242.09 down(f(g(x0))) 543.95/242.09 down(f(c)) 543.95/242.09 down(f(fresh_constant)) 543.95/242.09 down(g(a)) 543.95/242.09 down(g(f(x0))) 543.95/242.09 down(g(b)) 543.95/242.09 down(g(c)) 543.95/242.09 down(g(fresh_constant)) 543.95/242.09 down(f(f(a))) 543.95/242.09 down(f(f(b))) 543.95/242.09 down(f(f(g(x0)))) 543.95/242.09 down(f(f(c))) 543.95/242.09 down(f(f(fresh_constant))) 543.95/242.09 down(g(g(a))) 543.95/242.09 down(g(g(f(x0)))) 543.95/242.09 down(g(g(b))) 543.95/242.09 down(g(g(c))) 543.95/242.09 down(g(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) 543.95/242.09 down(f(f(f(g(x0))))) 543.95/242.09 down(f(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) 543.95/242.09 down(g(g(g(f(x0))))) 543.95/242.09 down(g(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(x0)))))) 543.95/242.09 down(f(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(x0)))))) 543.95/242.09 down(g(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(x0))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(x0))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 f_flat(up(x0)) 543.95/242.09 g_flat(up(x0)) 543.95/242.09 543.95/242.09 We have to consider all minimal (P,Q,R)-chains. 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (995) TransformationProof (EQUIVALENT) 543.95/242.09 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(b))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.09 543.95/242.09 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b)))))))))))) 543.95/242.09 543.95/242.09 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (996) 543.95/242.09 Obligation: 543.95/242.09 Q DP problem: 543.95/242.09 The TRS P consists of the following rules: 543.95/242.09 543.95/242.09 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.09 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.09 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.09 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.09 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.09 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.09 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.09 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.09 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.09 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.09 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.09 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.09 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.09 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.09 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.09 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.09 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.09 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.09 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.09 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.09 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.09 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.09 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.09 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.09 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.09 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.09 543.95/242.09 The TRS R consists of the following rules: 543.95/242.09 543.95/242.09 down(a) -> up(f(a)) 543.95/242.09 down(b) -> up(g(b)) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.09 down(f(a)) -> f_flat(down(a)) 543.95/242.09 down(f(b)) -> f_flat(down(b)) 543.95/242.09 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.09 down(f(c)) -> f_flat(down(c)) 543.95/242.09 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.09 down(g(a)) -> g_flat(down(a)) 543.95/242.09 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.09 down(g(b)) -> g_flat(down(b)) 543.95/242.09 down(g(c)) -> g_flat(down(c)) 543.95/242.09 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.09 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.09 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.09 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.09 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.09 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.09 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.09 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.09 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.09 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.09 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.09 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.09 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.09 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.09 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.09 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.09 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.09 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.09 543.95/242.09 The set Q consists of the following terms: 543.95/242.09 543.95/242.09 down(a) 543.95/242.09 down(b) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.09 down(f(a)) 543.95/242.09 down(f(b)) 543.95/242.09 down(f(g(x0))) 543.95/242.09 down(f(c)) 543.95/242.09 down(f(fresh_constant)) 543.95/242.09 down(g(a)) 543.95/242.09 down(g(f(x0))) 543.95/242.09 down(g(b)) 543.95/242.09 down(g(c)) 543.95/242.09 down(g(fresh_constant)) 543.95/242.09 down(f(f(a))) 543.95/242.09 down(f(f(b))) 543.95/242.09 down(f(f(g(x0)))) 543.95/242.09 down(f(f(c))) 543.95/242.09 down(f(f(fresh_constant))) 543.95/242.09 down(g(g(a))) 543.95/242.09 down(g(g(f(x0)))) 543.95/242.09 down(g(g(b))) 543.95/242.09 down(g(g(c))) 543.95/242.09 down(g(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) 543.95/242.09 down(f(f(f(g(x0))))) 543.95/242.09 down(f(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) 543.95/242.09 down(g(g(g(f(x0))))) 543.95/242.09 down(g(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(x0)))))) 543.95/242.09 down(f(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(x0)))))) 543.95/242.09 down(g(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(x0))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(x0))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 f_flat(up(x0)) 543.95/242.09 g_flat(up(x0)) 543.95/242.09 543.95/242.09 We have to consider all minimal (P,Q,R)-chains. 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (997) TransformationProof (EQUIVALENT) 543.95/242.09 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(g(x0)))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.09 543.95/242.09 (TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0))))))))))))) 543.95/242.09 543.95/242.09 543.95/242.09 ---------------------------------------- 543.95/242.09 543.95/242.09 (998) 543.95/242.09 Obligation: 543.95/242.09 Q DP problem: 543.95/242.09 The TRS P consists of the following rules: 543.95/242.09 543.95/242.09 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.09 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.09 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.09 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.09 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.09 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.09 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.09 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.09 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.09 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.09 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.09 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.09 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.09 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.09 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.09 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.09 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.09 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.09 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.09 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.09 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.09 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.09 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.09 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.09 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.09 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) 543.95/242.09 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.09 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.09 543.95/242.09 The TRS R consists of the following rules: 543.95/242.09 543.95/242.09 down(a) -> up(f(a)) 543.95/242.09 down(b) -> up(g(b)) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.09 down(f(a)) -> f_flat(down(a)) 543.95/242.09 down(f(b)) -> f_flat(down(b)) 543.95/242.09 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.09 down(f(c)) -> f_flat(down(c)) 543.95/242.09 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.09 down(g(a)) -> g_flat(down(a)) 543.95/242.09 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.09 down(g(b)) -> g_flat(down(b)) 543.95/242.09 down(g(c)) -> g_flat(down(c)) 543.95/242.09 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.09 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.09 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.09 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.09 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.09 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.09 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.09 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.09 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.09 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.09 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.09 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.09 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.09 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.09 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.09 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.09 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.09 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.09 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.09 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.09 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.09 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.09 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.09 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.09 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.09 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.09 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.09 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.09 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.09 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.09 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.09 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.09 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.09 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.09 543.95/242.09 The set Q consists of the following terms: 543.95/242.09 543.95/242.09 down(a) 543.95/242.09 down(b) 543.95/242.09 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.09 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.09 down(f(a)) 543.95/242.09 down(f(b)) 543.95/242.09 down(f(g(x0))) 543.95/242.09 down(f(c)) 543.95/242.09 down(f(fresh_constant)) 543.95/242.09 down(g(a)) 543.95/242.09 down(g(f(x0))) 543.95/242.09 down(g(b)) 543.95/242.09 down(g(c)) 543.95/242.09 down(g(fresh_constant)) 543.95/242.09 down(f(f(a))) 543.95/242.09 down(f(f(b))) 543.95/242.09 down(f(f(g(x0)))) 543.95/242.09 down(f(f(c))) 543.95/242.09 down(f(f(fresh_constant))) 543.95/242.09 down(g(g(a))) 543.95/242.09 down(g(g(f(x0)))) 543.95/242.09 down(g(g(b))) 543.95/242.09 down(g(g(c))) 543.95/242.09 down(g(g(fresh_constant))) 543.95/242.09 down(f(f(f(a)))) 543.95/242.09 down(f(f(f(b)))) 543.95/242.09 down(f(f(f(g(x0))))) 543.95/242.09 down(f(f(f(c)))) 543.95/242.09 down(f(f(f(fresh_constant)))) 543.95/242.09 down(g(g(g(a)))) 543.95/242.09 down(g(g(g(f(x0))))) 543.95/242.09 down(g(g(g(b)))) 543.95/242.09 down(g(g(g(c)))) 543.95/242.09 down(g(g(g(fresh_constant)))) 543.95/242.09 down(f(f(f(f(a))))) 543.95/242.09 down(f(f(f(f(b))))) 543.95/242.09 down(f(f(f(f(g(x0)))))) 543.95/242.09 down(f(f(f(f(c))))) 543.95/242.09 down(f(f(f(f(fresh_constant))))) 543.95/242.09 down(g(g(g(g(a))))) 543.95/242.09 down(g(g(g(g(f(x0)))))) 543.95/242.09 down(g(g(g(g(b))))) 543.95/242.09 down(g(g(g(g(c))))) 543.95/242.09 down(g(g(g(g(fresh_constant))))) 543.95/242.09 down(f(f(f(f(f(a)))))) 543.95/242.09 down(f(f(f(f(f(b)))))) 543.95/242.09 down(f(f(f(f(f(g(x0))))))) 543.95/242.09 down(f(f(f(f(f(c)))))) 543.95/242.09 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.09 down(g(g(g(g(g(a)))))) 543.95/242.09 down(g(g(g(g(g(f(x0))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 f_flat(up(x0)) 543.95/242.10 g_flat(up(x0)) 543.95/242.10 543.95/242.10 We have to consider all minimal (P,Q,R)-chains. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (999) TransformationProof (EQUIVALENT) 543.95/242.10 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.10 543.95/242.10 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 543.95/242.10 543.95/242.10 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1000) 543.95/242.10 Obligation: 543.95/242.10 Q DP problem: 543.95/242.10 The TRS P consists of the following rules: 543.95/242.10 543.95/242.10 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.10 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.10 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.10 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.10 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.10 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.10 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.10 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.10 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.10 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.10 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.10 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.10 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.10 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.10 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.10 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.10 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.10 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.10 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.10 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.10 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.10 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.10 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.10 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.10 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.10 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.10 543.95/242.10 The TRS R consists of the following rules: 543.95/242.10 543.95/242.10 down(a) -> up(f(a)) 543.95/242.10 down(b) -> up(g(b)) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.10 down(f(a)) -> f_flat(down(a)) 543.95/242.10 down(f(b)) -> f_flat(down(b)) 543.95/242.10 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.10 down(f(c)) -> f_flat(down(c)) 543.95/242.10 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.10 down(g(a)) -> g_flat(down(a)) 543.95/242.10 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.10 down(g(b)) -> g_flat(down(b)) 543.95/242.10 down(g(c)) -> g_flat(down(c)) 543.95/242.10 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.10 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.10 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.10 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.10 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.10 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.10 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.10 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.10 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.10 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.10 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.10 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.10 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.10 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.10 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.10 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.10 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.10 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.10 543.95/242.10 The set Q consists of the following terms: 543.95/242.10 543.95/242.10 down(a) 543.95/242.10 down(b) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.10 down(f(a)) 543.95/242.10 down(f(b)) 543.95/242.10 down(f(g(x0))) 543.95/242.10 down(f(c)) 543.95/242.10 down(f(fresh_constant)) 543.95/242.10 down(g(a)) 543.95/242.10 down(g(f(x0))) 543.95/242.10 down(g(b)) 543.95/242.10 down(g(c)) 543.95/242.10 down(g(fresh_constant)) 543.95/242.10 down(f(f(a))) 543.95/242.10 down(f(f(b))) 543.95/242.10 down(f(f(g(x0)))) 543.95/242.10 down(f(f(c))) 543.95/242.10 down(f(f(fresh_constant))) 543.95/242.10 down(g(g(a))) 543.95/242.10 down(g(g(f(x0)))) 543.95/242.10 down(g(g(b))) 543.95/242.10 down(g(g(c))) 543.95/242.10 down(g(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) 543.95/242.10 down(f(f(f(g(x0))))) 543.95/242.10 down(f(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) 543.95/242.10 down(g(g(g(f(x0))))) 543.95/242.10 down(g(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(x0)))))) 543.95/242.10 down(f(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(x0)))))) 543.95/242.10 down(g(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(x0))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(x0))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 f_flat(up(x0)) 543.95/242.10 g_flat(up(x0)) 543.95/242.10 543.95/242.10 We have to consider all minimal (P,Q,R)-chains. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1001) TransformationProof (EQUIVALENT) 543.95/242.10 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.10 543.95/242.10 (TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c)))))))))),TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c))))))))))) 543.95/242.10 543.95/242.10 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1002) 543.95/242.10 Obligation: 543.95/242.10 Q DP problem: 543.95/242.10 The TRS P consists of the following rules: 543.95/242.10 543.95/242.10 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.10 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.10 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.10 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.10 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.10 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.10 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.10 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.10 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.10 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.10 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.10 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.10 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.10 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.10 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.10 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.10 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.10 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.10 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.10 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.10 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.10 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.10 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.10 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.10 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.10 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(c)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c)))))))))) 543.95/242.10 543.95/242.10 The TRS R consists of the following rules: 543.95/242.10 543.95/242.10 down(a) -> up(f(a)) 543.95/242.10 down(b) -> up(g(b)) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.10 down(f(a)) -> f_flat(down(a)) 543.95/242.10 down(f(b)) -> f_flat(down(b)) 543.95/242.10 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.10 down(f(c)) -> f_flat(down(c)) 543.95/242.10 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.10 down(g(a)) -> g_flat(down(a)) 543.95/242.10 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.10 down(g(b)) -> g_flat(down(b)) 543.95/242.10 down(g(c)) -> g_flat(down(c)) 543.95/242.10 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.10 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.10 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.10 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.10 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.10 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.10 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.10 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.10 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.10 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.10 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.10 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.10 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.10 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.10 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.10 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.10 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.10 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.10 543.95/242.10 The set Q consists of the following terms: 543.95/242.10 543.95/242.10 down(a) 543.95/242.10 down(b) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.10 down(f(a)) 543.95/242.10 down(f(b)) 543.95/242.10 down(f(g(x0))) 543.95/242.10 down(f(c)) 543.95/242.10 down(f(fresh_constant)) 543.95/242.10 down(g(a)) 543.95/242.10 down(g(f(x0))) 543.95/242.10 down(g(b)) 543.95/242.10 down(g(c)) 543.95/242.10 down(g(fresh_constant)) 543.95/242.10 down(f(f(a))) 543.95/242.10 down(f(f(b))) 543.95/242.10 down(f(f(g(x0)))) 543.95/242.10 down(f(f(c))) 543.95/242.10 down(f(f(fresh_constant))) 543.95/242.10 down(g(g(a))) 543.95/242.10 down(g(g(f(x0)))) 543.95/242.10 down(g(g(b))) 543.95/242.10 down(g(g(c))) 543.95/242.10 down(g(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) 543.95/242.10 down(f(f(f(g(x0))))) 543.95/242.10 down(f(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) 543.95/242.10 down(g(g(g(f(x0))))) 543.95/242.10 down(g(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(x0)))))) 543.95/242.10 down(f(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(x0)))))) 543.95/242.10 down(g(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(x0))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(x0))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 f_flat(up(x0)) 543.95/242.10 g_flat(up(x0)) 543.95/242.10 543.95/242.10 We have to consider all minimal (P,Q,R)-chains. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1003) DependencyGraphProof (EQUIVALENT) 543.95/242.10 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1004) 543.95/242.10 Obligation: 543.95/242.10 Q DP problem: 543.95/242.10 The TRS P consists of the following rules: 543.95/242.10 543.95/242.10 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.10 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.10 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.10 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.10 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.10 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.10 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.10 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) 543.95/242.10 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.10 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.10 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.10 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.10 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.10 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.10 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) 543.95/242.10 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.10 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.10 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.10 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.10 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.10 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.10 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.10 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.10 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.10 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.10 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.10 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.10 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.10 543.95/242.10 The TRS R consists of the following rules: 543.95/242.10 543.95/242.10 down(a) -> up(f(a)) 543.95/242.10 down(b) -> up(g(b)) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.10 down(f(a)) -> f_flat(down(a)) 543.95/242.10 down(f(b)) -> f_flat(down(b)) 543.95/242.10 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.10 down(f(c)) -> f_flat(down(c)) 543.95/242.10 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.10 down(g(a)) -> g_flat(down(a)) 543.95/242.10 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.10 down(g(b)) -> g_flat(down(b)) 543.95/242.10 down(g(c)) -> g_flat(down(c)) 543.95/242.10 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.10 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.10 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.10 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.10 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.10 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.10 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.10 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.10 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.10 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.10 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.10 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.10 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.10 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.10 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.10 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.10 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.10 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.10 543.95/242.10 The set Q consists of the following terms: 543.95/242.10 543.95/242.10 down(a) 543.95/242.10 down(b) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.10 down(f(a)) 543.95/242.10 down(f(b)) 543.95/242.10 down(f(g(x0))) 543.95/242.10 down(f(c)) 543.95/242.10 down(f(fresh_constant)) 543.95/242.10 down(g(a)) 543.95/242.10 down(g(f(x0))) 543.95/242.10 down(g(b)) 543.95/242.10 down(g(c)) 543.95/242.10 down(g(fresh_constant)) 543.95/242.10 down(f(f(a))) 543.95/242.10 down(f(f(b))) 543.95/242.10 down(f(f(g(x0)))) 543.95/242.10 down(f(f(c))) 543.95/242.10 down(f(f(fresh_constant))) 543.95/242.10 down(g(g(a))) 543.95/242.10 down(g(g(f(x0)))) 543.95/242.10 down(g(g(b))) 543.95/242.10 down(g(g(c))) 543.95/242.10 down(g(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) 543.95/242.10 down(f(f(f(g(x0))))) 543.95/242.10 down(f(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) 543.95/242.10 down(g(g(g(f(x0))))) 543.95/242.10 down(g(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(x0)))))) 543.95/242.10 down(f(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(x0)))))) 543.95/242.10 down(g(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(x0))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(x0))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 f_flat(up(x0)) 543.95/242.10 g_flat(up(x0)) 543.95/242.10 543.95/242.10 We have to consider all minimal (P,Q,R)-chains. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1005) TransformationProof (EQUIVALENT) 543.95/242.10 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.10 543.95/242.10 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 543.95/242.10 543.95/242.10 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1006) 543.95/242.10 Obligation: 543.95/242.10 Q DP problem: 543.95/242.10 The TRS P consists of the following rules: 543.95/242.10 543.95/242.10 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.10 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.10 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.10 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.10 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.10 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.10 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.10 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.10 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.10 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.10 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.10 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.10 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.10 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) 543.95/242.10 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.10 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.10 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.10 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.10 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.10 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.10 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.10 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.10 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.10 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.10 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.10 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.10 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))) 543.95/242.10 543.95/242.10 The TRS R consists of the following rules: 543.95/242.10 543.95/242.10 down(a) -> up(f(a)) 543.95/242.10 down(b) -> up(g(b)) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.10 down(f(a)) -> f_flat(down(a)) 543.95/242.10 down(f(b)) -> f_flat(down(b)) 543.95/242.10 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.10 down(f(c)) -> f_flat(down(c)) 543.95/242.10 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.10 down(g(a)) -> g_flat(down(a)) 543.95/242.10 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.10 down(g(b)) -> g_flat(down(b)) 543.95/242.10 down(g(c)) -> g_flat(down(c)) 543.95/242.10 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.10 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.10 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.10 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.10 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.10 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.10 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.10 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.10 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.10 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.10 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.10 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.10 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.10 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.10 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.10 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.10 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.10 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.10 543.95/242.10 The set Q consists of the following terms: 543.95/242.10 543.95/242.10 down(a) 543.95/242.10 down(b) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.10 down(f(a)) 543.95/242.10 down(f(b)) 543.95/242.10 down(f(g(x0))) 543.95/242.10 down(f(c)) 543.95/242.10 down(f(fresh_constant)) 543.95/242.10 down(g(a)) 543.95/242.10 down(g(f(x0))) 543.95/242.10 down(g(b)) 543.95/242.10 down(g(c)) 543.95/242.10 down(g(fresh_constant)) 543.95/242.10 down(f(f(a))) 543.95/242.10 down(f(f(b))) 543.95/242.10 down(f(f(g(x0)))) 543.95/242.10 down(f(f(c))) 543.95/242.10 down(f(f(fresh_constant))) 543.95/242.10 down(g(g(a))) 543.95/242.10 down(g(g(f(x0)))) 543.95/242.10 down(g(g(b))) 543.95/242.10 down(g(g(c))) 543.95/242.10 down(g(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) 543.95/242.10 down(f(f(f(g(x0))))) 543.95/242.10 down(f(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) 543.95/242.10 down(g(g(g(f(x0))))) 543.95/242.10 down(g(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(x0)))))) 543.95/242.10 down(f(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(x0)))))) 543.95/242.10 down(g(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(x0))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(x0))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 f_flat(up(x0)) 543.95/242.10 g_flat(up(x0)) 543.95/242.10 543.95/242.10 We have to consider all minimal (P,Q,R)-chains. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1007) TransformationProof (EQUIVALENT) 543.95/242.10 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.10 543.95/242.10 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 543.95/242.10 543.95/242.10 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1008) 543.95/242.10 Obligation: 543.95/242.10 Q DP problem: 543.95/242.10 The TRS P consists of the following rules: 543.95/242.10 543.95/242.10 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.10 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.10 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.10 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.10 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.10 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.10 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.10 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.10 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.10 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.10 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.10 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.10 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.10 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.10 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.10 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.10 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.10 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.10 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.10 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.10 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.10 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.10 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.10 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.10 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.10 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))) 543.95/242.10 543.95/242.10 The TRS R consists of the following rules: 543.95/242.10 543.95/242.10 down(a) -> up(f(a)) 543.95/242.10 down(b) -> up(g(b)) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.10 down(f(a)) -> f_flat(down(a)) 543.95/242.10 down(f(b)) -> f_flat(down(b)) 543.95/242.10 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.10 down(f(c)) -> f_flat(down(c)) 543.95/242.10 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.10 down(g(a)) -> g_flat(down(a)) 543.95/242.10 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.10 down(g(b)) -> g_flat(down(b)) 543.95/242.10 down(g(c)) -> g_flat(down(c)) 543.95/242.10 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.10 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.10 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.10 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.10 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.10 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.10 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.10 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.10 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.10 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.10 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.10 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.10 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.10 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.10 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.10 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.10 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.10 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.10 543.95/242.10 The set Q consists of the following terms: 543.95/242.10 543.95/242.10 down(a) 543.95/242.10 down(b) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.10 down(f(a)) 543.95/242.10 down(f(b)) 543.95/242.10 down(f(g(x0))) 543.95/242.10 down(f(c)) 543.95/242.10 down(f(fresh_constant)) 543.95/242.10 down(g(a)) 543.95/242.10 down(g(f(x0))) 543.95/242.10 down(g(b)) 543.95/242.10 down(g(c)) 543.95/242.10 down(g(fresh_constant)) 543.95/242.10 down(f(f(a))) 543.95/242.10 down(f(f(b))) 543.95/242.10 down(f(f(g(x0)))) 543.95/242.10 down(f(f(c))) 543.95/242.10 down(f(f(fresh_constant))) 543.95/242.10 down(g(g(a))) 543.95/242.10 down(g(g(f(x0)))) 543.95/242.10 down(g(g(b))) 543.95/242.10 down(g(g(c))) 543.95/242.10 down(g(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) 543.95/242.10 down(f(f(f(g(x0))))) 543.95/242.10 down(f(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) 543.95/242.10 down(g(g(g(f(x0))))) 543.95/242.10 down(g(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(x0)))))) 543.95/242.10 down(f(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(x0)))))) 543.95/242.10 down(g(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(x0))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(x0))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 f_flat(up(x0)) 543.95/242.10 g_flat(up(x0)) 543.95/242.10 543.95/242.10 We have to consider all minimal (P,Q,R)-chains. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1009) TransformationProof (EQUIVALENT) 543.95/242.10 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.10 543.95/242.10 (TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant)))))))))),TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant))))))))))) 543.95/242.10 543.95/242.10 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1010) 543.95/242.10 Obligation: 543.95/242.10 Q DP problem: 543.95/242.10 The TRS P consists of the following rules: 543.95/242.10 543.95/242.10 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.10 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.10 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.10 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.10 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.10 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.10 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.10 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.10 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.10 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.10 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.10 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.10 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.10 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.10 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.10 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.10 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.10 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.10 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.10 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.10 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.10 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.10 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.10 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.10 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.10 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant)))))))))) 543.95/242.10 543.95/242.10 The TRS R consists of the following rules: 543.95/242.10 543.95/242.10 down(a) -> up(f(a)) 543.95/242.10 down(b) -> up(g(b)) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.10 down(f(a)) -> f_flat(down(a)) 543.95/242.10 down(f(b)) -> f_flat(down(b)) 543.95/242.10 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.10 down(f(c)) -> f_flat(down(c)) 543.95/242.10 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.10 down(g(a)) -> g_flat(down(a)) 543.95/242.10 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.10 down(g(b)) -> g_flat(down(b)) 543.95/242.10 down(g(c)) -> g_flat(down(c)) 543.95/242.10 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.10 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.10 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.10 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.10 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.10 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.10 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.10 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.10 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.10 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.10 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.10 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.10 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.10 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.10 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.10 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.10 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.10 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.10 543.95/242.10 The set Q consists of the following terms: 543.95/242.10 543.95/242.10 down(a) 543.95/242.10 down(b) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.10 down(f(a)) 543.95/242.10 down(f(b)) 543.95/242.10 down(f(g(x0))) 543.95/242.10 down(f(c)) 543.95/242.10 down(f(fresh_constant)) 543.95/242.10 down(g(a)) 543.95/242.10 down(g(f(x0))) 543.95/242.10 down(g(b)) 543.95/242.10 down(g(c)) 543.95/242.10 down(g(fresh_constant)) 543.95/242.10 down(f(f(a))) 543.95/242.10 down(f(f(b))) 543.95/242.10 down(f(f(g(x0)))) 543.95/242.10 down(f(f(c))) 543.95/242.10 down(f(f(fresh_constant))) 543.95/242.10 down(g(g(a))) 543.95/242.10 down(g(g(f(x0)))) 543.95/242.10 down(g(g(b))) 543.95/242.10 down(g(g(c))) 543.95/242.10 down(g(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) 543.95/242.10 down(f(f(f(g(x0))))) 543.95/242.10 down(f(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) 543.95/242.10 down(g(g(g(f(x0))))) 543.95/242.10 down(g(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(x0)))))) 543.95/242.10 down(f(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(x0)))))) 543.95/242.10 down(g(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(x0))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(x0))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 f_flat(up(x0)) 543.95/242.10 g_flat(up(x0)) 543.95/242.10 543.95/242.10 We have to consider all minimal (P,Q,R)-chains. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1011) DependencyGraphProof (EQUIVALENT) 543.95/242.10 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1012) 543.95/242.10 Obligation: 543.95/242.10 Q DP problem: 543.95/242.10 The TRS P consists of the following rules: 543.95/242.10 543.95/242.10 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.10 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.10 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.10 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.10 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.10 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.10 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.10 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))) 543.95/242.10 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.10 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.10 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.10 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.10 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.10 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.10 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))) 543.95/242.10 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.10 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.10 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.10 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.10 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.10 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.10 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.10 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.10 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.10 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.10 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.10 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.10 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.10 543.95/242.10 The TRS R consists of the following rules: 543.95/242.10 543.95/242.10 down(a) -> up(f(a)) 543.95/242.10 down(b) -> up(g(b)) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.10 down(f(a)) -> f_flat(down(a)) 543.95/242.10 down(f(b)) -> f_flat(down(b)) 543.95/242.10 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.10 down(f(c)) -> f_flat(down(c)) 543.95/242.10 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.10 down(g(a)) -> g_flat(down(a)) 543.95/242.10 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.10 down(g(b)) -> g_flat(down(b)) 543.95/242.10 down(g(c)) -> g_flat(down(c)) 543.95/242.10 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.10 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.10 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.10 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.10 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.10 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.10 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.10 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.10 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.10 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.10 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.10 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.10 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.10 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.10 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.10 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.10 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.10 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.10 543.95/242.10 The set Q consists of the following terms: 543.95/242.10 543.95/242.10 down(a) 543.95/242.10 down(b) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.10 down(f(a)) 543.95/242.10 down(f(b)) 543.95/242.10 down(f(g(x0))) 543.95/242.10 down(f(c)) 543.95/242.10 down(f(fresh_constant)) 543.95/242.10 down(g(a)) 543.95/242.10 down(g(f(x0))) 543.95/242.10 down(g(b)) 543.95/242.10 down(g(c)) 543.95/242.10 down(g(fresh_constant)) 543.95/242.10 down(f(f(a))) 543.95/242.10 down(f(f(b))) 543.95/242.10 down(f(f(g(x0)))) 543.95/242.10 down(f(f(c))) 543.95/242.10 down(f(f(fresh_constant))) 543.95/242.10 down(g(g(a))) 543.95/242.10 down(g(g(f(x0)))) 543.95/242.10 down(g(g(b))) 543.95/242.10 down(g(g(c))) 543.95/242.10 down(g(g(fresh_constant))) 543.95/242.10 down(f(f(f(a)))) 543.95/242.10 down(f(f(f(b)))) 543.95/242.10 down(f(f(f(g(x0))))) 543.95/242.10 down(f(f(f(c)))) 543.95/242.10 down(f(f(f(fresh_constant)))) 543.95/242.10 down(g(g(g(a)))) 543.95/242.10 down(g(g(g(f(x0))))) 543.95/242.10 down(g(g(g(b)))) 543.95/242.10 down(g(g(g(c)))) 543.95/242.10 down(g(g(g(fresh_constant)))) 543.95/242.10 down(f(f(f(f(a))))) 543.95/242.10 down(f(f(f(f(b))))) 543.95/242.10 down(f(f(f(f(g(x0)))))) 543.95/242.10 down(f(f(f(f(c))))) 543.95/242.10 down(f(f(f(f(fresh_constant))))) 543.95/242.10 down(g(g(g(g(a))))) 543.95/242.10 down(g(g(g(g(f(x0)))))) 543.95/242.10 down(g(g(g(g(b))))) 543.95/242.10 down(g(g(g(g(c))))) 543.95/242.10 down(g(g(g(g(fresh_constant))))) 543.95/242.10 down(f(f(f(f(f(a)))))) 543.95/242.10 down(f(f(f(f(f(b)))))) 543.95/242.10 down(f(f(f(f(f(g(x0))))))) 543.95/242.10 down(f(f(f(f(f(c)))))) 543.95/242.10 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.10 down(g(g(g(g(g(a)))))) 543.95/242.10 down(g(g(g(g(g(f(x0))))))) 543.95/242.10 down(g(g(g(g(g(b)))))) 543.95/242.10 down(g(g(g(g(g(c)))))) 543.95/242.10 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.10 down(f(f(f(f(f(f(a))))))) 543.95/242.10 down(f(f(f(f(f(f(b))))))) 543.95/242.10 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.10 down(f(f(f(f(f(f(c))))))) 543.95/242.10 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.10 down(g(g(g(g(g(g(a))))))) 543.95/242.10 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.10 down(g(g(g(g(g(g(b))))))) 543.95/242.10 down(g(g(g(g(g(g(c))))))) 543.95/242.10 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.10 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.10 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.10 f_flat(up(x0)) 543.95/242.10 g_flat(up(x0)) 543.95/242.10 543.95/242.10 We have to consider all minimal (P,Q,R)-chains. 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1013) TransformationProof (EQUIVALENT) 543.95/242.10 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.10 543.95/242.10 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 543.95/242.10 543.95/242.10 543.95/242.10 ---------------------------------------- 543.95/242.10 543.95/242.10 (1014) 543.95/242.10 Obligation: 543.95/242.10 Q DP problem: 543.95/242.10 The TRS P consists of the following rules: 543.95/242.10 543.95/242.10 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.10 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.10 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.10 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.10 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.10 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.10 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.10 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.10 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.10 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.10 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.10 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.10 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.10 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.10 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))) 543.95/242.10 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.10 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.10 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.10 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.10 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.10 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.10 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.10 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.10 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.10 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.10 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.10 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.10 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.10 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.10 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.95/242.10 543.95/242.10 The TRS R consists of the following rules: 543.95/242.10 543.95/242.10 down(a) -> up(f(a)) 543.95/242.10 down(b) -> up(g(b)) 543.95/242.10 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.10 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.10 down(f(a)) -> f_flat(down(a)) 543.95/242.10 down(f(b)) -> f_flat(down(b)) 543.95/242.10 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.10 down(f(c)) -> f_flat(down(c)) 543.95/242.10 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.10 down(g(a)) -> g_flat(down(a)) 543.95/242.10 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.10 down(g(b)) -> g_flat(down(b)) 543.95/242.10 down(g(c)) -> g_flat(down(c)) 543.95/242.10 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.10 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.10 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.10 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.10 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.10 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.11 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.11 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.11 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.11 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.11 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.11 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.11 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.11 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.11 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.11 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.11 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.11 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.11 543.95/242.11 The set Q consists of the following terms: 543.95/242.11 543.95/242.11 down(a) 543.95/242.11 down(b) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.11 down(f(a)) 543.95/242.11 down(f(b)) 543.95/242.11 down(f(g(x0))) 543.95/242.11 down(f(c)) 543.95/242.11 down(f(fresh_constant)) 543.95/242.11 down(g(a)) 543.95/242.11 down(g(f(x0))) 543.95/242.11 down(g(b)) 543.95/242.11 down(g(c)) 543.95/242.11 down(g(fresh_constant)) 543.95/242.11 down(f(f(a))) 543.95/242.11 down(f(f(b))) 543.95/242.11 down(f(f(g(x0)))) 543.95/242.11 down(f(f(c))) 543.95/242.11 down(f(f(fresh_constant))) 543.95/242.11 down(g(g(a))) 543.95/242.11 down(g(g(f(x0)))) 543.95/242.11 down(g(g(b))) 543.95/242.11 down(g(g(c))) 543.95/242.11 down(g(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) 543.95/242.11 down(f(f(f(g(x0))))) 543.95/242.11 down(f(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) 543.95/242.11 down(g(g(g(f(x0))))) 543.95/242.11 down(g(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(x0)))))) 543.95/242.11 down(f(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(x0)))))) 543.95/242.11 down(g(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(x0))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(x0))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 f_flat(up(x0)) 543.95/242.11 g_flat(up(x0)) 543.95/242.11 543.95/242.11 We have to consider all minimal (P,Q,R)-chains. 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1015) TransformationProof (EQUIVALENT) 543.95/242.11 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.11 543.95/242.11 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 543.95/242.11 543.95/242.11 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1016) 543.95/242.11 Obligation: 543.95/242.11 Q DP problem: 543.95/242.11 The TRS P consists of the following rules: 543.95/242.11 543.95/242.11 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.11 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.11 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.11 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.11 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.11 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.11 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.11 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.11 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.11 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.11 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.11 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.11 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.11 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.11 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.11 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.11 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.11 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.11 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.11 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.11 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.11 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.11 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.11 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.11 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.11 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.95/242.11 543.95/242.11 The TRS R consists of the following rules: 543.95/242.11 543.95/242.11 down(a) -> up(f(a)) 543.95/242.11 down(b) -> up(g(b)) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.11 down(f(a)) -> f_flat(down(a)) 543.95/242.11 down(f(b)) -> f_flat(down(b)) 543.95/242.11 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.11 down(f(c)) -> f_flat(down(c)) 543.95/242.11 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.11 down(g(a)) -> g_flat(down(a)) 543.95/242.11 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.11 down(g(b)) -> g_flat(down(b)) 543.95/242.11 down(g(c)) -> g_flat(down(c)) 543.95/242.11 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.11 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.11 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.11 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.11 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.11 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.11 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.11 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.11 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.11 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.11 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.11 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.11 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.11 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.11 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.11 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.11 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.11 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.11 543.95/242.11 The set Q consists of the following terms: 543.95/242.11 543.95/242.11 down(a) 543.95/242.11 down(b) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.11 down(f(a)) 543.95/242.11 down(f(b)) 543.95/242.11 down(f(g(x0))) 543.95/242.11 down(f(c)) 543.95/242.11 down(f(fresh_constant)) 543.95/242.11 down(g(a)) 543.95/242.11 down(g(f(x0))) 543.95/242.11 down(g(b)) 543.95/242.11 down(g(c)) 543.95/242.11 down(g(fresh_constant)) 543.95/242.11 down(f(f(a))) 543.95/242.11 down(f(f(b))) 543.95/242.11 down(f(f(g(x0)))) 543.95/242.11 down(f(f(c))) 543.95/242.11 down(f(f(fresh_constant))) 543.95/242.11 down(g(g(a))) 543.95/242.11 down(g(g(f(x0)))) 543.95/242.11 down(g(g(b))) 543.95/242.11 down(g(g(c))) 543.95/242.11 down(g(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) 543.95/242.11 down(f(f(f(g(x0))))) 543.95/242.11 down(f(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) 543.95/242.11 down(g(g(g(f(x0))))) 543.95/242.11 down(g(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(x0)))))) 543.95/242.11 down(f(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(x0)))))) 543.95/242.11 down(g(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(x0))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(x0))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 f_flat(up(x0)) 543.95/242.11 g_flat(up(x0)) 543.95/242.11 543.95/242.11 We have to consider all minimal (P,Q,R)-chains. 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1017) TransformationProof (EQUIVALENT) 543.95/242.11 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(a))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.11 543.95/242.11 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a)))))))))))) 543.95/242.11 543.95/242.11 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1018) 543.95/242.11 Obligation: 543.95/242.11 Q DP problem: 543.95/242.11 The TRS P consists of the following rules: 543.95/242.11 543.95/242.11 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.11 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.11 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.11 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.11 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.11 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.11 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.11 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.11 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.11 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.11 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.11 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.11 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.11 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.11 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.11 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.11 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.11 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.11 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.11 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.11 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.11 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.11 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.11 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.11 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.11 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.95/242.11 543.95/242.11 The TRS R consists of the following rules: 543.95/242.11 543.95/242.11 down(a) -> up(f(a)) 543.95/242.11 down(b) -> up(g(b)) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.11 down(f(a)) -> f_flat(down(a)) 543.95/242.11 down(f(b)) -> f_flat(down(b)) 543.95/242.11 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.11 down(f(c)) -> f_flat(down(c)) 543.95/242.11 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.11 down(g(a)) -> g_flat(down(a)) 543.95/242.11 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.11 down(g(b)) -> g_flat(down(b)) 543.95/242.11 down(g(c)) -> g_flat(down(c)) 543.95/242.11 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.11 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.11 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.11 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.11 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.11 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.11 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.11 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.11 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.11 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.11 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.11 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.11 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.11 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.11 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.11 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.11 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.11 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.11 543.95/242.11 The set Q consists of the following terms: 543.95/242.11 543.95/242.11 down(a) 543.95/242.11 down(b) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.11 down(f(a)) 543.95/242.11 down(f(b)) 543.95/242.11 down(f(g(x0))) 543.95/242.11 down(f(c)) 543.95/242.11 down(f(fresh_constant)) 543.95/242.11 down(g(a)) 543.95/242.11 down(g(f(x0))) 543.95/242.11 down(g(b)) 543.95/242.11 down(g(c)) 543.95/242.11 down(g(fresh_constant)) 543.95/242.11 down(f(f(a))) 543.95/242.11 down(f(f(b))) 543.95/242.11 down(f(f(g(x0)))) 543.95/242.11 down(f(f(c))) 543.95/242.11 down(f(f(fresh_constant))) 543.95/242.11 down(g(g(a))) 543.95/242.11 down(g(g(f(x0)))) 543.95/242.11 down(g(g(b))) 543.95/242.11 down(g(g(c))) 543.95/242.11 down(g(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) 543.95/242.11 down(f(f(f(g(x0))))) 543.95/242.11 down(f(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) 543.95/242.11 down(g(g(g(f(x0))))) 543.95/242.11 down(g(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(x0)))))) 543.95/242.11 down(f(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(x0)))))) 543.95/242.11 down(g(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(x0))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(x0))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 f_flat(up(x0)) 543.95/242.11 g_flat(up(x0)) 543.95/242.11 543.95/242.11 We have to consider all minimal (P,Q,R)-chains. 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1019) TransformationProof (EQUIVALENT) 543.95/242.11 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(f(x0)))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.11 543.95/242.11 (TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0))))))))))))) 543.95/242.11 543.95/242.11 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1020) 543.95/242.11 Obligation: 543.95/242.11 Q DP problem: 543.95/242.11 The TRS P consists of the following rules: 543.95/242.11 543.95/242.11 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.11 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.11 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.11 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.11 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.11 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.11 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.11 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.11 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.11 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.11 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.11 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.11 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.11 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.11 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.11 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.11 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.11 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.11 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.11 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.11 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.11 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.11 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.11 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.11 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.11 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.95/242.11 543.95/242.11 The TRS R consists of the following rules: 543.95/242.11 543.95/242.11 down(a) -> up(f(a)) 543.95/242.11 down(b) -> up(g(b)) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.11 down(f(a)) -> f_flat(down(a)) 543.95/242.11 down(f(b)) -> f_flat(down(b)) 543.95/242.11 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.11 down(f(c)) -> f_flat(down(c)) 543.95/242.11 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.11 down(g(a)) -> g_flat(down(a)) 543.95/242.11 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.11 down(g(b)) -> g_flat(down(b)) 543.95/242.11 down(g(c)) -> g_flat(down(c)) 543.95/242.11 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.11 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.11 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.11 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.11 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.11 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.11 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.11 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.11 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.11 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.11 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.11 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.11 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.11 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.11 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.11 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.11 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.11 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.11 543.95/242.11 The set Q consists of the following terms: 543.95/242.11 543.95/242.11 down(a) 543.95/242.11 down(b) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.11 down(f(a)) 543.95/242.11 down(f(b)) 543.95/242.11 down(f(g(x0))) 543.95/242.11 down(f(c)) 543.95/242.11 down(f(fresh_constant)) 543.95/242.11 down(g(a)) 543.95/242.11 down(g(f(x0))) 543.95/242.11 down(g(b)) 543.95/242.11 down(g(c)) 543.95/242.11 down(g(fresh_constant)) 543.95/242.11 down(f(f(a))) 543.95/242.11 down(f(f(b))) 543.95/242.11 down(f(f(g(x0)))) 543.95/242.11 down(f(f(c))) 543.95/242.11 down(f(f(fresh_constant))) 543.95/242.11 down(g(g(a))) 543.95/242.11 down(g(g(f(x0)))) 543.95/242.11 down(g(g(b))) 543.95/242.11 down(g(g(c))) 543.95/242.11 down(g(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) 543.95/242.11 down(f(f(f(g(x0))))) 543.95/242.11 down(f(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) 543.95/242.11 down(g(g(g(f(x0))))) 543.95/242.11 down(g(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(x0)))))) 543.95/242.11 down(f(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(x0)))))) 543.95/242.11 down(g(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(x0))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(x0))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 f_flat(up(x0)) 543.95/242.11 g_flat(up(x0)) 543.95/242.11 543.95/242.11 We have to consider all minimal (P,Q,R)-chains. 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1021) TransformationProof (EQUIVALENT) 543.95/242.11 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(c))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.11 543.95/242.11 (TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c)))))))))))) 543.95/242.11 543.95/242.11 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1022) 543.95/242.11 Obligation: 543.95/242.11 Q DP problem: 543.95/242.11 The TRS P consists of the following rules: 543.95/242.11 543.95/242.11 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.11 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.11 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.11 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.11 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.11 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.11 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.11 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.11 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.11 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.11 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.11 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.11 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.11 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.11 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.11 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.11 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.11 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.11 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.11 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.11 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.11 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) 543.95/242.11 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.11 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.11 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.11 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.95/242.11 543.95/242.11 The TRS R consists of the following rules: 543.95/242.11 543.95/242.11 down(a) -> up(f(a)) 543.95/242.11 down(b) -> up(g(b)) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.11 down(f(a)) -> f_flat(down(a)) 543.95/242.11 down(f(b)) -> f_flat(down(b)) 543.95/242.11 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.11 down(f(c)) -> f_flat(down(c)) 543.95/242.11 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.11 down(g(a)) -> g_flat(down(a)) 543.95/242.11 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.11 down(g(b)) -> g_flat(down(b)) 543.95/242.11 down(g(c)) -> g_flat(down(c)) 543.95/242.11 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.11 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.11 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.11 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.11 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.11 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.11 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.11 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.11 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.11 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.11 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.11 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.11 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.11 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.11 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.11 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.11 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.11 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.11 543.95/242.11 The set Q consists of the following terms: 543.95/242.11 543.95/242.11 down(a) 543.95/242.11 down(b) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.11 down(f(a)) 543.95/242.11 down(f(b)) 543.95/242.11 down(f(g(x0))) 543.95/242.11 down(f(c)) 543.95/242.11 down(f(fresh_constant)) 543.95/242.11 down(g(a)) 543.95/242.11 down(g(f(x0))) 543.95/242.11 down(g(b)) 543.95/242.11 down(g(c)) 543.95/242.11 down(g(fresh_constant)) 543.95/242.11 down(f(f(a))) 543.95/242.11 down(f(f(b))) 543.95/242.11 down(f(f(g(x0)))) 543.95/242.11 down(f(f(c))) 543.95/242.11 down(f(f(fresh_constant))) 543.95/242.11 down(g(g(a))) 543.95/242.11 down(g(g(f(x0)))) 543.95/242.11 down(g(g(b))) 543.95/242.11 down(g(g(c))) 543.95/242.11 down(g(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) 543.95/242.11 down(f(f(f(g(x0))))) 543.95/242.11 down(f(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) 543.95/242.11 down(g(g(g(f(x0))))) 543.95/242.11 down(g(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(x0)))))) 543.95/242.11 down(f(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(x0)))))) 543.95/242.11 down(g(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(x0))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(x0))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 f_flat(up(x0)) 543.95/242.11 g_flat(up(x0)) 543.95/242.11 543.95/242.11 We have to consider all minimal (P,Q,R)-chains. 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1023) TransformationProof (EQUIVALENT) 543.95/242.11 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(f(fresh_constant))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.11 543.95/242.11 (TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant)))))))))))) 543.95/242.11 543.95/242.11 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1024) 543.95/242.11 Obligation: 543.95/242.11 Q DP problem: 543.95/242.11 The TRS P consists of the following rules: 543.95/242.11 543.95/242.11 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.11 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.11 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.11 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.11 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.11 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.11 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.11 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.11 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.11 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.11 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.11 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.11 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.11 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.11 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.11 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.11 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.11 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.11 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.11 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.11 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.11 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.11 TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) 543.95/242.11 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.11 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.11 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.95/242.11 543.95/242.11 The TRS R consists of the following rules: 543.95/242.11 543.95/242.11 down(a) -> up(f(a)) 543.95/242.11 down(b) -> up(g(b)) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.11 down(f(a)) -> f_flat(down(a)) 543.95/242.11 down(f(b)) -> f_flat(down(b)) 543.95/242.11 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.11 down(f(c)) -> f_flat(down(c)) 543.95/242.11 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.11 down(g(a)) -> g_flat(down(a)) 543.95/242.11 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.11 down(g(b)) -> g_flat(down(b)) 543.95/242.11 down(g(c)) -> g_flat(down(c)) 543.95/242.11 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.11 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.11 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.11 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.11 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.11 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.11 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.11 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.11 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.11 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.11 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.11 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.11 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.11 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.11 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.11 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.11 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.11 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.11 543.95/242.11 The set Q consists of the following terms: 543.95/242.11 543.95/242.11 down(a) 543.95/242.11 down(b) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.11 down(f(a)) 543.95/242.11 down(f(b)) 543.95/242.11 down(f(g(x0))) 543.95/242.11 down(f(c)) 543.95/242.11 down(f(fresh_constant)) 543.95/242.11 down(g(a)) 543.95/242.11 down(g(f(x0))) 543.95/242.11 down(g(b)) 543.95/242.11 down(g(c)) 543.95/242.11 down(g(fresh_constant)) 543.95/242.11 down(f(f(a))) 543.95/242.11 down(f(f(b))) 543.95/242.11 down(f(f(g(x0)))) 543.95/242.11 down(f(f(c))) 543.95/242.11 down(f(f(fresh_constant))) 543.95/242.11 down(g(g(a))) 543.95/242.11 down(g(g(f(x0)))) 543.95/242.11 down(g(g(b))) 543.95/242.11 down(g(g(c))) 543.95/242.11 down(g(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) 543.95/242.11 down(f(f(f(g(x0))))) 543.95/242.11 down(f(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) 543.95/242.11 down(g(g(g(f(x0))))) 543.95/242.11 down(g(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(x0)))))) 543.95/242.11 down(f(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(x0)))))) 543.95/242.11 down(g(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(x0))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(x0))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 f_flat(up(x0)) 543.95/242.11 g_flat(up(x0)) 543.95/242.11 543.95/242.11 We have to consider all minimal (P,Q,R)-chains. 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1025) TransformationProof (EQUIVALENT) 543.95/242.11 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(b)))))) -> TOP(f_flat(up(f(f(f(g(b))))))) at position [0] we obtained the following new rules [LPAR04]: 543.95/242.11 543.95/242.11 (TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))),TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b)))))))) 543.95/242.11 543.95/242.11 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1026) 543.95/242.11 Obligation: 543.95/242.11 Q DP problem: 543.95/242.11 The TRS P consists of the following rules: 543.95/242.11 543.95/242.11 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.11 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.11 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.11 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.11 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.11 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.11 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.11 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.11 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.11 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.11 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.11 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.11 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.11 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.11 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.11 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.11 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.11 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.11 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.11 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.11 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.11 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.11 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.11 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.95/242.11 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.95/242.11 543.95/242.11 The TRS R consists of the following rules: 543.95/242.11 543.95/242.11 down(a) -> up(f(a)) 543.95/242.11 down(b) -> up(g(b)) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.11 down(f(a)) -> f_flat(down(a)) 543.95/242.11 down(f(b)) -> f_flat(down(b)) 543.95/242.11 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.11 down(f(c)) -> f_flat(down(c)) 543.95/242.11 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.11 down(g(a)) -> g_flat(down(a)) 543.95/242.11 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.11 down(g(b)) -> g_flat(down(b)) 543.95/242.11 down(g(c)) -> g_flat(down(c)) 543.95/242.11 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.11 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.11 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.11 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.11 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.11 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.11 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.11 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.11 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.11 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.11 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.11 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.11 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.11 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.11 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.11 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.11 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.11 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.11 543.95/242.11 The set Q consists of the following terms: 543.95/242.11 543.95/242.11 down(a) 543.95/242.11 down(b) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.11 down(f(a)) 543.95/242.11 down(f(b)) 543.95/242.11 down(f(g(x0))) 543.95/242.11 down(f(c)) 543.95/242.11 down(f(fresh_constant)) 543.95/242.11 down(g(a)) 543.95/242.11 down(g(f(x0))) 543.95/242.11 down(g(b)) 543.95/242.11 down(g(c)) 543.95/242.11 down(g(fresh_constant)) 543.95/242.11 down(f(f(a))) 543.95/242.11 down(f(f(b))) 543.95/242.11 down(f(f(g(x0)))) 543.95/242.11 down(f(f(c))) 543.95/242.11 down(f(f(fresh_constant))) 543.95/242.11 down(g(g(a))) 543.95/242.11 down(g(g(f(x0)))) 543.95/242.11 down(g(g(b))) 543.95/242.11 down(g(g(c))) 543.95/242.11 down(g(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) 543.95/242.11 down(f(f(f(g(x0))))) 543.95/242.11 down(f(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) 543.95/242.11 down(g(g(g(f(x0))))) 543.95/242.11 down(g(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(x0)))))) 543.95/242.11 down(f(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(x0)))))) 543.95/242.11 down(g(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(x0))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(x0))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 f_flat(up(x0)) 543.95/242.11 g_flat(up(x0)) 543.95/242.11 543.95/242.11 We have to consider all minimal (P,Q,R)-chains. 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1027) TransformationProof (EQUIVALENT) 543.95/242.11 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(g(b)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.11 543.95/242.11 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b))))))))) 543.95/242.11 543.95/242.11 543.95/242.11 ---------------------------------------- 543.95/242.11 543.95/242.11 (1028) 543.95/242.11 Obligation: 543.95/242.11 Q DP problem: 543.95/242.11 The TRS P consists of the following rules: 543.95/242.11 543.95/242.11 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.11 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.11 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.11 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.11 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.11 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.11 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.11 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.11 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.11 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.11 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.11 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.11 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.11 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.11 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.11 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.11 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.11 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.11 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.11 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.11 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.11 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.11 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.11 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.95/242.11 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.95/242.11 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.95/242.11 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.95/242.11 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.95/242.11 543.95/242.11 The TRS R consists of the following rules: 543.95/242.11 543.95/242.11 down(a) -> up(f(a)) 543.95/242.11 down(b) -> up(g(b)) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.11 down(f(a)) -> f_flat(down(a)) 543.95/242.11 down(f(b)) -> f_flat(down(b)) 543.95/242.11 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.11 down(f(c)) -> f_flat(down(c)) 543.95/242.11 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.11 down(g(a)) -> g_flat(down(a)) 543.95/242.11 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.11 down(g(b)) -> g_flat(down(b)) 543.95/242.11 down(g(c)) -> g_flat(down(c)) 543.95/242.11 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.11 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.11 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.11 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.11 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.11 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.11 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.11 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.11 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.11 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.11 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.11 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.11 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.11 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.11 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.11 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.11 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.11 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.11 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.11 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.11 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.11 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.11 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.11 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.11 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.11 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.11 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.11 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.11 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.11 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.11 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.11 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.11 543.95/242.11 The set Q consists of the following terms: 543.95/242.11 543.95/242.11 down(a) 543.95/242.11 down(b) 543.95/242.11 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.11 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.11 down(f(a)) 543.95/242.11 down(f(b)) 543.95/242.11 down(f(g(x0))) 543.95/242.11 down(f(c)) 543.95/242.11 down(f(fresh_constant)) 543.95/242.11 down(g(a)) 543.95/242.11 down(g(f(x0))) 543.95/242.11 down(g(b)) 543.95/242.11 down(g(c)) 543.95/242.11 down(g(fresh_constant)) 543.95/242.11 down(f(f(a))) 543.95/242.11 down(f(f(b))) 543.95/242.11 down(f(f(g(x0)))) 543.95/242.11 down(f(f(c))) 543.95/242.11 down(f(f(fresh_constant))) 543.95/242.11 down(g(g(a))) 543.95/242.11 down(g(g(f(x0)))) 543.95/242.11 down(g(g(b))) 543.95/242.11 down(g(g(c))) 543.95/242.11 down(g(g(fresh_constant))) 543.95/242.11 down(f(f(f(a)))) 543.95/242.11 down(f(f(f(b)))) 543.95/242.11 down(f(f(f(g(x0))))) 543.95/242.11 down(f(f(f(c)))) 543.95/242.11 down(f(f(f(fresh_constant)))) 543.95/242.11 down(g(g(g(a)))) 543.95/242.11 down(g(g(g(f(x0))))) 543.95/242.11 down(g(g(g(b)))) 543.95/242.11 down(g(g(g(c)))) 543.95/242.11 down(g(g(g(fresh_constant)))) 543.95/242.11 down(f(f(f(f(a))))) 543.95/242.11 down(f(f(f(f(b))))) 543.95/242.11 down(f(f(f(f(g(x0)))))) 543.95/242.11 down(f(f(f(f(c))))) 543.95/242.11 down(f(f(f(f(fresh_constant))))) 543.95/242.11 down(g(g(g(g(a))))) 543.95/242.11 down(g(g(g(g(f(x0)))))) 543.95/242.11 down(g(g(g(g(b))))) 543.95/242.11 down(g(g(g(g(c))))) 543.95/242.11 down(g(g(g(g(fresh_constant))))) 543.95/242.11 down(f(f(f(f(f(a)))))) 543.95/242.11 down(f(f(f(f(f(b)))))) 543.95/242.11 down(f(f(f(f(f(g(x0))))))) 543.95/242.11 down(f(f(f(f(f(c)))))) 543.95/242.11 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.11 down(g(g(g(g(g(a)))))) 543.95/242.11 down(g(g(g(g(g(f(x0))))))) 543.95/242.11 down(g(g(g(g(g(b)))))) 543.95/242.11 down(g(g(g(g(g(c)))))) 543.95/242.12 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.12 down(f(f(f(f(f(f(a))))))) 543.95/242.12 down(f(f(f(f(f(f(b))))))) 543.95/242.12 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.12 down(f(f(f(f(f(f(c))))))) 543.95/242.12 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.12 down(g(g(g(g(g(g(a))))))) 543.95/242.12 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.12 down(g(g(g(g(g(g(b))))))) 543.95/242.12 down(g(g(g(g(g(g(c))))))) 543.95/242.12 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.12 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(b))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(c))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.12 f_flat(up(x0)) 543.95/242.12 g_flat(up(x0)) 543.95/242.12 543.95/242.12 We have to consider all minimal (P,Q,R)-chains. 543.95/242.12 ---------------------------------------- 543.95/242.12 543.95/242.12 (1029) TransformationProof (EQUIVALENT) 543.95/242.12 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.95/242.12 543.95/242.12 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 543.95/242.12 543.95/242.12 543.95/242.12 ---------------------------------------- 543.95/242.12 543.95/242.12 (1030) 543.95/242.12 Obligation: 543.95/242.12 Q DP problem: 543.95/242.12 The TRS P consists of the following rules: 543.95/242.12 543.95/242.12 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.95/242.12 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.95/242.12 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.95/242.12 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.95/242.12 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.95/242.12 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.95/242.12 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.95/242.12 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.95/242.12 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.95/242.12 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.95/242.12 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.95/242.12 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.95/242.12 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.95/242.12 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.95/242.12 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.95/242.12 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.95/242.12 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.95/242.12 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.95/242.12 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.95/242.12 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.95/242.12 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.95/242.12 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.95/242.12 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.95/242.12 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.95/242.12 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.95/242.12 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.95/242.12 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.95/242.12 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.95/242.12 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.95/242.12 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.95/242.12 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.95/242.12 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.95/242.12 543.95/242.12 The TRS R consists of the following rules: 543.95/242.12 543.95/242.12 down(a) -> up(f(a)) 543.95/242.12 down(b) -> up(g(b)) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.95/242.12 down(f(a)) -> f_flat(down(a)) 543.95/242.12 down(f(b)) -> f_flat(down(b)) 543.95/242.12 down(f(g(y4))) -> f_flat(down(g(y4))) 543.95/242.12 down(f(c)) -> f_flat(down(c)) 543.95/242.12 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.95/242.12 down(g(a)) -> g_flat(down(a)) 543.95/242.12 down(g(f(y6))) -> g_flat(down(f(y6))) 543.95/242.12 down(g(b)) -> g_flat(down(b)) 543.95/242.12 down(g(c)) -> g_flat(down(c)) 543.95/242.12 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.95/242.12 down(f(f(a))) -> f_flat(down(f(a))) 543.95/242.12 down(f(f(b))) -> f_flat(down(f(b))) 543.95/242.12 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.95/242.12 down(f(f(c))) -> f_flat(down(f(c))) 543.95/242.12 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.95/242.12 down(g(g(a))) -> g_flat(down(g(a))) 543.95/242.12 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.95/242.12 down(g(g(b))) -> g_flat(down(g(b))) 543.95/242.12 down(g(g(c))) -> g_flat(down(g(c))) 543.95/242.12 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.95/242.12 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.95/242.12 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.95/242.12 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.95/242.12 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.95/242.12 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.95/242.12 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.95/242.12 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.95/242.12 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.95/242.12 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.95/242.12 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.95/242.12 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.95/242.12 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.95/242.12 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.95/242.12 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.95/242.12 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.95/242.12 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.95/242.12 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.95/242.12 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.95/242.12 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.95/242.12 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.95/242.12 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.95/242.12 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.95/242.12 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.95/242.12 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.95/242.12 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.95/242.12 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.95/242.12 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.95/242.12 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.95/242.12 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.95/242.12 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.95/242.12 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.95/242.12 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.95/242.12 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.95/242.12 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.95/242.12 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.95/242.12 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.95/242.12 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.95/242.12 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.95/242.12 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.95/242.12 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.95/242.12 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.95/242.12 g_flat(up(x_1)) -> up(g(x_1)) 543.95/242.12 f_flat(up(x_1)) -> up(f(x_1)) 543.95/242.12 543.95/242.12 The set Q consists of the following terms: 543.95/242.12 543.95/242.12 down(a) 543.95/242.12 down(b) 543.95/242.12 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.95/242.12 down(f(a)) 543.95/242.12 down(f(b)) 543.95/242.12 down(f(g(x0))) 543.95/242.12 down(f(c)) 543.95/242.12 down(f(fresh_constant)) 543.95/242.12 down(g(a)) 543.95/242.12 down(g(f(x0))) 543.95/242.12 down(g(b)) 543.95/242.12 down(g(c)) 543.95/242.12 down(g(fresh_constant)) 543.95/242.12 down(f(f(a))) 543.95/242.12 down(f(f(b))) 543.95/242.12 down(f(f(g(x0)))) 543.95/242.12 down(f(f(c))) 543.95/242.12 down(f(f(fresh_constant))) 543.95/242.12 down(g(g(a))) 543.95/242.12 down(g(g(f(x0)))) 543.95/242.12 down(g(g(b))) 543.95/242.12 down(g(g(c))) 543.95/242.12 down(g(g(fresh_constant))) 543.95/242.12 down(f(f(f(a)))) 543.95/242.12 down(f(f(f(b)))) 543.95/242.12 down(f(f(f(g(x0))))) 543.95/242.12 down(f(f(f(c)))) 543.95/242.12 down(f(f(f(fresh_constant)))) 543.95/242.12 down(g(g(g(a)))) 543.95/242.12 down(g(g(g(f(x0))))) 543.95/242.12 down(g(g(g(b)))) 543.95/242.12 down(g(g(g(c)))) 543.95/242.12 down(g(g(g(fresh_constant)))) 543.95/242.12 down(f(f(f(f(a))))) 543.95/242.12 down(f(f(f(f(b))))) 543.95/242.12 down(f(f(f(f(g(x0)))))) 543.95/242.12 down(f(f(f(f(c))))) 543.95/242.12 down(f(f(f(f(fresh_constant))))) 543.95/242.12 down(g(g(g(g(a))))) 543.95/242.12 down(g(g(g(g(f(x0)))))) 543.95/242.12 down(g(g(g(g(b))))) 543.95/242.12 down(g(g(g(g(c))))) 543.95/242.12 down(g(g(g(g(fresh_constant))))) 543.95/242.12 down(f(f(f(f(f(a)))))) 543.95/242.12 down(f(f(f(f(f(b)))))) 543.95/242.12 down(f(f(f(f(f(g(x0))))))) 543.95/242.12 down(f(f(f(f(f(c)))))) 543.95/242.12 down(f(f(f(f(f(fresh_constant)))))) 543.95/242.12 down(g(g(g(g(g(a)))))) 543.95/242.12 down(g(g(g(g(g(f(x0))))))) 543.95/242.12 down(g(g(g(g(g(b)))))) 543.95/242.12 down(g(g(g(g(g(c)))))) 543.95/242.12 down(g(g(g(g(g(fresh_constant)))))) 543.95/242.12 down(f(f(f(f(f(f(a))))))) 543.95/242.12 down(f(f(f(f(f(f(b))))))) 543.95/242.12 down(f(f(f(f(f(f(g(x0)))))))) 543.95/242.12 down(f(f(f(f(f(f(c))))))) 543.95/242.12 down(f(f(f(f(f(f(fresh_constant))))))) 543.95/242.12 down(g(g(g(g(g(g(a))))))) 543.95/242.12 down(g(g(g(g(g(g(f(x0)))))))) 543.95/242.12 down(g(g(g(g(g(g(b))))))) 543.95/242.12 down(g(g(g(g(g(g(c))))))) 543.95/242.12 down(g(g(g(g(g(g(fresh_constant))))))) 543.95/242.12 down(f(f(f(f(f(f(f(a)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(b)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(g(x0))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(c)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(a)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(f(x0))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(b)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(c)))))))) 543.95/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(a))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(b))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(c))))))))) 543.95/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(a))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.95/242.12 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 f_flat(up(x0)) 543.98/242.12 g_flat(up(x0)) 543.98/242.12 543.98/242.12 We have to consider all minimal (P,Q,R)-chains. 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1031) TransformationProof (EQUIVALENT) 543.98/242.12 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.12 543.98/242.12 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 543.98/242.12 543.98/242.12 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1032) 543.98/242.12 Obligation: 543.98/242.12 Q DP problem: 543.98/242.12 The TRS P consists of the following rules: 543.98/242.12 543.98/242.12 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.12 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.12 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.12 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.12 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.12 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.12 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.12 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.12 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.12 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.12 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.12 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.12 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.12 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.12 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.12 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.12 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.12 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.12 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.12 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.12 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.12 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.98/242.12 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.98/242.12 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.12 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.12 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.12 543.98/242.12 The TRS R consists of the following rules: 543.98/242.12 543.98/242.12 down(a) -> up(f(a)) 543.98/242.12 down(b) -> up(g(b)) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.12 down(f(a)) -> f_flat(down(a)) 543.98/242.12 down(f(b)) -> f_flat(down(b)) 543.98/242.12 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.12 down(f(c)) -> f_flat(down(c)) 543.98/242.12 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.12 down(g(a)) -> g_flat(down(a)) 543.98/242.12 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.12 down(g(b)) -> g_flat(down(b)) 543.98/242.12 down(g(c)) -> g_flat(down(c)) 543.98/242.12 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.12 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.12 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.12 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.12 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.12 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.12 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.12 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.12 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.12 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.12 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.12 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.12 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.12 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.12 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.12 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.12 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.12 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.12 543.98/242.12 The set Q consists of the following terms: 543.98/242.12 543.98/242.12 down(a) 543.98/242.12 down(b) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.12 down(f(a)) 543.98/242.12 down(f(b)) 543.98/242.12 down(f(g(x0))) 543.98/242.12 down(f(c)) 543.98/242.12 down(f(fresh_constant)) 543.98/242.12 down(g(a)) 543.98/242.12 down(g(f(x0))) 543.98/242.12 down(g(b)) 543.98/242.12 down(g(c)) 543.98/242.12 down(g(fresh_constant)) 543.98/242.12 down(f(f(a))) 543.98/242.12 down(f(f(b))) 543.98/242.12 down(f(f(g(x0)))) 543.98/242.12 down(f(f(c))) 543.98/242.12 down(f(f(fresh_constant))) 543.98/242.12 down(g(g(a))) 543.98/242.12 down(g(g(f(x0)))) 543.98/242.12 down(g(g(b))) 543.98/242.12 down(g(g(c))) 543.98/242.12 down(g(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) 543.98/242.12 down(f(f(f(g(x0))))) 543.98/242.12 down(f(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) 543.98/242.12 down(g(g(g(f(x0))))) 543.98/242.12 down(g(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(x0)))))) 543.98/242.12 down(f(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(x0)))))) 543.98/242.12 down(g(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(x0))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(x0))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 f_flat(up(x0)) 543.98/242.12 g_flat(up(x0)) 543.98/242.12 543.98/242.12 We have to consider all minimal (P,Q,R)-chains. 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1033) TransformationProof (EQUIVALENT) 543.98/242.12 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.12 543.98/242.12 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 543.98/242.12 543.98/242.12 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1034) 543.98/242.12 Obligation: 543.98/242.12 Q DP problem: 543.98/242.12 The TRS P consists of the following rules: 543.98/242.12 543.98/242.12 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.12 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.12 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.12 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.12 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.12 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.12 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.12 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.12 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.12 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.12 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.12 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.12 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.12 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.12 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.12 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.12 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.12 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.12 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.12 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.12 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.12 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.98/242.12 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.98/242.12 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.12 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.12 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.12 543.98/242.12 The TRS R consists of the following rules: 543.98/242.12 543.98/242.12 down(a) -> up(f(a)) 543.98/242.12 down(b) -> up(g(b)) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.12 down(f(a)) -> f_flat(down(a)) 543.98/242.12 down(f(b)) -> f_flat(down(b)) 543.98/242.12 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.12 down(f(c)) -> f_flat(down(c)) 543.98/242.12 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.12 down(g(a)) -> g_flat(down(a)) 543.98/242.12 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.12 down(g(b)) -> g_flat(down(b)) 543.98/242.12 down(g(c)) -> g_flat(down(c)) 543.98/242.12 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.12 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.12 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.12 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.12 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.12 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.12 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.12 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.12 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.12 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.12 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.12 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.12 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.12 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.12 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.12 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.12 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.12 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.12 543.98/242.12 The set Q consists of the following terms: 543.98/242.12 543.98/242.12 down(a) 543.98/242.12 down(b) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.12 down(f(a)) 543.98/242.12 down(f(b)) 543.98/242.12 down(f(g(x0))) 543.98/242.12 down(f(c)) 543.98/242.12 down(f(fresh_constant)) 543.98/242.12 down(g(a)) 543.98/242.12 down(g(f(x0))) 543.98/242.12 down(g(b)) 543.98/242.12 down(g(c)) 543.98/242.12 down(g(fresh_constant)) 543.98/242.12 down(f(f(a))) 543.98/242.12 down(f(f(b))) 543.98/242.12 down(f(f(g(x0)))) 543.98/242.12 down(f(f(c))) 543.98/242.12 down(f(f(fresh_constant))) 543.98/242.12 down(g(g(a))) 543.98/242.12 down(g(g(f(x0)))) 543.98/242.12 down(g(g(b))) 543.98/242.12 down(g(g(c))) 543.98/242.12 down(g(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) 543.98/242.12 down(f(f(f(g(x0))))) 543.98/242.12 down(f(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) 543.98/242.12 down(g(g(g(f(x0))))) 543.98/242.12 down(g(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(x0)))))) 543.98/242.12 down(f(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(x0)))))) 543.98/242.12 down(g(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(x0))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(x0))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 f_flat(up(x0)) 543.98/242.12 g_flat(up(x0)) 543.98/242.12 543.98/242.12 We have to consider all minimal (P,Q,R)-chains. 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1035) TransformationProof (EQUIVALENT) 543.98/242.12 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.12 543.98/242.12 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 543.98/242.12 543.98/242.12 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1036) 543.98/242.12 Obligation: 543.98/242.12 Q DP problem: 543.98/242.12 The TRS P consists of the following rules: 543.98/242.12 543.98/242.12 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.12 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.12 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.12 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.12 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.12 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.12 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.12 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.12 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.12 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.12 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.12 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.12 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.12 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.12 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.12 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.12 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.12 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.12 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.12 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.12 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.12 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.98/242.12 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.98/242.12 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.12 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.12 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.12 543.98/242.12 The TRS R consists of the following rules: 543.98/242.12 543.98/242.12 down(a) -> up(f(a)) 543.98/242.12 down(b) -> up(g(b)) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.12 down(f(a)) -> f_flat(down(a)) 543.98/242.12 down(f(b)) -> f_flat(down(b)) 543.98/242.12 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.12 down(f(c)) -> f_flat(down(c)) 543.98/242.12 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.12 down(g(a)) -> g_flat(down(a)) 543.98/242.12 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.12 down(g(b)) -> g_flat(down(b)) 543.98/242.12 down(g(c)) -> g_flat(down(c)) 543.98/242.12 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.12 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.12 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.12 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.12 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.12 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.12 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.12 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.12 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.12 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.12 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.12 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.12 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.12 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.12 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.12 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.12 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.12 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.12 543.98/242.12 The set Q consists of the following terms: 543.98/242.12 543.98/242.12 down(a) 543.98/242.12 down(b) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.12 down(f(a)) 543.98/242.12 down(f(b)) 543.98/242.12 down(f(g(x0))) 543.98/242.12 down(f(c)) 543.98/242.12 down(f(fresh_constant)) 543.98/242.12 down(g(a)) 543.98/242.12 down(g(f(x0))) 543.98/242.12 down(g(b)) 543.98/242.12 down(g(c)) 543.98/242.12 down(g(fresh_constant)) 543.98/242.12 down(f(f(a))) 543.98/242.12 down(f(f(b))) 543.98/242.12 down(f(f(g(x0)))) 543.98/242.12 down(f(f(c))) 543.98/242.12 down(f(f(fresh_constant))) 543.98/242.12 down(g(g(a))) 543.98/242.12 down(g(g(f(x0)))) 543.98/242.12 down(g(g(b))) 543.98/242.12 down(g(g(c))) 543.98/242.12 down(g(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) 543.98/242.12 down(f(f(f(g(x0))))) 543.98/242.12 down(f(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) 543.98/242.12 down(g(g(g(f(x0))))) 543.98/242.12 down(g(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(x0)))))) 543.98/242.12 down(f(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(x0)))))) 543.98/242.12 down(g(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(x0))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(x0))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 f_flat(up(x0)) 543.98/242.12 g_flat(up(x0)) 543.98/242.12 543.98/242.12 We have to consider all minimal (P,Q,R)-chains. 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1037) TransformationProof (EQUIVALENT) 543.98/242.12 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(b))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.12 543.98/242.12 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b)))))))))))) 543.98/242.12 543.98/242.12 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1038) 543.98/242.12 Obligation: 543.98/242.12 Q DP problem: 543.98/242.12 The TRS P consists of the following rules: 543.98/242.12 543.98/242.12 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.12 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.12 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.12 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.12 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.12 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.12 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.12 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.12 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.12 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.12 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.12 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.12 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.12 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.12 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.12 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.12 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.12 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.12 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.12 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.12 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.12 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.98/242.12 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.98/242.12 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.12 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.12 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.12 543.98/242.12 The TRS R consists of the following rules: 543.98/242.12 543.98/242.12 down(a) -> up(f(a)) 543.98/242.12 down(b) -> up(g(b)) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.12 down(f(a)) -> f_flat(down(a)) 543.98/242.12 down(f(b)) -> f_flat(down(b)) 543.98/242.12 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.12 down(f(c)) -> f_flat(down(c)) 543.98/242.12 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.12 down(g(a)) -> g_flat(down(a)) 543.98/242.12 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.12 down(g(b)) -> g_flat(down(b)) 543.98/242.12 down(g(c)) -> g_flat(down(c)) 543.98/242.12 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.12 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.12 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.12 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.12 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.12 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.12 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.12 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.12 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.12 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.12 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.12 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.12 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.12 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.12 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.12 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.12 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.12 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.12 543.98/242.12 The set Q consists of the following terms: 543.98/242.12 543.98/242.12 down(a) 543.98/242.12 down(b) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.12 down(f(a)) 543.98/242.12 down(f(b)) 543.98/242.12 down(f(g(x0))) 543.98/242.12 down(f(c)) 543.98/242.12 down(f(fresh_constant)) 543.98/242.12 down(g(a)) 543.98/242.12 down(g(f(x0))) 543.98/242.12 down(g(b)) 543.98/242.12 down(g(c)) 543.98/242.12 down(g(fresh_constant)) 543.98/242.12 down(f(f(a))) 543.98/242.12 down(f(f(b))) 543.98/242.12 down(f(f(g(x0)))) 543.98/242.12 down(f(f(c))) 543.98/242.12 down(f(f(fresh_constant))) 543.98/242.12 down(g(g(a))) 543.98/242.12 down(g(g(f(x0)))) 543.98/242.12 down(g(g(b))) 543.98/242.12 down(g(g(c))) 543.98/242.12 down(g(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) 543.98/242.12 down(f(f(f(g(x0))))) 543.98/242.12 down(f(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) 543.98/242.12 down(g(g(g(f(x0))))) 543.98/242.12 down(g(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(x0)))))) 543.98/242.12 down(f(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(x0)))))) 543.98/242.12 down(g(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(x0))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(x0))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 f_flat(up(x0)) 543.98/242.12 g_flat(up(x0)) 543.98/242.12 543.98/242.12 We have to consider all minimal (P,Q,R)-chains. 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1039) TransformationProof (EQUIVALENT) 543.98/242.12 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(c))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.12 543.98/242.12 (TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c)))))))))))) 543.98/242.12 543.98/242.12 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1040) 543.98/242.12 Obligation: 543.98/242.12 Q DP problem: 543.98/242.12 The TRS P consists of the following rules: 543.98/242.12 543.98/242.12 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.12 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.12 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.12 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.12 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.12 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.12 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.12 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.12 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.12 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.12 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.12 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.12 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.12 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.12 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.12 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.12 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.12 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.12 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.12 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.12 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.12 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) 543.98/242.12 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.98/242.12 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.12 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.12 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.12 543.98/242.12 The TRS R consists of the following rules: 543.98/242.12 543.98/242.12 down(a) -> up(f(a)) 543.98/242.12 down(b) -> up(g(b)) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.12 down(f(a)) -> f_flat(down(a)) 543.98/242.12 down(f(b)) -> f_flat(down(b)) 543.98/242.12 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.12 down(f(c)) -> f_flat(down(c)) 543.98/242.12 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.12 down(g(a)) -> g_flat(down(a)) 543.98/242.12 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.12 down(g(b)) -> g_flat(down(b)) 543.98/242.12 down(g(c)) -> g_flat(down(c)) 543.98/242.12 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.12 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.12 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.12 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.12 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.12 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.12 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.12 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.12 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.12 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.12 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.12 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.12 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.12 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.12 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.12 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.12 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.12 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.12 543.98/242.12 The set Q consists of the following terms: 543.98/242.12 543.98/242.12 down(a) 543.98/242.12 down(b) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.12 down(f(a)) 543.98/242.12 down(f(b)) 543.98/242.12 down(f(g(x0))) 543.98/242.12 down(f(c)) 543.98/242.12 down(f(fresh_constant)) 543.98/242.12 down(g(a)) 543.98/242.12 down(g(f(x0))) 543.98/242.12 down(g(b)) 543.98/242.12 down(g(c)) 543.98/242.12 down(g(fresh_constant)) 543.98/242.12 down(f(f(a))) 543.98/242.12 down(f(f(b))) 543.98/242.12 down(f(f(g(x0)))) 543.98/242.12 down(f(f(c))) 543.98/242.12 down(f(f(fresh_constant))) 543.98/242.12 down(g(g(a))) 543.98/242.12 down(g(g(f(x0)))) 543.98/242.12 down(g(g(b))) 543.98/242.12 down(g(g(c))) 543.98/242.12 down(g(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) 543.98/242.12 down(f(f(f(g(x0))))) 543.98/242.12 down(f(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) 543.98/242.12 down(g(g(g(f(x0))))) 543.98/242.12 down(g(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(x0)))))) 543.98/242.12 down(f(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(x0)))))) 543.98/242.12 down(g(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(x0))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(x0))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 f_flat(up(x0)) 543.98/242.12 g_flat(up(x0)) 543.98/242.12 543.98/242.12 We have to consider all minimal (P,Q,R)-chains. 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1041) TransformationProof (EQUIVALENT) 543.98/242.12 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(g(fresh_constant))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.12 543.98/242.12 (TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant)))))))))))) 543.98/242.12 543.98/242.12 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1042) 543.98/242.12 Obligation: 543.98/242.12 Q DP problem: 543.98/242.12 The TRS P consists of the following rules: 543.98/242.12 543.98/242.12 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.12 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.12 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.12 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.12 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.12 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.12 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.12 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.12 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.12 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.12 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.12 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.12 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.12 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.12 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.12 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.12 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.12 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.12 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.12 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.12 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.12 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.12 TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) 543.98/242.12 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.12 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.12 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.98/242.12 543.98/242.12 The TRS R consists of the following rules: 543.98/242.12 543.98/242.12 down(a) -> up(f(a)) 543.98/242.12 down(b) -> up(g(b)) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.12 down(f(a)) -> f_flat(down(a)) 543.98/242.12 down(f(b)) -> f_flat(down(b)) 543.98/242.12 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.12 down(f(c)) -> f_flat(down(c)) 543.98/242.12 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.12 down(g(a)) -> g_flat(down(a)) 543.98/242.12 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.12 down(g(b)) -> g_flat(down(b)) 543.98/242.12 down(g(c)) -> g_flat(down(c)) 543.98/242.12 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.12 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.12 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.12 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.12 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.12 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.12 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.12 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.12 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.12 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.12 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.12 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.12 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.12 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.12 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.12 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.12 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.12 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.12 543.98/242.12 The set Q consists of the following terms: 543.98/242.12 543.98/242.12 down(a) 543.98/242.12 down(b) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.12 down(f(a)) 543.98/242.12 down(f(b)) 543.98/242.12 down(f(g(x0))) 543.98/242.12 down(f(c)) 543.98/242.12 down(f(fresh_constant)) 543.98/242.12 down(g(a)) 543.98/242.12 down(g(f(x0))) 543.98/242.12 down(g(b)) 543.98/242.12 down(g(c)) 543.98/242.12 down(g(fresh_constant)) 543.98/242.12 down(f(f(a))) 543.98/242.12 down(f(f(b))) 543.98/242.12 down(f(f(g(x0)))) 543.98/242.12 down(f(f(c))) 543.98/242.12 down(f(f(fresh_constant))) 543.98/242.12 down(g(g(a))) 543.98/242.12 down(g(g(f(x0)))) 543.98/242.12 down(g(g(b))) 543.98/242.12 down(g(g(c))) 543.98/242.12 down(g(g(fresh_constant))) 543.98/242.12 down(f(f(f(a)))) 543.98/242.12 down(f(f(f(b)))) 543.98/242.12 down(f(f(f(g(x0))))) 543.98/242.12 down(f(f(f(c)))) 543.98/242.12 down(f(f(f(fresh_constant)))) 543.98/242.12 down(g(g(g(a)))) 543.98/242.12 down(g(g(g(f(x0))))) 543.98/242.12 down(g(g(g(b)))) 543.98/242.12 down(g(g(g(c)))) 543.98/242.12 down(g(g(g(fresh_constant)))) 543.98/242.12 down(f(f(f(f(a))))) 543.98/242.12 down(f(f(f(f(b))))) 543.98/242.12 down(f(f(f(f(g(x0)))))) 543.98/242.12 down(f(f(f(f(c))))) 543.98/242.12 down(f(f(f(f(fresh_constant))))) 543.98/242.12 down(g(g(g(g(a))))) 543.98/242.12 down(g(g(g(g(f(x0)))))) 543.98/242.12 down(g(g(g(g(b))))) 543.98/242.12 down(g(g(g(g(c))))) 543.98/242.12 down(g(g(g(g(fresh_constant))))) 543.98/242.12 down(f(f(f(f(f(a)))))) 543.98/242.12 down(f(f(f(f(f(b)))))) 543.98/242.12 down(f(f(f(f(f(g(x0))))))) 543.98/242.12 down(f(f(f(f(f(c)))))) 543.98/242.12 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.12 down(g(g(g(g(g(a)))))) 543.98/242.12 down(g(g(g(g(g(f(x0))))))) 543.98/242.12 down(g(g(g(g(g(b)))))) 543.98/242.12 down(g(g(g(g(g(c)))))) 543.98/242.12 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.12 down(f(f(f(f(f(f(a))))))) 543.98/242.12 down(f(f(f(f(f(f(b))))))) 543.98/242.12 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.12 down(f(f(f(f(f(f(c))))))) 543.98/242.12 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.12 down(g(g(g(g(g(g(a))))))) 543.98/242.12 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.12 down(g(g(g(g(g(g(b))))))) 543.98/242.12 down(g(g(g(g(g(g(c))))))) 543.98/242.12 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.12 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.12 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.12 f_flat(up(x0)) 543.98/242.12 g_flat(up(x0)) 543.98/242.12 543.98/242.12 We have to consider all minimal (P,Q,R)-chains. 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1043) TransformationProof (EQUIVALENT) 543.98/242.12 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(a)))))) -> TOP(g_flat(up(g(g(g(f(a))))))) at position [0] we obtained the following new rules [LPAR04]: 543.98/242.12 543.98/242.12 (TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))),TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a)))))))) 543.98/242.12 543.98/242.12 543.98/242.12 ---------------------------------------- 543.98/242.12 543.98/242.12 (1044) 543.98/242.12 Obligation: 543.98/242.12 Q DP problem: 543.98/242.12 The TRS P consists of the following rules: 543.98/242.12 543.98/242.12 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.12 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.12 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.12 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.12 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.12 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.12 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.12 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.12 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.12 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.12 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.12 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.12 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.12 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.12 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.12 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.12 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.12 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.12 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.12 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.12 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.12 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.12 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.12 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.12 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.12 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.12 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.12 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.98/242.12 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 543.98/242.12 543.98/242.12 The TRS R consists of the following rules: 543.98/242.12 543.98/242.12 down(a) -> up(f(a)) 543.98/242.12 down(b) -> up(g(b)) 543.98/242.12 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.12 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.12 down(f(a)) -> f_flat(down(a)) 543.98/242.12 down(f(b)) -> f_flat(down(b)) 543.98/242.12 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.12 down(f(c)) -> f_flat(down(c)) 543.98/242.12 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.13 down(g(a)) -> g_flat(down(a)) 543.98/242.13 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.13 down(g(b)) -> g_flat(down(b)) 543.98/242.13 down(g(c)) -> g_flat(down(c)) 543.98/242.13 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.13 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.13 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.13 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.13 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.13 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.13 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.13 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.13 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.13 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.13 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.13 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.13 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.13 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.13 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.13 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.13 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.13 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.13 543.98/242.13 The set Q consists of the following terms: 543.98/242.13 543.98/242.13 down(a) 543.98/242.13 down(b) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.13 down(f(a)) 543.98/242.13 down(f(b)) 543.98/242.13 down(f(g(x0))) 543.98/242.13 down(f(c)) 543.98/242.13 down(f(fresh_constant)) 543.98/242.13 down(g(a)) 543.98/242.13 down(g(f(x0))) 543.98/242.13 down(g(b)) 543.98/242.13 down(g(c)) 543.98/242.13 down(g(fresh_constant)) 543.98/242.13 down(f(f(a))) 543.98/242.13 down(f(f(b))) 543.98/242.13 down(f(f(g(x0)))) 543.98/242.13 down(f(f(c))) 543.98/242.13 down(f(f(fresh_constant))) 543.98/242.13 down(g(g(a))) 543.98/242.13 down(g(g(f(x0)))) 543.98/242.13 down(g(g(b))) 543.98/242.13 down(g(g(c))) 543.98/242.13 down(g(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) 543.98/242.13 down(f(f(f(g(x0))))) 543.98/242.13 down(f(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) 543.98/242.13 down(g(g(g(f(x0))))) 543.98/242.13 down(g(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(x0)))))) 543.98/242.13 down(f(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(x0)))))) 543.98/242.13 down(g(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(x0))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(x0))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 f_flat(up(x0)) 543.98/242.13 g_flat(up(x0)) 543.98/242.13 543.98/242.13 We have to consider all minimal (P,Q,R)-chains. 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1045) TransformationProof (EQUIVALENT) 543.98/242.13 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(f(a)))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.13 543.98/242.13 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a))))))))) 543.98/242.13 543.98/242.13 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1046) 543.98/242.13 Obligation: 543.98/242.13 Q DP problem: 543.98/242.13 The TRS P consists of the following rules: 543.98/242.13 543.98/242.13 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.13 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.13 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.13 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.13 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.13 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.13 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.13 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.13 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.13 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.13 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.13 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.13 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.13 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.13 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.13 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.13 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.13 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.13 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.13 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.13 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.13 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.13 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.13 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.98/242.13 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 543.98/242.13 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 543.98/242.13 543.98/242.13 The TRS R consists of the following rules: 543.98/242.13 543.98/242.13 down(a) -> up(f(a)) 543.98/242.13 down(b) -> up(g(b)) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.13 down(f(a)) -> f_flat(down(a)) 543.98/242.13 down(f(b)) -> f_flat(down(b)) 543.98/242.13 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.13 down(f(c)) -> f_flat(down(c)) 543.98/242.13 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.13 down(g(a)) -> g_flat(down(a)) 543.98/242.13 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.13 down(g(b)) -> g_flat(down(b)) 543.98/242.13 down(g(c)) -> g_flat(down(c)) 543.98/242.13 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.13 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.13 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.13 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.13 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.13 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.13 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.13 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.13 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.13 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.13 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.13 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.13 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.13 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.13 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.13 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.13 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.13 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.13 543.98/242.13 The set Q consists of the following terms: 543.98/242.13 543.98/242.13 down(a) 543.98/242.13 down(b) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.13 down(f(a)) 543.98/242.13 down(f(b)) 543.98/242.13 down(f(g(x0))) 543.98/242.13 down(f(c)) 543.98/242.13 down(f(fresh_constant)) 543.98/242.13 down(g(a)) 543.98/242.13 down(g(f(x0))) 543.98/242.13 down(g(b)) 543.98/242.13 down(g(c)) 543.98/242.13 down(g(fresh_constant)) 543.98/242.13 down(f(f(a))) 543.98/242.13 down(f(f(b))) 543.98/242.13 down(f(f(g(x0)))) 543.98/242.13 down(f(f(c))) 543.98/242.13 down(f(f(fresh_constant))) 543.98/242.13 down(g(g(a))) 543.98/242.13 down(g(g(f(x0)))) 543.98/242.13 down(g(g(b))) 543.98/242.13 down(g(g(c))) 543.98/242.13 down(g(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) 543.98/242.13 down(f(f(f(g(x0))))) 543.98/242.13 down(f(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) 543.98/242.13 down(g(g(g(f(x0))))) 543.98/242.13 down(g(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(x0)))))) 543.98/242.13 down(f(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(x0)))))) 543.98/242.13 down(g(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(x0))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(x0))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 f_flat(up(x0)) 543.98/242.13 g_flat(up(x0)) 543.98/242.13 543.98/242.13 We have to consider all minimal (P,Q,R)-chains. 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1047) TransformationProof (EQUIVALENT) 543.98/242.13 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.13 543.98/242.13 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 543.98/242.13 543.98/242.13 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1048) 543.98/242.13 Obligation: 543.98/242.13 Q DP problem: 543.98/242.13 The TRS P consists of the following rules: 543.98/242.13 543.98/242.13 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.13 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.13 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.13 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.13 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.13 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.13 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.13 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.13 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.13 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.13 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.13 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.13 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.13 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.13 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.13 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.13 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.13 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.13 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.13 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.13 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.13 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.13 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.13 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.98/242.13 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 543.98/242.13 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 543.98/242.13 543.98/242.13 The TRS R consists of the following rules: 543.98/242.13 543.98/242.13 down(a) -> up(f(a)) 543.98/242.13 down(b) -> up(g(b)) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.13 down(f(a)) -> f_flat(down(a)) 543.98/242.13 down(f(b)) -> f_flat(down(b)) 543.98/242.13 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.13 down(f(c)) -> f_flat(down(c)) 543.98/242.13 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.13 down(g(a)) -> g_flat(down(a)) 543.98/242.13 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.13 down(g(b)) -> g_flat(down(b)) 543.98/242.13 down(g(c)) -> g_flat(down(c)) 543.98/242.13 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.13 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.13 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.13 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.13 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.13 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.13 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.13 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.13 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.13 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.13 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.13 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.13 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.13 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.13 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.13 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.13 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.13 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.13 543.98/242.13 The set Q consists of the following terms: 543.98/242.13 543.98/242.13 down(a) 543.98/242.13 down(b) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.13 down(f(a)) 543.98/242.13 down(f(b)) 543.98/242.13 down(f(g(x0))) 543.98/242.13 down(f(c)) 543.98/242.13 down(f(fresh_constant)) 543.98/242.13 down(g(a)) 543.98/242.13 down(g(f(x0))) 543.98/242.13 down(g(b)) 543.98/242.13 down(g(c)) 543.98/242.13 down(g(fresh_constant)) 543.98/242.13 down(f(f(a))) 543.98/242.13 down(f(f(b))) 543.98/242.13 down(f(f(g(x0)))) 543.98/242.13 down(f(f(c))) 543.98/242.13 down(f(f(fresh_constant))) 543.98/242.13 down(g(g(a))) 543.98/242.13 down(g(g(f(x0)))) 543.98/242.13 down(g(g(b))) 543.98/242.13 down(g(g(c))) 543.98/242.13 down(g(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) 543.98/242.13 down(f(f(f(g(x0))))) 543.98/242.13 down(f(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) 543.98/242.13 down(g(g(g(f(x0))))) 543.98/242.13 down(g(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(x0)))))) 543.98/242.13 down(f(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(x0)))))) 543.98/242.13 down(g(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(x0))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(x0))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 f_flat(up(x0)) 543.98/242.13 g_flat(up(x0)) 543.98/242.13 543.98/242.13 We have to consider all minimal (P,Q,R)-chains. 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1049) TransformationProof (EQUIVALENT) 543.98/242.13 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.13 543.98/242.13 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 543.98/242.13 543.98/242.13 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1050) 543.98/242.13 Obligation: 543.98/242.13 Q DP problem: 543.98/242.13 The TRS P consists of the following rules: 543.98/242.13 543.98/242.13 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.13 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.13 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.13 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.13 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.13 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.13 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.13 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.13 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.13 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.13 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.13 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.13 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.13 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.13 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.13 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.13 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.13 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.13 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.13 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.13 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.13 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.13 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.13 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.98/242.13 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 543.98/242.13 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 543.98/242.13 543.98/242.13 The TRS R consists of the following rules: 543.98/242.13 543.98/242.13 down(a) -> up(f(a)) 543.98/242.13 down(b) -> up(g(b)) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.13 down(f(a)) -> f_flat(down(a)) 543.98/242.13 down(f(b)) -> f_flat(down(b)) 543.98/242.13 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.13 down(f(c)) -> f_flat(down(c)) 543.98/242.13 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.13 down(g(a)) -> g_flat(down(a)) 543.98/242.13 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.13 down(g(b)) -> g_flat(down(b)) 543.98/242.13 down(g(c)) -> g_flat(down(c)) 543.98/242.13 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.13 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.13 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.13 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.13 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.13 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.13 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.13 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.13 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.13 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.13 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.13 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.13 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.13 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.13 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.13 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.13 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.13 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.13 543.98/242.13 The set Q consists of the following terms: 543.98/242.13 543.98/242.13 down(a) 543.98/242.13 down(b) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.13 down(f(a)) 543.98/242.13 down(f(b)) 543.98/242.13 down(f(g(x0))) 543.98/242.13 down(f(c)) 543.98/242.13 down(f(fresh_constant)) 543.98/242.13 down(g(a)) 543.98/242.13 down(g(f(x0))) 543.98/242.13 down(g(b)) 543.98/242.13 down(g(c)) 543.98/242.13 down(g(fresh_constant)) 543.98/242.13 down(f(f(a))) 543.98/242.13 down(f(f(b))) 543.98/242.13 down(f(f(g(x0)))) 543.98/242.13 down(f(f(c))) 543.98/242.13 down(f(f(fresh_constant))) 543.98/242.13 down(g(g(a))) 543.98/242.13 down(g(g(f(x0)))) 543.98/242.13 down(g(g(b))) 543.98/242.13 down(g(g(c))) 543.98/242.13 down(g(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) 543.98/242.13 down(f(f(f(g(x0))))) 543.98/242.13 down(f(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) 543.98/242.13 down(g(g(g(f(x0))))) 543.98/242.13 down(g(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(x0)))))) 543.98/242.13 down(f(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(x0)))))) 543.98/242.13 down(g(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(x0))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(x0))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 f_flat(up(x0)) 543.98/242.13 g_flat(up(x0)) 543.98/242.13 543.98/242.13 We have to consider all minimal (P,Q,R)-chains. 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1051) TransformationProof (EQUIVALENT) 543.98/242.13 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.13 543.98/242.13 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 543.98/242.13 543.98/242.13 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1052) 543.98/242.13 Obligation: 543.98/242.13 Q DP problem: 543.98/242.13 The TRS P consists of the following rules: 543.98/242.13 543.98/242.13 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.13 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.13 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.13 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.13 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.13 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.13 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.13 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.13 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.13 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.13 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.13 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.13 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.13 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.13 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.13 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.13 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.13 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.13 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.13 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.13 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.13 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.13 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.13 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.98/242.13 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 543.98/242.13 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 543.98/242.13 543.98/242.13 The TRS R consists of the following rules: 543.98/242.13 543.98/242.13 down(a) -> up(f(a)) 543.98/242.13 down(b) -> up(g(b)) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.13 down(f(a)) -> f_flat(down(a)) 543.98/242.13 down(f(b)) -> f_flat(down(b)) 543.98/242.13 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.13 down(f(c)) -> f_flat(down(c)) 543.98/242.13 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.13 down(g(a)) -> g_flat(down(a)) 543.98/242.13 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.13 down(g(b)) -> g_flat(down(b)) 543.98/242.13 down(g(c)) -> g_flat(down(c)) 543.98/242.13 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.13 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.13 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.13 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.13 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.13 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.13 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.13 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.13 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.13 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.13 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.13 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.13 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.13 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.13 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.13 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.13 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.13 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.13 543.98/242.13 The set Q consists of the following terms: 543.98/242.13 543.98/242.13 down(a) 543.98/242.13 down(b) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.13 down(f(a)) 543.98/242.13 down(f(b)) 543.98/242.13 down(f(g(x0))) 543.98/242.13 down(f(c)) 543.98/242.13 down(f(fresh_constant)) 543.98/242.13 down(g(a)) 543.98/242.13 down(g(f(x0))) 543.98/242.13 down(g(b)) 543.98/242.13 down(g(c)) 543.98/242.13 down(g(fresh_constant)) 543.98/242.13 down(f(f(a))) 543.98/242.13 down(f(f(b))) 543.98/242.13 down(f(f(g(x0)))) 543.98/242.13 down(f(f(c))) 543.98/242.13 down(f(f(fresh_constant))) 543.98/242.13 down(g(g(a))) 543.98/242.13 down(g(g(f(x0)))) 543.98/242.13 down(g(g(b))) 543.98/242.13 down(g(g(c))) 543.98/242.13 down(g(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) 543.98/242.13 down(f(f(f(g(x0))))) 543.98/242.13 down(f(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) 543.98/242.13 down(g(g(g(f(x0))))) 543.98/242.13 down(g(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(x0)))))) 543.98/242.13 down(f(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(x0)))))) 543.98/242.13 down(g(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(x0))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(x0))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 f_flat(up(x0)) 543.98/242.13 g_flat(up(x0)) 543.98/242.13 543.98/242.13 We have to consider all minimal (P,Q,R)-chains. 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1053) TransformationProof (EQUIVALENT) 543.98/242.13 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(a))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.13 543.98/242.13 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a)))))))))))) 543.98/242.13 543.98/242.13 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1054) 543.98/242.13 Obligation: 543.98/242.13 Q DP problem: 543.98/242.13 The TRS P consists of the following rules: 543.98/242.13 543.98/242.13 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.13 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.13 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.13 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.13 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.13 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.13 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.13 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.13 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.13 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.13 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.13 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.13 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.13 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.13 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.13 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.13 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.13 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.13 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.13 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.13 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.13 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.13 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.13 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.98/242.13 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 543.98/242.13 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 543.98/242.13 543.98/242.13 The TRS R consists of the following rules: 543.98/242.13 543.98/242.13 down(a) -> up(f(a)) 543.98/242.13 down(b) -> up(g(b)) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.13 down(f(a)) -> f_flat(down(a)) 543.98/242.13 down(f(b)) -> f_flat(down(b)) 543.98/242.13 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.13 down(f(c)) -> f_flat(down(c)) 543.98/242.13 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.13 down(g(a)) -> g_flat(down(a)) 543.98/242.13 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.13 down(g(b)) -> g_flat(down(b)) 543.98/242.13 down(g(c)) -> g_flat(down(c)) 543.98/242.13 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.13 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.13 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.13 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.13 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.13 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.13 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.13 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.13 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.13 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.13 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.13 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.13 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.13 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.13 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.13 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.13 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.13 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.13 543.98/242.13 The set Q consists of the following terms: 543.98/242.13 543.98/242.13 down(a) 543.98/242.13 down(b) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.13 down(f(a)) 543.98/242.13 down(f(b)) 543.98/242.13 down(f(g(x0))) 543.98/242.13 down(f(c)) 543.98/242.13 down(f(fresh_constant)) 543.98/242.13 down(g(a)) 543.98/242.13 down(g(f(x0))) 543.98/242.13 down(g(b)) 543.98/242.13 down(g(c)) 543.98/242.13 down(g(fresh_constant)) 543.98/242.13 down(f(f(a))) 543.98/242.13 down(f(f(b))) 543.98/242.13 down(f(f(g(x0)))) 543.98/242.13 down(f(f(c))) 543.98/242.13 down(f(f(fresh_constant))) 543.98/242.13 down(g(g(a))) 543.98/242.13 down(g(g(f(x0)))) 543.98/242.13 down(g(g(b))) 543.98/242.13 down(g(g(c))) 543.98/242.13 down(g(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) 543.98/242.13 down(f(f(f(g(x0))))) 543.98/242.13 down(f(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) 543.98/242.13 down(g(g(g(f(x0))))) 543.98/242.13 down(g(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(x0)))))) 543.98/242.13 down(f(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(x0)))))) 543.98/242.13 down(g(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(x0))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(x0))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 f_flat(up(x0)) 543.98/242.13 g_flat(up(x0)) 543.98/242.13 543.98/242.13 We have to consider all minimal (P,Q,R)-chains. 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1055) TransformationProof (EQUIVALENT) 543.98/242.13 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(b))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.13 543.98/242.13 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b)))))))))))) 543.98/242.13 543.98/242.13 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1056) 543.98/242.13 Obligation: 543.98/242.13 Q DP problem: 543.98/242.13 The TRS P consists of the following rules: 543.98/242.13 543.98/242.13 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.13 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.13 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.13 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.13 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.13 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.13 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.13 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.13 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.13 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.13 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.13 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.13 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.13 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.13 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.13 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.13 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.13 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.13 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.13 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.13 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.13 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.13 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.13 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.98/242.13 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 543.98/242.13 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 543.98/242.13 543.98/242.13 The TRS R consists of the following rules: 543.98/242.13 543.98/242.13 down(a) -> up(f(a)) 543.98/242.13 down(b) -> up(g(b)) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.13 down(f(a)) -> f_flat(down(a)) 543.98/242.13 down(f(b)) -> f_flat(down(b)) 543.98/242.13 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.13 down(f(c)) -> f_flat(down(c)) 543.98/242.13 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.13 down(g(a)) -> g_flat(down(a)) 543.98/242.13 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.13 down(g(b)) -> g_flat(down(b)) 543.98/242.13 down(g(c)) -> g_flat(down(c)) 543.98/242.13 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.13 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.13 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.13 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.13 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.13 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.13 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.13 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.13 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.13 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.13 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.13 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.13 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.13 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.13 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.13 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.13 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 g_flat(up(x_1)) -> up(g(x_1)) 543.98/242.13 f_flat(up(x_1)) -> up(f(x_1)) 543.98/242.13 543.98/242.13 The set Q consists of the following terms: 543.98/242.13 543.98/242.13 down(a) 543.98/242.13 down(b) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 543.98/242.13 down(f(a)) 543.98/242.13 down(f(b)) 543.98/242.13 down(f(g(x0))) 543.98/242.13 down(f(c)) 543.98/242.13 down(f(fresh_constant)) 543.98/242.13 down(g(a)) 543.98/242.13 down(g(f(x0))) 543.98/242.13 down(g(b)) 543.98/242.13 down(g(c)) 543.98/242.13 down(g(fresh_constant)) 543.98/242.13 down(f(f(a))) 543.98/242.13 down(f(f(b))) 543.98/242.13 down(f(f(g(x0)))) 543.98/242.13 down(f(f(c))) 543.98/242.13 down(f(f(fresh_constant))) 543.98/242.13 down(g(g(a))) 543.98/242.13 down(g(g(f(x0)))) 543.98/242.13 down(g(g(b))) 543.98/242.13 down(g(g(c))) 543.98/242.13 down(g(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) 543.98/242.13 down(f(f(f(g(x0))))) 543.98/242.13 down(f(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) 543.98/242.13 down(g(g(g(f(x0))))) 543.98/242.13 down(g(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(x0)))))) 543.98/242.13 down(f(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(x0)))))) 543.98/242.13 down(g(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(x0))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(x0))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) 543.98/242.13 down(g(g(g(g(g(fresh_constant)))))) 543.98/242.13 down(f(f(f(f(f(f(a))))))) 543.98/242.13 down(f(f(f(f(f(f(b))))))) 543.98/242.13 down(f(f(f(f(f(f(g(x0)))))))) 543.98/242.13 down(f(f(f(f(f(f(c))))))) 543.98/242.13 down(f(f(f(f(f(f(fresh_constant))))))) 543.98/242.13 down(g(g(g(g(g(g(a))))))) 543.98/242.13 down(g(g(g(g(g(g(f(x0)))))))) 543.98/242.13 down(g(g(g(g(g(g(b))))))) 543.98/242.13 down(g(g(g(g(g(g(c))))))) 543.98/242.13 down(g(g(g(g(g(g(fresh_constant))))))) 543.98/242.13 down(f(f(f(f(f(f(f(a)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(b)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(g(x0))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(c)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(a)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(f(x0))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(b)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(c)))))))) 543.98/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(b))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(c))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(a))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(c))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 543.98/242.13 f_flat(up(x0)) 543.98/242.13 g_flat(up(x0)) 543.98/242.13 543.98/242.13 We have to consider all minimal (P,Q,R)-chains. 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1057) TransformationProof (EQUIVALENT) 543.98/242.13 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(g(x0)))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 543.98/242.13 543.98/242.13 (TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))))) 543.98/242.13 543.98/242.13 543.98/242.13 ---------------------------------------- 543.98/242.13 543.98/242.13 (1058) 543.98/242.13 Obligation: 543.98/242.13 Q DP problem: 543.98/242.13 The TRS P consists of the following rules: 543.98/242.13 543.98/242.13 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 543.98/242.13 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 543.98/242.13 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 543.98/242.13 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 543.98/242.13 TOP(up(f(a))) -> TOP(up(f(f(a)))) 543.98/242.13 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 543.98/242.13 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 543.98/242.13 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 543.98/242.13 TOP(up(f(b))) -> TOP(up(f(g(b)))) 543.98/242.13 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 543.98/242.13 TOP(up(g(b))) -> TOP(up(g(g(b)))) 543.98/242.13 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 543.98/242.13 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 543.98/242.13 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 543.98/242.13 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 543.98/242.13 TOP(up(g(a))) -> TOP(up(g(f(a)))) 543.98/242.13 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 543.98/242.13 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 543.98/242.13 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 543.98/242.13 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 543.98/242.13 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 543.98/242.13 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 543.98/242.13 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 543.98/242.13 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 543.98/242.13 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 543.98/242.13 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 543.98/242.13 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 543.98/242.13 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 543.98/242.13 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 543.98/242.13 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 543.98/242.13 543.98/242.13 The TRS R consists of the following rules: 543.98/242.13 543.98/242.13 down(a) -> up(f(a)) 543.98/242.13 down(b) -> up(g(b)) 543.98/242.13 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 543.98/242.13 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 543.98/242.13 down(f(a)) -> f_flat(down(a)) 543.98/242.13 down(f(b)) -> f_flat(down(b)) 543.98/242.13 down(f(g(y4))) -> f_flat(down(g(y4))) 543.98/242.13 down(f(c)) -> f_flat(down(c)) 543.98/242.13 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 543.98/242.13 down(g(a)) -> g_flat(down(a)) 543.98/242.13 down(g(f(y6))) -> g_flat(down(f(y6))) 543.98/242.13 down(g(b)) -> g_flat(down(b)) 543.98/242.13 down(g(c)) -> g_flat(down(c)) 543.98/242.13 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 543.98/242.13 down(f(f(a))) -> f_flat(down(f(a))) 543.98/242.13 down(f(f(b))) -> f_flat(down(f(b))) 543.98/242.13 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 543.98/242.13 down(f(f(c))) -> f_flat(down(f(c))) 543.98/242.13 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 543.98/242.13 down(g(g(a))) -> g_flat(down(g(a))) 543.98/242.13 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 543.98/242.13 down(g(g(b))) -> g_flat(down(g(b))) 543.98/242.13 down(g(g(c))) -> g_flat(down(g(c))) 543.98/242.13 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 543.98/242.13 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 543.98/242.13 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 543.98/242.13 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 543.98/242.13 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 543.98/242.13 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 543.98/242.13 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 543.98/242.13 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 543.98/242.13 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 543.98/242.13 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 543.98/242.13 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 543.98/242.13 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 543.98/242.13 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 543.98/242.13 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 543.98/242.13 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 543.98/242.13 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 543.98/242.13 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 543.98/242.13 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 543.98/242.13 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 543.98/242.13 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 543.98/242.13 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 543.98/242.13 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 543.98/242.13 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 543.98/242.13 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 543.98/242.13 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 543.98/242.13 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 543.98/242.13 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 543.98/242.13 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 543.98/242.13 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 543.98/242.13 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.13 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.13 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.13 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.13 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.13 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.13 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.13 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.13 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.13 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.13 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.13 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.13 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.13 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.13 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.13 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.13 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.13 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.13 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.13 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.13 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.13 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.13 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.13 544.00/242.13 The set Q consists of the following terms: 544.00/242.13 544.00/242.13 down(a) 544.00/242.13 down(b) 544.00/242.13 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.13 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.13 down(f(a)) 544.00/242.13 down(f(b)) 544.00/242.13 down(f(g(x0))) 544.00/242.13 down(f(c)) 544.00/242.13 down(f(fresh_constant)) 544.00/242.13 down(g(a)) 544.00/242.13 down(g(f(x0))) 544.00/242.13 down(g(b)) 544.00/242.13 down(g(c)) 544.00/242.13 down(g(fresh_constant)) 544.00/242.13 down(f(f(a))) 544.00/242.13 down(f(f(b))) 544.00/242.13 down(f(f(g(x0)))) 544.00/242.13 down(f(f(c))) 544.00/242.13 down(f(f(fresh_constant))) 544.00/242.13 down(g(g(a))) 544.00/242.13 down(g(g(f(x0)))) 544.00/242.13 down(g(g(b))) 544.00/242.13 down(g(g(c))) 544.00/242.13 down(g(g(fresh_constant))) 544.00/242.13 down(f(f(f(a)))) 544.00/242.13 down(f(f(f(b)))) 544.00/242.13 down(f(f(f(g(x0))))) 544.00/242.13 down(f(f(f(c)))) 544.00/242.13 down(f(f(f(fresh_constant)))) 544.00/242.13 down(g(g(g(a)))) 544.00/242.13 down(g(g(g(f(x0))))) 544.00/242.13 down(g(g(g(b)))) 544.00/242.13 down(g(g(g(c)))) 544.00/242.13 down(g(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(x0)))))) 544.00/242.14 down(f(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(x0)))))) 544.00/242.14 down(g(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(x0))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(x0))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 f_flat(up(x0)) 544.00/242.14 g_flat(up(x0)) 544.00/242.14 544.00/242.14 We have to consider all minimal (P,Q,R)-chains. 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1059) TransformationProof (EQUIVALENT) 544.00/242.14 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.14 544.00/242.14 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.14 544.00/242.14 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1060) 544.00/242.14 Obligation: 544.00/242.14 Q DP problem: 544.00/242.14 The TRS P consists of the following rules: 544.00/242.14 544.00/242.14 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.14 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.14 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.14 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.14 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.14 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.14 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.14 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.14 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.14 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.14 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.14 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.14 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.14 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.14 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.14 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.14 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.14 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.14 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.14 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.14 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.14 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 544.00/242.14 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.14 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.14 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.14 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.14 544.00/242.14 The TRS R consists of the following rules: 544.00/242.14 544.00/242.14 down(a) -> up(f(a)) 544.00/242.14 down(b) -> up(g(b)) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.14 down(f(a)) -> f_flat(down(a)) 544.00/242.14 down(f(b)) -> f_flat(down(b)) 544.00/242.14 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.14 down(f(c)) -> f_flat(down(c)) 544.00/242.14 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.14 down(g(a)) -> g_flat(down(a)) 544.00/242.14 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.14 down(g(b)) -> g_flat(down(b)) 544.00/242.14 down(g(c)) -> g_flat(down(c)) 544.00/242.14 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.14 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.14 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.14 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.14 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.14 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.14 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.14 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.14 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.14 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.14 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.14 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.14 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.14 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.14 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.14 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.14 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.14 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.14 544.00/242.14 The set Q consists of the following terms: 544.00/242.14 544.00/242.14 down(a) 544.00/242.14 down(b) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.14 down(f(a)) 544.00/242.14 down(f(b)) 544.00/242.14 down(f(g(x0))) 544.00/242.14 down(f(c)) 544.00/242.14 down(f(fresh_constant)) 544.00/242.14 down(g(a)) 544.00/242.14 down(g(f(x0))) 544.00/242.14 down(g(b)) 544.00/242.14 down(g(c)) 544.00/242.14 down(g(fresh_constant)) 544.00/242.14 down(f(f(a))) 544.00/242.14 down(f(f(b))) 544.00/242.14 down(f(f(g(x0)))) 544.00/242.14 down(f(f(c))) 544.00/242.14 down(f(f(fresh_constant))) 544.00/242.14 down(g(g(a))) 544.00/242.14 down(g(g(f(x0)))) 544.00/242.14 down(g(g(b))) 544.00/242.14 down(g(g(c))) 544.00/242.14 down(g(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) 544.00/242.14 down(f(f(f(g(x0))))) 544.00/242.14 down(f(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) 544.00/242.14 down(g(g(g(f(x0))))) 544.00/242.14 down(g(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(x0)))))) 544.00/242.14 down(f(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(x0)))))) 544.00/242.14 down(g(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(x0))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(x0))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 f_flat(up(x0)) 544.00/242.14 g_flat(up(x0)) 544.00/242.14 544.00/242.14 We have to consider all minimal (P,Q,R)-chains. 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1061) TransformationProof (EQUIVALENT) 544.00/242.14 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.14 544.00/242.14 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.00/242.14 544.00/242.14 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1062) 544.00/242.14 Obligation: 544.00/242.14 Q DP problem: 544.00/242.14 The TRS P consists of the following rules: 544.00/242.14 544.00/242.14 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.14 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.14 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.14 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.14 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.14 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.14 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.14 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.14 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.14 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.14 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.14 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.14 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.14 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.14 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.14 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.14 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.14 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.14 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.14 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.14 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.14 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 544.00/242.14 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.14 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.14 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.14 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))) 544.00/242.14 544.00/242.14 The TRS R consists of the following rules: 544.00/242.14 544.00/242.14 down(a) -> up(f(a)) 544.00/242.14 down(b) -> up(g(b)) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.14 down(f(a)) -> f_flat(down(a)) 544.00/242.14 down(f(b)) -> f_flat(down(b)) 544.00/242.14 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.14 down(f(c)) -> f_flat(down(c)) 544.00/242.14 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.14 down(g(a)) -> g_flat(down(a)) 544.00/242.14 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.14 down(g(b)) -> g_flat(down(b)) 544.00/242.14 down(g(c)) -> g_flat(down(c)) 544.00/242.14 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.14 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.14 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.14 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.14 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.14 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.14 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.14 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.14 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.14 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.14 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.14 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.14 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.14 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.14 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.14 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.14 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.14 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.14 544.00/242.14 The set Q consists of the following terms: 544.00/242.14 544.00/242.14 down(a) 544.00/242.14 down(b) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.14 down(f(a)) 544.00/242.14 down(f(b)) 544.00/242.14 down(f(g(x0))) 544.00/242.14 down(f(c)) 544.00/242.14 down(f(fresh_constant)) 544.00/242.14 down(g(a)) 544.00/242.14 down(g(f(x0))) 544.00/242.14 down(g(b)) 544.00/242.14 down(g(c)) 544.00/242.14 down(g(fresh_constant)) 544.00/242.14 down(f(f(a))) 544.00/242.14 down(f(f(b))) 544.00/242.14 down(f(f(g(x0)))) 544.00/242.14 down(f(f(c))) 544.00/242.14 down(f(f(fresh_constant))) 544.00/242.14 down(g(g(a))) 544.00/242.14 down(g(g(f(x0)))) 544.00/242.14 down(g(g(b))) 544.00/242.14 down(g(g(c))) 544.00/242.14 down(g(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) 544.00/242.14 down(f(f(f(g(x0))))) 544.00/242.14 down(f(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) 544.00/242.14 down(g(g(g(f(x0))))) 544.00/242.14 down(g(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(x0)))))) 544.00/242.14 down(f(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(x0)))))) 544.00/242.14 down(g(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(x0))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(x0))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 f_flat(up(x0)) 544.00/242.14 g_flat(up(x0)) 544.00/242.14 544.00/242.14 We have to consider all minimal (P,Q,R)-chains. 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1063) TransformationProof (EQUIVALENT) 544.00/242.14 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.14 544.00/242.14 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.00/242.14 544.00/242.14 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1064) 544.00/242.14 Obligation: 544.00/242.14 Q DP problem: 544.00/242.14 The TRS P consists of the following rules: 544.00/242.14 544.00/242.14 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.14 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.14 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.14 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.14 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.14 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.14 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.14 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.14 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.14 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.14 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.14 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.14 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.14 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.14 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.14 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.14 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.14 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.14 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.14 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.14 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.14 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 544.00/242.14 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.14 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.14 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.14 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))) 544.00/242.14 544.00/242.14 The TRS R consists of the following rules: 544.00/242.14 544.00/242.14 down(a) -> up(f(a)) 544.00/242.14 down(b) -> up(g(b)) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.14 down(f(a)) -> f_flat(down(a)) 544.00/242.14 down(f(b)) -> f_flat(down(b)) 544.00/242.14 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.14 down(f(c)) -> f_flat(down(c)) 544.00/242.14 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.14 down(g(a)) -> g_flat(down(a)) 544.00/242.14 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.14 down(g(b)) -> g_flat(down(b)) 544.00/242.14 down(g(c)) -> g_flat(down(c)) 544.00/242.14 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.14 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.14 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.14 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.14 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.14 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.14 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.14 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.14 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.14 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.14 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.14 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.14 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.14 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.14 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.14 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.14 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.14 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.14 544.00/242.14 The set Q consists of the following terms: 544.00/242.14 544.00/242.14 down(a) 544.00/242.14 down(b) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.14 down(f(a)) 544.00/242.14 down(f(b)) 544.00/242.14 down(f(g(x0))) 544.00/242.14 down(f(c)) 544.00/242.14 down(f(fresh_constant)) 544.00/242.14 down(g(a)) 544.00/242.14 down(g(f(x0))) 544.00/242.14 down(g(b)) 544.00/242.14 down(g(c)) 544.00/242.14 down(g(fresh_constant)) 544.00/242.14 down(f(f(a))) 544.00/242.14 down(f(f(b))) 544.00/242.14 down(f(f(g(x0)))) 544.00/242.14 down(f(f(c))) 544.00/242.14 down(f(f(fresh_constant))) 544.00/242.14 down(g(g(a))) 544.00/242.14 down(g(g(f(x0)))) 544.00/242.14 down(g(g(b))) 544.00/242.14 down(g(g(c))) 544.00/242.14 down(g(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) 544.00/242.14 down(f(f(f(g(x0))))) 544.00/242.14 down(f(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) 544.00/242.14 down(g(g(g(f(x0))))) 544.00/242.14 down(g(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(x0)))))) 544.00/242.14 down(f(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(x0)))))) 544.00/242.14 down(g(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(x0))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(x0))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 f_flat(up(x0)) 544.00/242.14 g_flat(up(x0)) 544.00/242.14 544.00/242.14 We have to consider all minimal (P,Q,R)-chains. 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1065) TransformationProof (EQUIVALENT) 544.00/242.14 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(a))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.14 544.00/242.14 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a)))))))))))) 544.00/242.14 544.00/242.14 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1066) 544.00/242.14 Obligation: 544.00/242.14 Q DP problem: 544.00/242.14 The TRS P consists of the following rules: 544.00/242.14 544.00/242.14 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.14 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.14 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.14 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.14 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.14 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.14 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.14 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.14 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.14 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.14 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.14 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.14 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.14 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.14 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.14 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.14 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.14 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.14 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.14 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.14 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.14 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 544.00/242.14 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.14 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.14 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.14 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.14 544.00/242.14 The TRS R consists of the following rules: 544.00/242.14 544.00/242.14 down(a) -> up(f(a)) 544.00/242.14 down(b) -> up(g(b)) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.14 down(f(a)) -> f_flat(down(a)) 544.00/242.14 down(f(b)) -> f_flat(down(b)) 544.00/242.14 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.14 down(f(c)) -> f_flat(down(c)) 544.00/242.14 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.14 down(g(a)) -> g_flat(down(a)) 544.00/242.14 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.14 down(g(b)) -> g_flat(down(b)) 544.00/242.14 down(g(c)) -> g_flat(down(c)) 544.00/242.14 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.14 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.14 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.14 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.14 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.14 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.14 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.14 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.14 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.14 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.14 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.14 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.14 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.14 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.14 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.14 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.14 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.14 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.14 544.00/242.14 The set Q consists of the following terms: 544.00/242.14 544.00/242.14 down(a) 544.00/242.14 down(b) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.14 down(f(a)) 544.00/242.14 down(f(b)) 544.00/242.14 down(f(g(x0))) 544.00/242.14 down(f(c)) 544.00/242.14 down(f(fresh_constant)) 544.00/242.14 down(g(a)) 544.00/242.14 down(g(f(x0))) 544.00/242.14 down(g(b)) 544.00/242.14 down(g(c)) 544.00/242.14 down(g(fresh_constant)) 544.00/242.14 down(f(f(a))) 544.00/242.14 down(f(f(b))) 544.00/242.14 down(f(f(g(x0)))) 544.00/242.14 down(f(f(c))) 544.00/242.14 down(f(f(fresh_constant))) 544.00/242.14 down(g(g(a))) 544.00/242.14 down(g(g(f(x0)))) 544.00/242.14 down(g(g(b))) 544.00/242.14 down(g(g(c))) 544.00/242.14 down(g(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) 544.00/242.14 down(f(f(f(g(x0))))) 544.00/242.14 down(f(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) 544.00/242.14 down(g(g(g(f(x0))))) 544.00/242.14 down(g(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(x0)))))) 544.00/242.14 down(f(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(x0)))))) 544.00/242.14 down(g(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(x0))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(x0))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 f_flat(up(x0)) 544.00/242.14 g_flat(up(x0)) 544.00/242.14 544.00/242.14 We have to consider all minimal (P,Q,R)-chains. 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1067) TransformationProof (EQUIVALENT) 544.00/242.14 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(f(x0)))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.14 544.00/242.14 (TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))))) 544.00/242.14 544.00/242.14 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1068) 544.00/242.14 Obligation: 544.00/242.14 Q DP problem: 544.00/242.14 The TRS P consists of the following rules: 544.00/242.14 544.00/242.14 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.14 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.14 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.14 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.14 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.14 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.14 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.14 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.14 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.14 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.14 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.14 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.14 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.14 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.14 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.14 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.14 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.14 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.14 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.14 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.14 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.14 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 544.00/242.14 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.14 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.14 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.14 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.14 544.00/242.14 The TRS R consists of the following rules: 544.00/242.14 544.00/242.14 down(a) -> up(f(a)) 544.00/242.14 down(b) -> up(g(b)) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.14 down(f(a)) -> f_flat(down(a)) 544.00/242.14 down(f(b)) -> f_flat(down(b)) 544.00/242.14 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.14 down(f(c)) -> f_flat(down(c)) 544.00/242.14 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.14 down(g(a)) -> g_flat(down(a)) 544.00/242.14 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.14 down(g(b)) -> g_flat(down(b)) 544.00/242.14 down(g(c)) -> g_flat(down(c)) 544.00/242.14 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.14 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.14 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.14 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.14 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.14 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.14 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.14 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.14 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.14 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.14 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.14 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.14 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.14 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.14 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.14 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.14 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.14 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.14 544.00/242.14 The set Q consists of the following terms: 544.00/242.14 544.00/242.14 down(a) 544.00/242.14 down(b) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.14 down(f(a)) 544.00/242.14 down(f(b)) 544.00/242.14 down(f(g(x0))) 544.00/242.14 down(f(c)) 544.00/242.14 down(f(fresh_constant)) 544.00/242.14 down(g(a)) 544.00/242.14 down(g(f(x0))) 544.00/242.14 down(g(b)) 544.00/242.14 down(g(c)) 544.00/242.14 down(g(fresh_constant)) 544.00/242.14 down(f(f(a))) 544.00/242.14 down(f(f(b))) 544.00/242.14 down(f(f(g(x0)))) 544.00/242.14 down(f(f(c))) 544.00/242.14 down(f(f(fresh_constant))) 544.00/242.14 down(g(g(a))) 544.00/242.14 down(g(g(f(x0)))) 544.00/242.14 down(g(g(b))) 544.00/242.14 down(g(g(c))) 544.00/242.14 down(g(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) 544.00/242.14 down(f(f(f(g(x0))))) 544.00/242.14 down(f(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) 544.00/242.14 down(g(g(g(f(x0))))) 544.00/242.14 down(g(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(x0)))))) 544.00/242.14 down(f(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(x0)))))) 544.00/242.14 down(g(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(x0))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(x0))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 f_flat(up(x0)) 544.00/242.14 g_flat(up(x0)) 544.00/242.14 544.00/242.14 We have to consider all minimal (P,Q,R)-chains. 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1069) TransformationProof (EQUIVALENT) 544.00/242.14 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(c))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.14 544.00/242.14 (TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c)))))))))))) 544.00/242.14 544.00/242.14 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1070) 544.00/242.14 Obligation: 544.00/242.14 Q DP problem: 544.00/242.14 The TRS P consists of the following rules: 544.00/242.14 544.00/242.14 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.14 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.14 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.14 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.14 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.14 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.14 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.14 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.14 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.14 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.14 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.14 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.14 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.14 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.14 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.14 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.14 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.14 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.14 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.14 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.14 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.14 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 544.00/242.14 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.14 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.14 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.14 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(c))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(c))))))))))) 544.00/242.14 544.00/242.14 The TRS R consists of the following rules: 544.00/242.14 544.00/242.14 down(a) -> up(f(a)) 544.00/242.14 down(b) -> up(g(b)) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.14 down(f(a)) -> f_flat(down(a)) 544.00/242.14 down(f(b)) -> f_flat(down(b)) 544.00/242.14 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.14 down(f(c)) -> f_flat(down(c)) 544.00/242.14 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.14 down(g(a)) -> g_flat(down(a)) 544.00/242.14 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.14 down(g(b)) -> g_flat(down(b)) 544.00/242.14 down(g(c)) -> g_flat(down(c)) 544.00/242.14 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.14 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.14 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.14 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.14 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.14 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.14 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.14 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.14 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.14 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.14 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.14 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.14 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.14 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.14 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.14 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.14 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.14 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.14 544.00/242.14 The set Q consists of the following terms: 544.00/242.14 544.00/242.14 down(a) 544.00/242.14 down(b) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.14 down(f(a)) 544.00/242.14 down(f(b)) 544.00/242.14 down(f(g(x0))) 544.00/242.14 down(f(c)) 544.00/242.14 down(f(fresh_constant)) 544.00/242.14 down(g(a)) 544.00/242.14 down(g(f(x0))) 544.00/242.14 down(g(b)) 544.00/242.14 down(g(c)) 544.00/242.14 down(g(fresh_constant)) 544.00/242.14 down(f(f(a))) 544.00/242.14 down(f(f(b))) 544.00/242.14 down(f(f(g(x0)))) 544.00/242.14 down(f(f(c))) 544.00/242.14 down(f(f(fresh_constant))) 544.00/242.14 down(g(g(a))) 544.00/242.14 down(g(g(f(x0)))) 544.00/242.14 down(g(g(b))) 544.00/242.14 down(g(g(c))) 544.00/242.14 down(g(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) 544.00/242.14 down(f(f(f(g(x0))))) 544.00/242.14 down(f(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) 544.00/242.14 down(g(g(g(f(x0))))) 544.00/242.14 down(g(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(x0)))))) 544.00/242.14 down(f(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(x0)))))) 544.00/242.14 down(g(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(x0))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(x0))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 f_flat(up(x0)) 544.00/242.14 g_flat(up(x0)) 544.00/242.14 544.00/242.14 We have to consider all minimal (P,Q,R)-chains. 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1071) DependencyGraphProof (EQUIVALENT) 544.00/242.14 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1072) 544.00/242.14 Obligation: 544.00/242.14 Q DP problem: 544.00/242.14 The TRS P consists of the following rules: 544.00/242.14 544.00/242.14 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.14 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.14 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.14 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.14 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.14 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.14 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.14 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))) 544.00/242.14 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.14 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.14 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.14 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.14 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.14 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.14 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))) 544.00/242.14 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.14 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.14 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.14 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.14 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.14 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.14 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.14 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.14 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 544.00/242.14 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.14 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.14 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.14 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.14 544.00/242.14 The TRS R consists of the following rules: 544.00/242.14 544.00/242.14 down(a) -> up(f(a)) 544.00/242.14 down(b) -> up(g(b)) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.14 down(f(a)) -> f_flat(down(a)) 544.00/242.14 down(f(b)) -> f_flat(down(b)) 544.00/242.14 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.14 down(f(c)) -> f_flat(down(c)) 544.00/242.14 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.14 down(g(a)) -> g_flat(down(a)) 544.00/242.14 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.14 down(g(b)) -> g_flat(down(b)) 544.00/242.14 down(g(c)) -> g_flat(down(c)) 544.00/242.14 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.14 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.14 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.14 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.14 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.14 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.14 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.14 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.14 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.14 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.14 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.14 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.14 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.14 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.14 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.14 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.14 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.14 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.14 544.00/242.14 The set Q consists of the following terms: 544.00/242.14 544.00/242.14 down(a) 544.00/242.14 down(b) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.14 down(f(a)) 544.00/242.14 down(f(b)) 544.00/242.14 down(f(g(x0))) 544.00/242.14 down(f(c)) 544.00/242.14 down(f(fresh_constant)) 544.00/242.14 down(g(a)) 544.00/242.14 down(g(f(x0))) 544.00/242.14 down(g(b)) 544.00/242.14 down(g(c)) 544.00/242.14 down(g(fresh_constant)) 544.00/242.14 down(f(f(a))) 544.00/242.14 down(f(f(b))) 544.00/242.14 down(f(f(g(x0)))) 544.00/242.14 down(f(f(c))) 544.00/242.14 down(f(f(fresh_constant))) 544.00/242.14 down(g(g(a))) 544.00/242.14 down(g(g(f(x0)))) 544.00/242.14 down(g(g(b))) 544.00/242.14 down(g(g(c))) 544.00/242.14 down(g(g(fresh_constant))) 544.00/242.14 down(f(f(f(a)))) 544.00/242.14 down(f(f(f(b)))) 544.00/242.14 down(f(f(f(g(x0))))) 544.00/242.14 down(f(f(f(c)))) 544.00/242.14 down(f(f(f(fresh_constant)))) 544.00/242.14 down(g(g(g(a)))) 544.00/242.14 down(g(g(g(f(x0))))) 544.00/242.14 down(g(g(g(b)))) 544.00/242.14 down(g(g(g(c)))) 544.00/242.14 down(g(g(g(fresh_constant)))) 544.00/242.14 down(f(f(f(f(a))))) 544.00/242.14 down(f(f(f(f(b))))) 544.00/242.14 down(f(f(f(f(g(x0)))))) 544.00/242.14 down(f(f(f(f(c))))) 544.00/242.14 down(f(f(f(f(fresh_constant))))) 544.00/242.14 down(g(g(g(g(a))))) 544.00/242.14 down(g(g(g(g(f(x0)))))) 544.00/242.14 down(g(g(g(g(b))))) 544.00/242.14 down(g(g(g(g(c))))) 544.00/242.14 down(g(g(g(g(fresh_constant))))) 544.00/242.14 down(f(f(f(f(f(a)))))) 544.00/242.14 down(f(f(f(f(f(b)))))) 544.00/242.14 down(f(f(f(f(f(g(x0))))))) 544.00/242.14 down(f(f(f(f(f(c)))))) 544.00/242.14 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.14 down(g(g(g(g(g(a)))))) 544.00/242.14 down(g(g(g(g(g(f(x0))))))) 544.00/242.14 down(g(g(g(g(g(b)))))) 544.00/242.14 down(g(g(g(g(g(c)))))) 544.00/242.14 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.14 down(f(f(f(f(f(f(a))))))) 544.00/242.14 down(f(f(f(f(f(f(b))))))) 544.00/242.14 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.14 down(f(f(f(f(f(f(c))))))) 544.00/242.14 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.14 down(g(g(g(g(g(g(a))))))) 544.00/242.14 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.14 down(g(g(g(g(g(g(b))))))) 544.00/242.14 down(g(g(g(g(g(g(c))))))) 544.00/242.14 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.14 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.14 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.14 f_flat(up(x0)) 544.00/242.14 g_flat(up(x0)) 544.00/242.14 544.00/242.14 We have to consider all minimal (P,Q,R)-chains. 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1073) TransformationProof (EQUIVALENT) 544.00/242.14 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.14 544.00/242.14 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.00/242.14 544.00/242.14 544.00/242.14 ---------------------------------------- 544.00/242.14 544.00/242.14 (1074) 544.00/242.14 Obligation: 544.00/242.14 Q DP problem: 544.00/242.14 The TRS P consists of the following rules: 544.00/242.14 544.00/242.14 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.14 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.14 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.14 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.14 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.14 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.14 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.14 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.14 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.14 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.14 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.14 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.14 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.14 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.14 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))) 544.00/242.14 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.14 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.14 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.14 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.14 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.14 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.14 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.14 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.14 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 544.00/242.14 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.14 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.14 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.14 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.14 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.14 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))) 544.00/242.14 544.00/242.14 The TRS R consists of the following rules: 544.00/242.14 544.00/242.14 down(a) -> up(f(a)) 544.00/242.14 down(b) -> up(g(b)) 544.00/242.14 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.14 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.14 down(f(a)) -> f_flat(down(a)) 544.00/242.14 down(f(b)) -> f_flat(down(b)) 544.00/242.14 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.14 down(f(c)) -> f_flat(down(c)) 544.00/242.14 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.15 down(g(a)) -> g_flat(down(a)) 544.00/242.15 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.15 down(g(b)) -> g_flat(down(b)) 544.00/242.15 down(g(c)) -> g_flat(down(c)) 544.00/242.15 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.15 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.15 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.15 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.15 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.15 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.15 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.15 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.15 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.15 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.15 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.15 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.15 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.15 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.15 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.15 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.15 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.15 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.15 544.00/242.15 The set Q consists of the following terms: 544.00/242.15 544.00/242.15 down(a) 544.00/242.15 down(b) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.15 down(f(a)) 544.00/242.15 down(f(b)) 544.00/242.15 down(f(g(x0))) 544.00/242.15 down(f(c)) 544.00/242.15 down(f(fresh_constant)) 544.00/242.15 down(g(a)) 544.00/242.15 down(g(f(x0))) 544.00/242.15 down(g(b)) 544.00/242.15 down(g(c)) 544.00/242.15 down(g(fresh_constant)) 544.00/242.15 down(f(f(a))) 544.00/242.15 down(f(f(b))) 544.00/242.15 down(f(f(g(x0)))) 544.00/242.15 down(f(f(c))) 544.00/242.15 down(f(f(fresh_constant))) 544.00/242.15 down(g(g(a))) 544.00/242.15 down(g(g(f(x0)))) 544.00/242.15 down(g(g(b))) 544.00/242.15 down(g(g(c))) 544.00/242.15 down(g(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) 544.00/242.15 down(f(f(f(g(x0))))) 544.00/242.15 down(f(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) 544.00/242.15 down(g(g(g(f(x0))))) 544.00/242.15 down(g(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(x0)))))) 544.00/242.15 down(f(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(x0)))))) 544.00/242.15 down(g(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(x0))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(x0))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 f_flat(up(x0)) 544.00/242.15 g_flat(up(x0)) 544.00/242.15 544.00/242.15 We have to consider all minimal (P,Q,R)-chains. 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1075) TransformationProof (EQUIVALENT) 544.00/242.15 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.15 544.00/242.15 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.00/242.15 544.00/242.15 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1076) 544.00/242.15 Obligation: 544.00/242.15 Q DP problem: 544.00/242.15 The TRS P consists of the following rules: 544.00/242.15 544.00/242.15 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.15 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.15 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.15 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.15 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.15 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.15 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.15 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.15 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.15 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.15 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.15 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.15 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.15 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.15 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.15 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.15 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.15 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.15 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.15 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.15 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.15 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) 544.00/242.15 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.15 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.15 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.15 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))) 544.00/242.15 544.00/242.15 The TRS R consists of the following rules: 544.00/242.15 544.00/242.15 down(a) -> up(f(a)) 544.00/242.15 down(b) -> up(g(b)) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.15 down(f(a)) -> f_flat(down(a)) 544.00/242.15 down(f(b)) -> f_flat(down(b)) 544.00/242.15 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.15 down(f(c)) -> f_flat(down(c)) 544.00/242.15 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.15 down(g(a)) -> g_flat(down(a)) 544.00/242.15 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.15 down(g(b)) -> g_flat(down(b)) 544.00/242.15 down(g(c)) -> g_flat(down(c)) 544.00/242.15 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.15 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.15 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.15 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.15 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.15 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.15 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.15 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.15 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.15 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.15 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.15 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.15 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.15 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.15 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.15 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.15 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.15 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.15 544.00/242.15 The set Q consists of the following terms: 544.00/242.15 544.00/242.15 down(a) 544.00/242.15 down(b) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.15 down(f(a)) 544.00/242.15 down(f(b)) 544.00/242.15 down(f(g(x0))) 544.00/242.15 down(f(c)) 544.00/242.15 down(f(fresh_constant)) 544.00/242.15 down(g(a)) 544.00/242.15 down(g(f(x0))) 544.00/242.15 down(g(b)) 544.00/242.15 down(g(c)) 544.00/242.15 down(g(fresh_constant)) 544.00/242.15 down(f(f(a))) 544.00/242.15 down(f(f(b))) 544.00/242.15 down(f(f(g(x0)))) 544.00/242.15 down(f(f(c))) 544.00/242.15 down(f(f(fresh_constant))) 544.00/242.15 down(g(g(a))) 544.00/242.15 down(g(g(f(x0)))) 544.00/242.15 down(g(g(b))) 544.00/242.15 down(g(g(c))) 544.00/242.15 down(g(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) 544.00/242.15 down(f(f(f(g(x0))))) 544.00/242.15 down(f(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) 544.00/242.15 down(g(g(g(f(x0))))) 544.00/242.15 down(g(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(x0)))))) 544.00/242.15 down(f(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(x0)))))) 544.00/242.15 down(g(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(x0))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(x0))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 f_flat(up(x0)) 544.00/242.15 g_flat(up(x0)) 544.00/242.15 544.00/242.15 We have to consider all minimal (P,Q,R)-chains. 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1077) TransformationProof (EQUIVALENT) 544.00/242.15 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(f(fresh_constant))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.15 544.00/242.15 (TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant)))))))))))) 544.00/242.15 544.00/242.15 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1078) 544.00/242.15 Obligation: 544.00/242.15 Q DP problem: 544.00/242.15 The TRS P consists of the following rules: 544.00/242.15 544.00/242.15 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.15 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.15 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.15 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.15 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.15 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.15 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.15 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.15 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.15 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.15 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.15 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.15 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.15 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.15 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.15 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.15 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.15 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.15 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.15 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.15 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.15 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.15 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.15 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.15 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.15 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(fresh_constant))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(fresh_constant))))))))))) 544.00/242.15 544.00/242.15 The TRS R consists of the following rules: 544.00/242.15 544.00/242.15 down(a) -> up(f(a)) 544.00/242.15 down(b) -> up(g(b)) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.15 down(f(a)) -> f_flat(down(a)) 544.00/242.15 down(f(b)) -> f_flat(down(b)) 544.00/242.15 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.15 down(f(c)) -> f_flat(down(c)) 544.00/242.15 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.15 down(g(a)) -> g_flat(down(a)) 544.00/242.15 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.15 down(g(b)) -> g_flat(down(b)) 544.00/242.15 down(g(c)) -> g_flat(down(c)) 544.00/242.15 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.15 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.15 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.15 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.15 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.15 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.15 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.15 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.15 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.15 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.15 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.15 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.15 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.15 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.15 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.15 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.15 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.15 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.15 544.00/242.15 The set Q consists of the following terms: 544.00/242.15 544.00/242.15 down(a) 544.00/242.15 down(b) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.15 down(f(a)) 544.00/242.15 down(f(b)) 544.00/242.15 down(f(g(x0))) 544.00/242.15 down(f(c)) 544.00/242.15 down(f(fresh_constant)) 544.00/242.15 down(g(a)) 544.00/242.15 down(g(f(x0))) 544.00/242.15 down(g(b)) 544.00/242.15 down(g(c)) 544.00/242.15 down(g(fresh_constant)) 544.00/242.15 down(f(f(a))) 544.00/242.15 down(f(f(b))) 544.00/242.15 down(f(f(g(x0)))) 544.00/242.15 down(f(f(c))) 544.00/242.15 down(f(f(fresh_constant))) 544.00/242.15 down(g(g(a))) 544.00/242.15 down(g(g(f(x0)))) 544.00/242.15 down(g(g(b))) 544.00/242.15 down(g(g(c))) 544.00/242.15 down(g(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) 544.00/242.15 down(f(f(f(g(x0))))) 544.00/242.15 down(f(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) 544.00/242.15 down(g(g(g(f(x0))))) 544.00/242.15 down(g(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(x0)))))) 544.00/242.15 down(f(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(x0)))))) 544.00/242.15 down(g(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(x0))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(x0))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 f_flat(up(x0)) 544.00/242.15 g_flat(up(x0)) 544.00/242.15 544.00/242.15 We have to consider all minimal (P,Q,R)-chains. 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1079) DependencyGraphProof (EQUIVALENT) 544.00/242.15 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1080) 544.00/242.15 Obligation: 544.00/242.15 Q DP problem: 544.00/242.15 The TRS P consists of the following rules: 544.00/242.15 544.00/242.15 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.15 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.15 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.15 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.15 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.15 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.15 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.15 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))) 544.00/242.15 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.15 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.15 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.15 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.15 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.15 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.15 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))) 544.00/242.15 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.15 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.15 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.15 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.15 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.15 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.15 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.15 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.15 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.15 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.15 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.15 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.15 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.15 544.00/242.15 The TRS R consists of the following rules: 544.00/242.15 544.00/242.15 down(a) -> up(f(a)) 544.00/242.15 down(b) -> up(g(b)) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.15 down(f(a)) -> f_flat(down(a)) 544.00/242.15 down(f(b)) -> f_flat(down(b)) 544.00/242.15 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.15 down(f(c)) -> f_flat(down(c)) 544.00/242.15 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.15 down(g(a)) -> g_flat(down(a)) 544.00/242.15 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.15 down(g(b)) -> g_flat(down(b)) 544.00/242.15 down(g(c)) -> g_flat(down(c)) 544.00/242.15 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.15 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.15 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.15 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.15 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.15 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.15 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.15 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.15 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.15 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.15 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.15 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.15 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.15 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.15 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.15 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.15 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.15 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.15 544.00/242.15 The set Q consists of the following terms: 544.00/242.15 544.00/242.15 down(a) 544.00/242.15 down(b) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.15 down(f(a)) 544.00/242.15 down(f(b)) 544.00/242.15 down(f(g(x0))) 544.00/242.15 down(f(c)) 544.00/242.15 down(f(fresh_constant)) 544.00/242.15 down(g(a)) 544.00/242.15 down(g(f(x0))) 544.00/242.15 down(g(b)) 544.00/242.15 down(g(c)) 544.00/242.15 down(g(fresh_constant)) 544.00/242.15 down(f(f(a))) 544.00/242.15 down(f(f(b))) 544.00/242.15 down(f(f(g(x0)))) 544.00/242.15 down(f(f(c))) 544.00/242.15 down(f(f(fresh_constant))) 544.00/242.15 down(g(g(a))) 544.00/242.15 down(g(g(f(x0)))) 544.00/242.15 down(g(g(b))) 544.00/242.15 down(g(g(c))) 544.00/242.15 down(g(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) 544.00/242.15 down(f(f(f(g(x0))))) 544.00/242.15 down(f(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) 544.00/242.15 down(g(g(g(f(x0))))) 544.00/242.15 down(g(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(x0)))))) 544.00/242.15 down(f(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(x0)))))) 544.00/242.15 down(g(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(x0))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(x0))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 f_flat(up(x0)) 544.00/242.15 g_flat(up(x0)) 544.00/242.15 544.00/242.15 We have to consider all minimal (P,Q,R)-chains. 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1081) TransformationProof (EQUIVALENT) 544.00/242.15 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.00/242.15 544.00/242.15 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.00/242.15 544.00/242.15 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1082) 544.00/242.15 Obligation: 544.00/242.15 Q DP problem: 544.00/242.15 The TRS P consists of the following rules: 544.00/242.15 544.00/242.15 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.15 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.15 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.15 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.15 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.15 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.15 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.15 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.15 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.15 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.15 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.15 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.15 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.15 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))) 544.00/242.15 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.15 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.15 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.15 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.15 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.15 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.15 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.15 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.15 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.15 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.15 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.15 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.15 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 544.00/242.15 The TRS R consists of the following rules: 544.00/242.15 544.00/242.15 down(a) -> up(f(a)) 544.00/242.15 down(b) -> up(g(b)) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.15 down(f(a)) -> f_flat(down(a)) 544.00/242.15 down(f(b)) -> f_flat(down(b)) 544.00/242.15 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.15 down(f(c)) -> f_flat(down(c)) 544.00/242.15 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.15 down(g(a)) -> g_flat(down(a)) 544.00/242.15 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.15 down(g(b)) -> g_flat(down(b)) 544.00/242.15 down(g(c)) -> g_flat(down(c)) 544.00/242.15 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.15 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.15 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.15 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.15 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.15 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.15 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.15 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.15 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.15 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.15 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.15 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.15 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.15 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.15 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.15 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.15 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.15 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.15 544.00/242.15 The set Q consists of the following terms: 544.00/242.15 544.00/242.15 down(a) 544.00/242.15 down(b) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.15 down(f(a)) 544.00/242.15 down(f(b)) 544.00/242.15 down(f(g(x0))) 544.00/242.15 down(f(c)) 544.00/242.15 down(f(fresh_constant)) 544.00/242.15 down(g(a)) 544.00/242.15 down(g(f(x0))) 544.00/242.15 down(g(b)) 544.00/242.15 down(g(c)) 544.00/242.15 down(g(fresh_constant)) 544.00/242.15 down(f(f(a))) 544.00/242.15 down(f(f(b))) 544.00/242.15 down(f(f(g(x0)))) 544.00/242.15 down(f(f(c))) 544.00/242.15 down(f(f(fresh_constant))) 544.00/242.15 down(g(g(a))) 544.00/242.15 down(g(g(f(x0)))) 544.00/242.15 down(g(g(b))) 544.00/242.15 down(g(g(c))) 544.00/242.15 down(g(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) 544.00/242.15 down(f(f(f(g(x0))))) 544.00/242.15 down(f(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) 544.00/242.15 down(g(g(g(f(x0))))) 544.00/242.15 down(g(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(x0)))))) 544.00/242.15 down(f(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(x0)))))) 544.00/242.15 down(g(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(x0))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(x0))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 f_flat(up(x0)) 544.00/242.15 g_flat(up(x0)) 544.00/242.15 544.00/242.15 We have to consider all minimal (P,Q,R)-chains. 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1083) TransformationProof (EQUIVALENT) 544.00/242.15 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.00/242.15 544.00/242.15 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.00/242.15 544.00/242.15 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1084) 544.00/242.15 Obligation: 544.00/242.15 Q DP problem: 544.00/242.15 The TRS P consists of the following rules: 544.00/242.15 544.00/242.15 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.15 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.15 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.15 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.15 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.15 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.15 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.15 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.15 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.15 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.15 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.15 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.15 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.15 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.15 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.15 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.15 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.15 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.15 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.15 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.15 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.15 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.15 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.15 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.15 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.15 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 544.00/242.15 The TRS R consists of the following rules: 544.00/242.15 544.00/242.15 down(a) -> up(f(a)) 544.00/242.15 down(b) -> up(g(b)) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.15 down(f(a)) -> f_flat(down(a)) 544.00/242.15 down(f(b)) -> f_flat(down(b)) 544.00/242.15 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.15 down(f(c)) -> f_flat(down(c)) 544.00/242.15 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.15 down(g(a)) -> g_flat(down(a)) 544.00/242.15 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.15 down(g(b)) -> g_flat(down(b)) 544.00/242.15 down(g(c)) -> g_flat(down(c)) 544.00/242.15 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.15 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.15 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.15 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.15 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.15 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.15 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.15 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.15 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.15 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.15 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.15 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.15 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.15 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.15 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.15 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.15 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.15 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.15 544.00/242.15 The set Q consists of the following terms: 544.00/242.15 544.00/242.15 down(a) 544.00/242.15 down(b) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.15 down(f(a)) 544.00/242.15 down(f(b)) 544.00/242.15 down(f(g(x0))) 544.00/242.15 down(f(c)) 544.00/242.15 down(f(fresh_constant)) 544.00/242.15 down(g(a)) 544.00/242.15 down(g(f(x0))) 544.00/242.15 down(g(b)) 544.00/242.15 down(g(c)) 544.00/242.15 down(g(fresh_constant)) 544.00/242.15 down(f(f(a))) 544.00/242.15 down(f(f(b))) 544.00/242.15 down(f(f(g(x0)))) 544.00/242.15 down(f(f(c))) 544.00/242.15 down(f(f(fresh_constant))) 544.00/242.15 down(g(g(a))) 544.00/242.15 down(g(g(f(x0)))) 544.00/242.15 down(g(g(b))) 544.00/242.15 down(g(g(c))) 544.00/242.15 down(g(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) 544.00/242.15 down(f(f(f(g(x0))))) 544.00/242.15 down(f(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) 544.00/242.15 down(g(g(g(f(x0))))) 544.00/242.15 down(g(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(x0)))))) 544.00/242.15 down(f(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(x0)))))) 544.00/242.15 down(g(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(x0))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(x0))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 f_flat(up(x0)) 544.00/242.15 g_flat(up(x0)) 544.00/242.15 544.00/242.15 We have to consider all minimal (P,Q,R)-chains. 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1085) TransformationProof (EQUIVALENT) 544.00/242.15 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(f_flat(up(f(f(f(g(b)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.00/242.15 544.00/242.15 (TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.15 544.00/242.15 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1086) 544.00/242.15 Obligation: 544.00/242.15 Q DP problem: 544.00/242.15 The TRS P consists of the following rules: 544.00/242.15 544.00/242.15 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.15 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.15 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.15 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.15 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.15 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.15 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.15 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.15 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.15 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.15 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.15 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.15 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.15 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.15 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.15 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.15 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.15 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.15 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.15 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.15 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.15 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.15 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.15 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.15 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.15 544.00/242.15 The TRS R consists of the following rules: 544.00/242.15 544.00/242.15 down(a) -> up(f(a)) 544.00/242.15 down(b) -> up(g(b)) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.15 down(f(a)) -> f_flat(down(a)) 544.00/242.15 down(f(b)) -> f_flat(down(b)) 544.00/242.15 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.15 down(f(c)) -> f_flat(down(c)) 544.00/242.15 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.15 down(g(a)) -> g_flat(down(a)) 544.00/242.15 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.15 down(g(b)) -> g_flat(down(b)) 544.00/242.15 down(g(c)) -> g_flat(down(c)) 544.00/242.15 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.15 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.15 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.15 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.15 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.15 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.15 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.15 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.15 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.15 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.15 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.15 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.15 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.15 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.15 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.15 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.15 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.15 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.15 544.00/242.15 The set Q consists of the following terms: 544.00/242.15 544.00/242.15 down(a) 544.00/242.15 down(b) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.15 down(f(a)) 544.00/242.15 down(f(b)) 544.00/242.15 down(f(g(x0))) 544.00/242.15 down(f(c)) 544.00/242.15 down(f(fresh_constant)) 544.00/242.15 down(g(a)) 544.00/242.15 down(g(f(x0))) 544.00/242.15 down(g(b)) 544.00/242.15 down(g(c)) 544.00/242.15 down(g(fresh_constant)) 544.00/242.15 down(f(f(a))) 544.00/242.15 down(f(f(b))) 544.00/242.15 down(f(f(g(x0)))) 544.00/242.15 down(f(f(c))) 544.00/242.15 down(f(f(fresh_constant))) 544.00/242.15 down(g(g(a))) 544.00/242.15 down(g(g(f(x0)))) 544.00/242.15 down(g(g(b))) 544.00/242.15 down(g(g(c))) 544.00/242.15 down(g(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) 544.00/242.15 down(f(f(f(g(x0))))) 544.00/242.15 down(f(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) 544.00/242.15 down(g(g(g(f(x0))))) 544.00/242.15 down(g(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(x0)))))) 544.00/242.15 down(f(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(x0)))))) 544.00/242.15 down(g(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(x0))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(x0))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 f_flat(up(x0)) 544.00/242.15 g_flat(up(x0)) 544.00/242.15 544.00/242.15 We have to consider all minimal (P,Q,R)-chains. 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1087) TransformationProof (EQUIVALENT) 544.00/242.15 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.15 544.00/242.15 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.15 544.00/242.15 544.00/242.15 ---------------------------------------- 544.00/242.15 544.00/242.15 (1088) 544.00/242.15 Obligation: 544.00/242.15 Q DP problem: 544.00/242.15 The TRS P consists of the following rules: 544.00/242.15 544.00/242.15 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.15 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.15 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.15 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.15 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.15 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.15 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.15 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.15 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.15 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.15 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.15 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.15 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.15 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.15 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.15 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.15 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.15 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.15 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.15 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.15 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.15 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.15 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.15 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.15 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.15 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.15 544.00/242.15 The TRS R consists of the following rules: 544.00/242.15 544.00/242.15 down(a) -> up(f(a)) 544.00/242.15 down(b) -> up(g(b)) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.15 down(f(a)) -> f_flat(down(a)) 544.00/242.15 down(f(b)) -> f_flat(down(b)) 544.00/242.15 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.15 down(f(c)) -> f_flat(down(c)) 544.00/242.15 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.15 down(g(a)) -> g_flat(down(a)) 544.00/242.15 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.15 down(g(b)) -> g_flat(down(b)) 544.00/242.15 down(g(c)) -> g_flat(down(c)) 544.00/242.15 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.15 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.15 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.15 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.15 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.15 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.15 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.15 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.15 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.15 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.15 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.15 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.15 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.15 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.15 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.15 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.15 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.15 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.15 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.15 544.00/242.15 The set Q consists of the following terms: 544.00/242.15 544.00/242.15 down(a) 544.00/242.15 down(b) 544.00/242.15 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.15 down(f(a)) 544.00/242.15 down(f(b)) 544.00/242.15 down(f(g(x0))) 544.00/242.15 down(f(c)) 544.00/242.15 down(f(fresh_constant)) 544.00/242.15 down(g(a)) 544.00/242.15 down(g(f(x0))) 544.00/242.15 down(g(b)) 544.00/242.15 down(g(c)) 544.00/242.15 down(g(fresh_constant)) 544.00/242.15 down(f(f(a))) 544.00/242.15 down(f(f(b))) 544.00/242.15 down(f(f(g(x0)))) 544.00/242.15 down(f(f(c))) 544.00/242.15 down(f(f(fresh_constant))) 544.00/242.15 down(g(g(a))) 544.00/242.15 down(g(g(f(x0)))) 544.00/242.15 down(g(g(b))) 544.00/242.15 down(g(g(c))) 544.00/242.15 down(g(g(fresh_constant))) 544.00/242.15 down(f(f(f(a)))) 544.00/242.15 down(f(f(f(b)))) 544.00/242.15 down(f(f(f(g(x0))))) 544.00/242.15 down(f(f(f(c)))) 544.00/242.15 down(f(f(f(fresh_constant)))) 544.00/242.15 down(g(g(g(a)))) 544.00/242.15 down(g(g(g(f(x0))))) 544.00/242.15 down(g(g(g(b)))) 544.00/242.15 down(g(g(g(c)))) 544.00/242.15 down(g(g(g(fresh_constant)))) 544.00/242.15 down(f(f(f(f(a))))) 544.00/242.15 down(f(f(f(f(b))))) 544.00/242.15 down(f(f(f(f(g(x0)))))) 544.00/242.15 down(f(f(f(f(c))))) 544.00/242.15 down(f(f(f(f(fresh_constant))))) 544.00/242.15 down(g(g(g(g(a))))) 544.00/242.15 down(g(g(g(g(f(x0)))))) 544.00/242.15 down(g(g(g(g(b))))) 544.00/242.15 down(g(g(g(g(c))))) 544.00/242.15 down(g(g(g(g(fresh_constant))))) 544.00/242.15 down(f(f(f(f(f(a)))))) 544.00/242.15 down(f(f(f(f(f(b)))))) 544.00/242.15 down(f(f(f(f(f(g(x0))))))) 544.00/242.15 down(f(f(f(f(f(c)))))) 544.00/242.15 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.15 down(g(g(g(g(g(a)))))) 544.00/242.15 down(g(g(g(g(g(f(x0))))))) 544.00/242.15 down(g(g(g(g(g(b)))))) 544.00/242.15 down(g(g(g(g(g(c)))))) 544.00/242.15 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.15 down(f(f(f(f(f(f(a))))))) 544.00/242.15 down(f(f(f(f(f(f(b))))))) 544.00/242.15 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.15 down(f(f(f(f(f(f(c))))))) 544.00/242.15 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.15 down(g(g(g(g(g(g(a))))))) 544.00/242.15 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.15 down(g(g(g(g(g(g(b))))))) 544.00/242.15 down(g(g(g(g(g(g(c))))))) 544.00/242.15 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.15 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.15 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.15 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.15 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 f_flat(up(x0)) 544.00/242.16 g_flat(up(x0)) 544.00/242.16 544.00/242.16 We have to consider all minimal (P,Q,R)-chains. 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1089) TransformationProof (EQUIVALENT) 544.00/242.16 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.16 544.00/242.16 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.16 544.00/242.16 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1090) 544.00/242.16 Obligation: 544.00/242.16 Q DP problem: 544.00/242.16 The TRS P consists of the following rules: 544.00/242.16 544.00/242.16 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.16 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.16 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.16 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.16 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.16 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.16 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.16 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.16 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.16 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.16 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.16 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.16 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.16 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.16 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.16 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.16 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.16 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.16 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.16 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.16 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.16 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.16 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.16 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.16 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.16 544.00/242.16 The TRS R consists of the following rules: 544.00/242.16 544.00/242.16 down(a) -> up(f(a)) 544.00/242.16 down(b) -> up(g(b)) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.16 down(f(a)) -> f_flat(down(a)) 544.00/242.16 down(f(b)) -> f_flat(down(b)) 544.00/242.16 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.16 down(f(c)) -> f_flat(down(c)) 544.00/242.16 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.16 down(g(a)) -> g_flat(down(a)) 544.00/242.16 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.16 down(g(b)) -> g_flat(down(b)) 544.00/242.16 down(g(c)) -> g_flat(down(c)) 544.00/242.16 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.16 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.16 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.16 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.16 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.16 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.16 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.16 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.16 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.16 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.16 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.16 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.16 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.16 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.16 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.16 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.16 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.16 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.16 544.00/242.16 The set Q consists of the following terms: 544.00/242.16 544.00/242.16 down(a) 544.00/242.16 down(b) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.16 down(f(a)) 544.00/242.16 down(f(b)) 544.00/242.16 down(f(g(x0))) 544.00/242.16 down(f(c)) 544.00/242.16 down(f(fresh_constant)) 544.00/242.16 down(g(a)) 544.00/242.16 down(g(f(x0))) 544.00/242.16 down(g(b)) 544.00/242.16 down(g(c)) 544.00/242.16 down(g(fresh_constant)) 544.00/242.16 down(f(f(a))) 544.00/242.16 down(f(f(b))) 544.00/242.16 down(f(f(g(x0)))) 544.00/242.16 down(f(f(c))) 544.00/242.16 down(f(f(fresh_constant))) 544.00/242.16 down(g(g(a))) 544.00/242.16 down(g(g(f(x0)))) 544.00/242.16 down(g(g(b))) 544.00/242.16 down(g(g(c))) 544.00/242.16 down(g(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) 544.00/242.16 down(f(f(f(g(x0))))) 544.00/242.16 down(f(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) 544.00/242.16 down(g(g(g(f(x0))))) 544.00/242.16 down(g(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(x0)))))) 544.00/242.16 down(f(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(x0)))))) 544.00/242.16 down(g(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(x0))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(x0))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 f_flat(up(x0)) 544.00/242.16 g_flat(up(x0)) 544.00/242.16 544.00/242.16 We have to consider all minimal (P,Q,R)-chains. 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1091) TransformationProof (EQUIVALENT) 544.00/242.16 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.16 544.00/242.16 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.16 544.00/242.16 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1092) 544.00/242.16 Obligation: 544.00/242.16 Q DP problem: 544.00/242.16 The TRS P consists of the following rules: 544.00/242.16 544.00/242.16 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.16 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.16 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.16 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.16 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.16 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.16 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.16 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.16 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.16 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.16 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.16 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.16 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.16 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.16 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.16 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.16 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.16 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.16 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.16 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.16 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.16 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.16 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.16 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.16 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.16 544.00/242.16 The TRS R consists of the following rules: 544.00/242.16 544.00/242.16 down(a) -> up(f(a)) 544.00/242.16 down(b) -> up(g(b)) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.16 down(f(a)) -> f_flat(down(a)) 544.00/242.16 down(f(b)) -> f_flat(down(b)) 544.00/242.16 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.16 down(f(c)) -> f_flat(down(c)) 544.00/242.16 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.16 down(g(a)) -> g_flat(down(a)) 544.00/242.16 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.16 down(g(b)) -> g_flat(down(b)) 544.00/242.16 down(g(c)) -> g_flat(down(c)) 544.00/242.16 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.16 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.16 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.16 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.16 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.16 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.16 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.16 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.16 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.16 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.16 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.16 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.16 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.16 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.16 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.16 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.16 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.16 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.16 544.00/242.16 The set Q consists of the following terms: 544.00/242.16 544.00/242.16 down(a) 544.00/242.16 down(b) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.16 down(f(a)) 544.00/242.16 down(f(b)) 544.00/242.16 down(f(g(x0))) 544.00/242.16 down(f(c)) 544.00/242.16 down(f(fresh_constant)) 544.00/242.16 down(g(a)) 544.00/242.16 down(g(f(x0))) 544.00/242.16 down(g(b)) 544.00/242.16 down(g(c)) 544.00/242.16 down(g(fresh_constant)) 544.00/242.16 down(f(f(a))) 544.00/242.16 down(f(f(b))) 544.00/242.16 down(f(f(g(x0)))) 544.00/242.16 down(f(f(c))) 544.00/242.16 down(f(f(fresh_constant))) 544.00/242.16 down(g(g(a))) 544.00/242.16 down(g(g(f(x0)))) 544.00/242.16 down(g(g(b))) 544.00/242.16 down(g(g(c))) 544.00/242.16 down(g(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) 544.00/242.16 down(f(f(f(g(x0))))) 544.00/242.16 down(f(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) 544.00/242.16 down(g(g(g(f(x0))))) 544.00/242.16 down(g(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(x0)))))) 544.00/242.16 down(f(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(x0)))))) 544.00/242.16 down(g(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(x0))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(x0))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 f_flat(up(x0)) 544.00/242.16 g_flat(up(x0)) 544.00/242.16 544.00/242.16 We have to consider all minimal (P,Q,R)-chains. 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1093) TransformationProof (EQUIVALENT) 544.00/242.16 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.16 544.00/242.16 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.16 544.00/242.16 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1094) 544.00/242.16 Obligation: 544.00/242.16 Q DP problem: 544.00/242.16 The TRS P consists of the following rules: 544.00/242.16 544.00/242.16 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.16 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.16 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.16 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.16 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.16 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.16 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.16 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.16 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.16 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.16 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.16 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.16 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.16 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.16 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.16 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.16 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.16 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.16 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.16 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.16 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.16 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.16 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.16 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.16 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.16 544.00/242.16 The TRS R consists of the following rules: 544.00/242.16 544.00/242.16 down(a) -> up(f(a)) 544.00/242.16 down(b) -> up(g(b)) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.16 down(f(a)) -> f_flat(down(a)) 544.00/242.16 down(f(b)) -> f_flat(down(b)) 544.00/242.16 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.16 down(f(c)) -> f_flat(down(c)) 544.00/242.16 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.16 down(g(a)) -> g_flat(down(a)) 544.00/242.16 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.16 down(g(b)) -> g_flat(down(b)) 544.00/242.16 down(g(c)) -> g_flat(down(c)) 544.00/242.16 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.16 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.16 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.16 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.16 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.16 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.16 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.16 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.16 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.16 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.16 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.16 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.16 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.16 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.16 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.16 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.16 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.16 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.16 544.00/242.16 The set Q consists of the following terms: 544.00/242.16 544.00/242.16 down(a) 544.00/242.16 down(b) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.16 down(f(a)) 544.00/242.16 down(f(b)) 544.00/242.16 down(f(g(x0))) 544.00/242.16 down(f(c)) 544.00/242.16 down(f(fresh_constant)) 544.00/242.16 down(g(a)) 544.00/242.16 down(g(f(x0))) 544.00/242.16 down(g(b)) 544.00/242.16 down(g(c)) 544.00/242.16 down(g(fresh_constant)) 544.00/242.16 down(f(f(a))) 544.00/242.16 down(f(f(b))) 544.00/242.16 down(f(f(g(x0)))) 544.00/242.16 down(f(f(c))) 544.00/242.16 down(f(f(fresh_constant))) 544.00/242.16 down(g(g(a))) 544.00/242.16 down(g(g(f(x0)))) 544.00/242.16 down(g(g(b))) 544.00/242.16 down(g(g(c))) 544.00/242.16 down(g(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) 544.00/242.16 down(f(f(f(g(x0))))) 544.00/242.16 down(f(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) 544.00/242.16 down(g(g(g(f(x0))))) 544.00/242.16 down(g(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(x0)))))) 544.00/242.16 down(f(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(x0)))))) 544.00/242.16 down(g(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(x0))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(x0))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 f_flat(up(x0)) 544.00/242.16 g_flat(up(x0)) 544.00/242.16 544.00/242.16 We have to consider all minimal (P,Q,R)-chains. 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1095) TransformationProof (EQUIVALENT) 544.00/242.16 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(a))))))))))) at position [0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.16 544.00/242.16 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a))))))))))))) 544.00/242.16 544.00/242.16 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1096) 544.00/242.16 Obligation: 544.00/242.16 Q DP problem: 544.00/242.16 The TRS P consists of the following rules: 544.00/242.16 544.00/242.16 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.16 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.16 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.16 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.16 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.16 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.16 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.16 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.16 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.16 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.16 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.16 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.16 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.16 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.16 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.16 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.16 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.16 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.16 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.16 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.16 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.16 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.16 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.16 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.16 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.16 544.00/242.16 The TRS R consists of the following rules: 544.00/242.16 544.00/242.16 down(a) -> up(f(a)) 544.00/242.16 down(b) -> up(g(b)) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.16 down(f(a)) -> f_flat(down(a)) 544.00/242.16 down(f(b)) -> f_flat(down(b)) 544.00/242.16 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.16 down(f(c)) -> f_flat(down(c)) 544.00/242.16 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.16 down(g(a)) -> g_flat(down(a)) 544.00/242.16 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.16 down(g(b)) -> g_flat(down(b)) 544.00/242.16 down(g(c)) -> g_flat(down(c)) 544.00/242.16 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.16 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.16 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.16 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.16 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.16 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.16 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.16 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.16 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.16 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.16 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.16 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.16 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.16 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.16 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.16 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.16 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.16 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.16 544.00/242.16 The set Q consists of the following terms: 544.00/242.16 544.00/242.16 down(a) 544.00/242.16 down(b) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.16 down(f(a)) 544.00/242.16 down(f(b)) 544.00/242.16 down(f(g(x0))) 544.00/242.16 down(f(c)) 544.00/242.16 down(f(fresh_constant)) 544.00/242.16 down(g(a)) 544.00/242.16 down(g(f(x0))) 544.00/242.16 down(g(b)) 544.00/242.16 down(g(c)) 544.00/242.16 down(g(fresh_constant)) 544.00/242.16 down(f(f(a))) 544.00/242.16 down(f(f(b))) 544.00/242.16 down(f(f(g(x0)))) 544.00/242.16 down(f(f(c))) 544.00/242.16 down(f(f(fresh_constant))) 544.00/242.16 down(g(g(a))) 544.00/242.16 down(g(g(f(x0)))) 544.00/242.16 down(g(g(b))) 544.00/242.16 down(g(g(c))) 544.00/242.16 down(g(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) 544.00/242.16 down(f(f(f(g(x0))))) 544.00/242.16 down(f(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) 544.00/242.16 down(g(g(g(f(x0))))) 544.00/242.16 down(g(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(x0)))))) 544.00/242.16 down(f(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(x0)))))) 544.00/242.16 down(g(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(x0))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(x0))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 f_flat(up(x0)) 544.00/242.16 g_flat(up(x0)) 544.00/242.16 544.00/242.16 We have to consider all minimal (P,Q,R)-chains. 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1097) TransformationProof (EQUIVALENT) 544.00/242.16 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(b))))))))))) at position [0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.16 544.00/242.16 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b))))))))))))) 544.00/242.16 544.00/242.16 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1098) 544.00/242.16 Obligation: 544.00/242.16 Q DP problem: 544.00/242.16 The TRS P consists of the following rules: 544.00/242.16 544.00/242.16 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.16 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.16 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.16 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.16 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.16 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.16 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.16 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.16 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.16 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.16 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.16 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.16 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.16 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.16 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.16 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.16 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.16 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.16 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.16 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.16 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.16 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.16 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.16 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.16 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.16 544.00/242.16 The TRS R consists of the following rules: 544.00/242.16 544.00/242.16 down(a) -> up(f(a)) 544.00/242.16 down(b) -> up(g(b)) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.16 down(f(a)) -> f_flat(down(a)) 544.00/242.16 down(f(b)) -> f_flat(down(b)) 544.00/242.16 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.16 down(f(c)) -> f_flat(down(c)) 544.00/242.16 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.16 down(g(a)) -> g_flat(down(a)) 544.00/242.16 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.16 down(g(b)) -> g_flat(down(b)) 544.00/242.16 down(g(c)) -> g_flat(down(c)) 544.00/242.16 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.16 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.16 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.16 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.16 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.16 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.16 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.16 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.16 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.16 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.16 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.16 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.16 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.16 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.16 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.16 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.16 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.16 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.16 544.00/242.16 The set Q consists of the following terms: 544.00/242.16 544.00/242.16 down(a) 544.00/242.16 down(b) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.16 down(f(a)) 544.00/242.16 down(f(b)) 544.00/242.16 down(f(g(x0))) 544.00/242.16 down(f(c)) 544.00/242.16 down(f(fresh_constant)) 544.00/242.16 down(g(a)) 544.00/242.16 down(g(f(x0))) 544.00/242.16 down(g(b)) 544.00/242.16 down(g(c)) 544.00/242.16 down(g(fresh_constant)) 544.00/242.16 down(f(f(a))) 544.00/242.16 down(f(f(b))) 544.00/242.16 down(f(f(g(x0)))) 544.00/242.16 down(f(f(c))) 544.00/242.16 down(f(f(fresh_constant))) 544.00/242.16 down(g(g(a))) 544.00/242.16 down(g(g(f(x0)))) 544.00/242.16 down(g(g(b))) 544.00/242.16 down(g(g(c))) 544.00/242.16 down(g(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) 544.00/242.16 down(f(f(f(g(x0))))) 544.00/242.16 down(f(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) 544.00/242.16 down(g(g(g(f(x0))))) 544.00/242.16 down(g(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(x0)))))) 544.00/242.16 down(f(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(x0)))))) 544.00/242.16 down(g(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(x0))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(x0))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 f_flat(up(x0)) 544.00/242.16 g_flat(up(x0)) 544.00/242.16 544.00/242.16 We have to consider all minimal (P,Q,R)-chains. 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1099) TransformationProof (EQUIVALENT) 544.00/242.16 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(b))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.16 544.00/242.16 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b)))))))))))) 544.00/242.16 544.00/242.16 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1100) 544.00/242.16 Obligation: 544.00/242.16 Q DP problem: 544.00/242.16 The TRS P consists of the following rules: 544.00/242.16 544.00/242.16 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.16 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.16 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.16 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.16 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.16 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.16 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.16 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.16 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.16 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.16 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.16 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.16 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.16 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.16 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.16 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.16 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.16 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.16 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.16 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.16 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.16 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.16 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.16 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.16 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.16 544.00/242.16 The TRS R consists of the following rules: 544.00/242.16 544.00/242.16 down(a) -> up(f(a)) 544.00/242.16 down(b) -> up(g(b)) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.16 down(f(a)) -> f_flat(down(a)) 544.00/242.16 down(f(b)) -> f_flat(down(b)) 544.00/242.16 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.16 down(f(c)) -> f_flat(down(c)) 544.00/242.16 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.16 down(g(a)) -> g_flat(down(a)) 544.00/242.16 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.16 down(g(b)) -> g_flat(down(b)) 544.00/242.16 down(g(c)) -> g_flat(down(c)) 544.00/242.16 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.16 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.16 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.16 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.16 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.16 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.16 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.16 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.16 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.16 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.16 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.16 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.16 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.16 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.16 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.16 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.16 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.16 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.16 544.00/242.16 The set Q consists of the following terms: 544.00/242.16 544.00/242.16 down(a) 544.00/242.16 down(b) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.16 down(f(a)) 544.00/242.16 down(f(b)) 544.00/242.16 down(f(g(x0))) 544.00/242.16 down(f(c)) 544.00/242.16 down(f(fresh_constant)) 544.00/242.16 down(g(a)) 544.00/242.16 down(g(f(x0))) 544.00/242.16 down(g(b)) 544.00/242.16 down(g(c)) 544.00/242.16 down(g(fresh_constant)) 544.00/242.16 down(f(f(a))) 544.00/242.16 down(f(f(b))) 544.00/242.16 down(f(f(g(x0)))) 544.00/242.16 down(f(f(c))) 544.00/242.16 down(f(f(fresh_constant))) 544.00/242.16 down(g(g(a))) 544.00/242.16 down(g(g(f(x0)))) 544.00/242.16 down(g(g(b))) 544.00/242.16 down(g(g(c))) 544.00/242.16 down(g(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) 544.00/242.16 down(f(f(f(g(x0))))) 544.00/242.16 down(f(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) 544.00/242.16 down(g(g(g(f(x0))))) 544.00/242.16 down(g(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(x0)))))) 544.00/242.16 down(f(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(x0)))))) 544.00/242.16 down(g(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(x0))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(x0))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 f_flat(up(x0)) 544.00/242.16 g_flat(up(x0)) 544.00/242.16 544.00/242.16 We have to consider all minimal (P,Q,R)-chains. 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1101) TransformationProof (EQUIVALENT) 544.00/242.16 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(c))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.16 544.00/242.16 (TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c)))))))))))) 544.00/242.16 544.00/242.16 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1102) 544.00/242.16 Obligation: 544.00/242.16 Q DP problem: 544.00/242.16 The TRS P consists of the following rules: 544.00/242.16 544.00/242.16 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.16 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.16 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.16 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.16 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.16 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.16 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.16 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.16 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.16 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.16 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.16 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.16 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.16 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.16 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.16 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.16 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.16 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.16 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.16 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.16 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.16 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.16 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.16 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.16 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(c))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(c))))))))))) 544.00/242.16 544.00/242.16 The TRS R consists of the following rules: 544.00/242.16 544.00/242.16 down(a) -> up(f(a)) 544.00/242.16 down(b) -> up(g(b)) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.16 down(f(a)) -> f_flat(down(a)) 544.00/242.16 down(f(b)) -> f_flat(down(b)) 544.00/242.16 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.16 down(f(c)) -> f_flat(down(c)) 544.00/242.16 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.16 down(g(a)) -> g_flat(down(a)) 544.00/242.16 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.16 down(g(b)) -> g_flat(down(b)) 544.00/242.16 down(g(c)) -> g_flat(down(c)) 544.00/242.16 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.16 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.16 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.16 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.16 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.16 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.16 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.16 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.16 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.16 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.16 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.16 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.16 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.16 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.16 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.16 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.16 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.16 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.16 544.00/242.16 The set Q consists of the following terms: 544.00/242.16 544.00/242.16 down(a) 544.00/242.16 down(b) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.16 down(f(a)) 544.00/242.16 down(f(b)) 544.00/242.16 down(f(g(x0))) 544.00/242.16 down(f(c)) 544.00/242.16 down(f(fresh_constant)) 544.00/242.16 down(g(a)) 544.00/242.16 down(g(f(x0))) 544.00/242.16 down(g(b)) 544.00/242.16 down(g(c)) 544.00/242.16 down(g(fresh_constant)) 544.00/242.16 down(f(f(a))) 544.00/242.16 down(f(f(b))) 544.00/242.16 down(f(f(g(x0)))) 544.00/242.16 down(f(f(c))) 544.00/242.16 down(f(f(fresh_constant))) 544.00/242.16 down(g(g(a))) 544.00/242.16 down(g(g(f(x0)))) 544.00/242.16 down(g(g(b))) 544.00/242.16 down(g(g(c))) 544.00/242.16 down(g(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) 544.00/242.16 down(f(f(f(g(x0))))) 544.00/242.16 down(f(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) 544.00/242.16 down(g(g(g(f(x0))))) 544.00/242.16 down(g(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(x0)))))) 544.00/242.16 down(f(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(x0)))))) 544.00/242.16 down(g(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(x0))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(x0))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) 544.00/242.16 down(f(f(f(f(f(f(b))))))) 544.00/242.16 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.16 down(f(f(f(f(f(f(c))))))) 544.00/242.16 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.16 down(g(g(g(g(g(g(a))))))) 544.00/242.16 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.16 down(g(g(g(g(g(g(b))))))) 544.00/242.16 down(g(g(g(g(g(g(c))))))) 544.00/242.16 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.16 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.16 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.16 f_flat(up(x0)) 544.00/242.16 g_flat(up(x0)) 544.00/242.16 544.00/242.16 We have to consider all minimal (P,Q,R)-chains. 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1103) DependencyGraphProof (EQUIVALENT) 544.00/242.16 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 544.00/242.16 ---------------------------------------- 544.00/242.16 544.00/242.16 (1104) 544.00/242.16 Obligation: 544.00/242.16 Q DP problem: 544.00/242.16 The TRS P consists of the following rules: 544.00/242.16 544.00/242.16 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.16 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.16 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.16 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.16 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.16 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.16 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.16 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) 544.00/242.16 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.16 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.16 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.16 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.16 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.16 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.16 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.16 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.16 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.16 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.16 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.16 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.16 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.16 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.16 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.16 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.16 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.16 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.16 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.16 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.16 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.16 544.00/242.16 The TRS R consists of the following rules: 544.00/242.16 544.00/242.16 down(a) -> up(f(a)) 544.00/242.16 down(b) -> up(g(b)) 544.00/242.16 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.16 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.16 down(f(a)) -> f_flat(down(a)) 544.00/242.16 down(f(b)) -> f_flat(down(b)) 544.00/242.16 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.16 down(f(c)) -> f_flat(down(c)) 544.00/242.16 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.16 down(g(a)) -> g_flat(down(a)) 544.00/242.16 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.16 down(g(b)) -> g_flat(down(b)) 544.00/242.16 down(g(c)) -> g_flat(down(c)) 544.00/242.16 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.16 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.16 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.16 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.16 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.16 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.16 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.16 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.16 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.16 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.16 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.16 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.16 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.16 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.16 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.16 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.16 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.16 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.16 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.16 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.16 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.16 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.16 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.16 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.16 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.16 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.16 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.16 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.16 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.16 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.16 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.16 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.16 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.16 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.16 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.16 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.16 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.16 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.16 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.16 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.16 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.16 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.17 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.17 544.00/242.17 The set Q consists of the following terms: 544.00/242.17 544.00/242.17 down(a) 544.00/242.17 down(b) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.17 down(f(a)) 544.00/242.17 down(f(b)) 544.00/242.17 down(f(g(x0))) 544.00/242.17 down(f(c)) 544.00/242.17 down(f(fresh_constant)) 544.00/242.17 down(g(a)) 544.00/242.17 down(g(f(x0))) 544.00/242.17 down(g(b)) 544.00/242.17 down(g(c)) 544.00/242.17 down(g(fresh_constant)) 544.00/242.17 down(f(f(a))) 544.00/242.17 down(f(f(b))) 544.00/242.17 down(f(f(g(x0)))) 544.00/242.17 down(f(f(c))) 544.00/242.17 down(f(f(fresh_constant))) 544.00/242.17 down(g(g(a))) 544.00/242.17 down(g(g(f(x0)))) 544.00/242.17 down(g(g(b))) 544.00/242.17 down(g(g(c))) 544.00/242.17 down(g(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) 544.00/242.17 down(f(f(f(g(x0))))) 544.00/242.17 down(f(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) 544.00/242.17 down(g(g(g(f(x0))))) 544.00/242.17 down(g(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(x0)))))) 544.00/242.17 down(f(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(x0)))))) 544.00/242.17 down(g(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(x0))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(x0))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 f_flat(up(x0)) 544.00/242.17 g_flat(up(x0)) 544.00/242.17 544.00/242.17 We have to consider all minimal (P,Q,R)-chains. 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1105) TransformationProof (EQUIVALENT) 544.00/242.17 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(a)))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.00/242.17 544.00/242.17 (TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))),TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a))))))))))) 544.00/242.17 544.00/242.17 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1106) 544.00/242.17 Obligation: 544.00/242.17 Q DP problem: 544.00/242.17 The TRS P consists of the following rules: 544.00/242.17 544.00/242.17 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.17 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.17 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.17 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.17 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.17 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.17 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.17 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.17 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.17 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.17 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.17 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.17 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.17 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.17 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.17 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.17 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.17 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.17 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.17 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.17 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.17 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.17 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.17 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 544.00/242.17 The TRS R consists of the following rules: 544.00/242.17 544.00/242.17 down(a) -> up(f(a)) 544.00/242.17 down(b) -> up(g(b)) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.17 down(f(a)) -> f_flat(down(a)) 544.00/242.17 down(f(b)) -> f_flat(down(b)) 544.00/242.17 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.17 down(f(c)) -> f_flat(down(c)) 544.00/242.17 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.17 down(g(a)) -> g_flat(down(a)) 544.00/242.17 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.17 down(g(b)) -> g_flat(down(b)) 544.00/242.17 down(g(c)) -> g_flat(down(c)) 544.00/242.17 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.17 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.17 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.17 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.17 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.17 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.17 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.17 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.17 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.17 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.17 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.17 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.17 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.17 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.17 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.17 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.17 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.17 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.17 544.00/242.17 The set Q consists of the following terms: 544.00/242.17 544.00/242.17 down(a) 544.00/242.17 down(b) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.17 down(f(a)) 544.00/242.17 down(f(b)) 544.00/242.17 down(f(g(x0))) 544.00/242.17 down(f(c)) 544.00/242.17 down(f(fresh_constant)) 544.00/242.17 down(g(a)) 544.00/242.17 down(g(f(x0))) 544.00/242.17 down(g(b)) 544.00/242.17 down(g(c)) 544.00/242.17 down(g(fresh_constant)) 544.00/242.17 down(f(f(a))) 544.00/242.17 down(f(f(b))) 544.00/242.17 down(f(f(g(x0)))) 544.00/242.17 down(f(f(c))) 544.00/242.17 down(f(f(fresh_constant))) 544.00/242.17 down(g(g(a))) 544.00/242.17 down(g(g(f(x0)))) 544.00/242.17 down(g(g(b))) 544.00/242.17 down(g(g(c))) 544.00/242.17 down(g(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) 544.00/242.17 down(f(f(f(g(x0))))) 544.00/242.17 down(f(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) 544.00/242.17 down(g(g(g(f(x0))))) 544.00/242.17 down(g(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(x0)))))) 544.00/242.17 down(f(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(x0)))))) 544.00/242.17 down(g(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(x0))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(x0))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 f_flat(up(x0)) 544.00/242.17 g_flat(up(x0)) 544.00/242.17 544.00/242.17 We have to consider all minimal (P,Q,R)-chains. 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1107) TransformationProof (EQUIVALENT) 544.00/242.17 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(b)))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.00/242.17 544.00/242.17 (TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))),TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b))))))))))) 544.00/242.17 544.00/242.17 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1108) 544.00/242.17 Obligation: 544.00/242.17 Q DP problem: 544.00/242.17 The TRS P consists of the following rules: 544.00/242.17 544.00/242.17 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.17 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.17 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.17 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.17 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.17 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.17 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.17 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.17 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.17 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.17 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.17 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.17 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.17 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.17 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.17 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.17 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.17 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.17 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.17 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.17 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.17 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) 544.00/242.17 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.17 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 544.00/242.17 The TRS R consists of the following rules: 544.00/242.17 544.00/242.17 down(a) -> up(f(a)) 544.00/242.17 down(b) -> up(g(b)) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.17 down(f(a)) -> f_flat(down(a)) 544.00/242.17 down(f(b)) -> f_flat(down(b)) 544.00/242.17 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.17 down(f(c)) -> f_flat(down(c)) 544.00/242.17 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.17 down(g(a)) -> g_flat(down(a)) 544.00/242.17 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.17 down(g(b)) -> g_flat(down(b)) 544.00/242.17 down(g(c)) -> g_flat(down(c)) 544.00/242.17 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.17 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.17 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.17 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.17 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.17 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.17 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.17 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.17 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.17 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.17 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.17 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.17 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.17 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.17 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.17 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.17 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.17 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.17 544.00/242.17 The set Q consists of the following terms: 544.00/242.17 544.00/242.17 down(a) 544.00/242.17 down(b) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.17 down(f(a)) 544.00/242.17 down(f(b)) 544.00/242.17 down(f(g(x0))) 544.00/242.17 down(f(c)) 544.00/242.17 down(f(fresh_constant)) 544.00/242.17 down(g(a)) 544.00/242.17 down(g(f(x0))) 544.00/242.17 down(g(b)) 544.00/242.17 down(g(c)) 544.00/242.17 down(g(fresh_constant)) 544.00/242.17 down(f(f(a))) 544.00/242.17 down(f(f(b))) 544.00/242.17 down(f(f(g(x0)))) 544.00/242.17 down(f(f(c))) 544.00/242.17 down(f(f(fresh_constant))) 544.00/242.17 down(g(g(a))) 544.00/242.17 down(g(g(f(x0)))) 544.00/242.17 down(g(g(b))) 544.00/242.17 down(g(g(c))) 544.00/242.17 down(g(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) 544.00/242.17 down(f(f(f(g(x0))))) 544.00/242.17 down(f(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) 544.00/242.17 down(g(g(g(f(x0))))) 544.00/242.17 down(g(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(x0)))))) 544.00/242.17 down(f(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(x0)))))) 544.00/242.17 down(g(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(x0))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(x0))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 f_flat(up(x0)) 544.00/242.17 g_flat(up(x0)) 544.00/242.17 544.00/242.17 We have to consider all minimal (P,Q,R)-chains. 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1109) TransformationProof (EQUIVALENT) 544.00/242.17 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(g(fresh_constant))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.17 544.00/242.17 (TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant)))))))))))) 544.00/242.17 544.00/242.17 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1110) 544.00/242.17 Obligation: 544.00/242.17 Q DP problem: 544.00/242.17 The TRS P consists of the following rules: 544.00/242.17 544.00/242.17 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.17 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.17 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.17 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.17 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.17 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.17 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.17 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.17 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.17 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.17 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.17 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.17 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.17 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.17 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.17 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.17 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.17 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.17 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.17 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.17 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.17 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.17 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(fresh_constant))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(fresh_constant))))))))))) 544.00/242.17 544.00/242.17 The TRS R consists of the following rules: 544.00/242.17 544.00/242.17 down(a) -> up(f(a)) 544.00/242.17 down(b) -> up(g(b)) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.17 down(f(a)) -> f_flat(down(a)) 544.00/242.17 down(f(b)) -> f_flat(down(b)) 544.00/242.17 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.17 down(f(c)) -> f_flat(down(c)) 544.00/242.17 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.17 down(g(a)) -> g_flat(down(a)) 544.00/242.17 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.17 down(g(b)) -> g_flat(down(b)) 544.00/242.17 down(g(c)) -> g_flat(down(c)) 544.00/242.17 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.17 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.17 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.17 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.17 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.17 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.17 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.17 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.17 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.17 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.17 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.17 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.17 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.17 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.17 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.17 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.17 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.17 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.17 544.00/242.17 The set Q consists of the following terms: 544.00/242.17 544.00/242.17 down(a) 544.00/242.17 down(b) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.17 down(f(a)) 544.00/242.17 down(f(b)) 544.00/242.17 down(f(g(x0))) 544.00/242.17 down(f(c)) 544.00/242.17 down(f(fresh_constant)) 544.00/242.17 down(g(a)) 544.00/242.17 down(g(f(x0))) 544.00/242.17 down(g(b)) 544.00/242.17 down(g(c)) 544.00/242.17 down(g(fresh_constant)) 544.00/242.17 down(f(f(a))) 544.00/242.17 down(f(f(b))) 544.00/242.17 down(f(f(g(x0)))) 544.00/242.17 down(f(f(c))) 544.00/242.17 down(f(f(fresh_constant))) 544.00/242.17 down(g(g(a))) 544.00/242.17 down(g(g(f(x0)))) 544.00/242.17 down(g(g(b))) 544.00/242.17 down(g(g(c))) 544.00/242.17 down(g(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) 544.00/242.17 down(f(f(f(g(x0))))) 544.00/242.17 down(f(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) 544.00/242.17 down(g(g(g(f(x0))))) 544.00/242.17 down(g(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(x0)))))) 544.00/242.17 down(f(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(x0)))))) 544.00/242.17 down(g(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(x0))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(x0))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 f_flat(up(x0)) 544.00/242.17 g_flat(up(x0)) 544.00/242.17 544.00/242.17 We have to consider all minimal (P,Q,R)-chains. 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1111) DependencyGraphProof (EQUIVALENT) 544.00/242.17 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1112) 544.00/242.17 Obligation: 544.00/242.17 Q DP problem: 544.00/242.17 The TRS P consists of the following rules: 544.00/242.17 544.00/242.17 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.17 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.17 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.17 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.17 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.17 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.17 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.17 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) 544.00/242.17 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.17 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.17 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.17 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.17 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.17 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.17 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.17 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.17 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.17 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.17 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.17 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.17 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.17 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.17 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.17 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.17 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.17 544.00/242.17 The TRS R consists of the following rules: 544.00/242.17 544.00/242.17 down(a) -> up(f(a)) 544.00/242.17 down(b) -> up(g(b)) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.17 down(f(a)) -> f_flat(down(a)) 544.00/242.17 down(f(b)) -> f_flat(down(b)) 544.00/242.17 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.17 down(f(c)) -> f_flat(down(c)) 544.00/242.17 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.17 down(g(a)) -> g_flat(down(a)) 544.00/242.17 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.17 down(g(b)) -> g_flat(down(b)) 544.00/242.17 down(g(c)) -> g_flat(down(c)) 544.00/242.17 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.17 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.17 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.17 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.17 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.17 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.17 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.17 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.17 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.17 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.17 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.17 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.17 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.17 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.17 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.17 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.17 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.17 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.17 544.00/242.17 The set Q consists of the following terms: 544.00/242.17 544.00/242.17 down(a) 544.00/242.17 down(b) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.17 down(f(a)) 544.00/242.17 down(f(b)) 544.00/242.17 down(f(g(x0))) 544.00/242.17 down(f(c)) 544.00/242.17 down(f(fresh_constant)) 544.00/242.17 down(g(a)) 544.00/242.17 down(g(f(x0))) 544.00/242.17 down(g(b)) 544.00/242.17 down(g(c)) 544.00/242.17 down(g(fresh_constant)) 544.00/242.17 down(f(f(a))) 544.00/242.17 down(f(f(b))) 544.00/242.17 down(f(f(g(x0)))) 544.00/242.17 down(f(f(c))) 544.00/242.17 down(f(f(fresh_constant))) 544.00/242.17 down(g(g(a))) 544.00/242.17 down(g(g(f(x0)))) 544.00/242.17 down(g(g(b))) 544.00/242.17 down(g(g(c))) 544.00/242.17 down(g(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) 544.00/242.17 down(f(f(f(g(x0))))) 544.00/242.17 down(f(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) 544.00/242.17 down(g(g(g(f(x0))))) 544.00/242.17 down(g(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(x0)))))) 544.00/242.17 down(f(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(x0)))))) 544.00/242.17 down(g(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(x0))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(x0))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 f_flat(up(x0)) 544.00/242.17 g_flat(up(x0)) 544.00/242.17 544.00/242.17 We have to consider all minimal (P,Q,R)-chains. 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1113) TransformationProof (EQUIVALENT) 544.00/242.17 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.17 544.00/242.17 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.17 544.00/242.17 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1114) 544.00/242.17 Obligation: 544.00/242.17 Q DP problem: 544.00/242.17 The TRS P consists of the following rules: 544.00/242.17 544.00/242.17 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.17 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.17 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.17 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.17 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.17 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.17 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.17 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.17 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.17 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.17 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.17 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.17 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) 544.00/242.17 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.17 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.17 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.17 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.17 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.17 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.17 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.17 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.17 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.17 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.17 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.17 544.00/242.17 The TRS R consists of the following rules: 544.00/242.17 544.00/242.17 down(a) -> up(f(a)) 544.00/242.17 down(b) -> up(g(b)) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.17 down(f(a)) -> f_flat(down(a)) 544.00/242.17 down(f(b)) -> f_flat(down(b)) 544.00/242.17 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.17 down(f(c)) -> f_flat(down(c)) 544.00/242.17 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.17 down(g(a)) -> g_flat(down(a)) 544.00/242.17 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.17 down(g(b)) -> g_flat(down(b)) 544.00/242.17 down(g(c)) -> g_flat(down(c)) 544.00/242.17 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.17 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.17 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.17 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.17 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.17 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.17 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.17 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.17 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.17 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.17 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.17 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.17 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.17 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.17 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.17 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.17 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.17 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.17 544.00/242.17 The set Q consists of the following terms: 544.00/242.17 544.00/242.17 down(a) 544.00/242.17 down(b) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.17 down(f(a)) 544.00/242.17 down(f(b)) 544.00/242.17 down(f(g(x0))) 544.00/242.17 down(f(c)) 544.00/242.17 down(f(fresh_constant)) 544.00/242.17 down(g(a)) 544.00/242.17 down(g(f(x0))) 544.00/242.17 down(g(b)) 544.00/242.17 down(g(c)) 544.00/242.17 down(g(fresh_constant)) 544.00/242.17 down(f(f(a))) 544.00/242.17 down(f(f(b))) 544.00/242.17 down(f(f(g(x0)))) 544.00/242.17 down(f(f(c))) 544.00/242.17 down(f(f(fresh_constant))) 544.00/242.17 down(g(g(a))) 544.00/242.17 down(g(g(f(x0)))) 544.00/242.17 down(g(g(b))) 544.00/242.17 down(g(g(c))) 544.00/242.17 down(g(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) 544.00/242.17 down(f(f(f(g(x0))))) 544.00/242.17 down(f(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) 544.00/242.17 down(g(g(g(f(x0))))) 544.00/242.17 down(g(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(x0)))))) 544.00/242.17 down(f(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(x0)))))) 544.00/242.17 down(g(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(x0))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(x0))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 f_flat(up(x0)) 544.00/242.17 g_flat(up(x0)) 544.00/242.17 544.00/242.17 We have to consider all minimal (P,Q,R)-chains. 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1115) TransformationProof (EQUIVALENT) 544.00/242.17 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.17 544.00/242.17 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.00/242.17 544.00/242.17 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1116) 544.00/242.17 Obligation: 544.00/242.17 Q DP problem: 544.00/242.17 The TRS P consists of the following rules: 544.00/242.17 544.00/242.17 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.17 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.17 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.17 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.17 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.17 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.17 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.17 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.17 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.17 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.17 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.17 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.17 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.17 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.17 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.17 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.17 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.17 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.17 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.17 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.17 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.17 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.17 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.17 544.00/242.17 The TRS R consists of the following rules: 544.00/242.17 544.00/242.17 down(a) -> up(f(a)) 544.00/242.17 down(b) -> up(g(b)) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.17 down(f(a)) -> f_flat(down(a)) 544.00/242.17 down(f(b)) -> f_flat(down(b)) 544.00/242.17 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.17 down(f(c)) -> f_flat(down(c)) 544.00/242.17 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.17 down(g(a)) -> g_flat(down(a)) 544.00/242.17 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.17 down(g(b)) -> g_flat(down(b)) 544.00/242.17 down(g(c)) -> g_flat(down(c)) 544.00/242.17 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.17 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.17 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.17 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.17 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.17 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.17 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.17 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.17 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.17 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.17 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.17 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.17 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.17 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.17 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.17 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.17 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.17 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.17 544.00/242.17 The set Q consists of the following terms: 544.00/242.17 544.00/242.17 down(a) 544.00/242.17 down(b) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.17 down(f(a)) 544.00/242.17 down(f(b)) 544.00/242.17 down(f(g(x0))) 544.00/242.17 down(f(c)) 544.00/242.17 down(f(fresh_constant)) 544.00/242.17 down(g(a)) 544.00/242.17 down(g(f(x0))) 544.00/242.17 down(g(b)) 544.00/242.17 down(g(c)) 544.00/242.17 down(g(fresh_constant)) 544.00/242.17 down(f(f(a))) 544.00/242.17 down(f(f(b))) 544.00/242.17 down(f(f(g(x0)))) 544.00/242.17 down(f(f(c))) 544.00/242.17 down(f(f(fresh_constant))) 544.00/242.17 down(g(g(a))) 544.00/242.17 down(g(g(f(x0)))) 544.00/242.17 down(g(g(b))) 544.00/242.17 down(g(g(c))) 544.00/242.17 down(g(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) 544.00/242.17 down(f(f(f(g(x0))))) 544.00/242.17 down(f(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) 544.00/242.17 down(g(g(g(f(x0))))) 544.00/242.17 down(g(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(x0)))))) 544.00/242.17 down(f(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(x0)))))) 544.00/242.17 down(g(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(x0))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(x0))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 f_flat(up(x0)) 544.00/242.17 g_flat(up(x0)) 544.00/242.17 544.00/242.17 We have to consider all minimal (P,Q,R)-chains. 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1117) TransformationProof (EQUIVALENT) 544.00/242.17 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(g_flat(up(g(g(g(f(a)))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.00/242.17 544.00/242.17 (TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.17 544.00/242.17 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1118) 544.00/242.17 Obligation: 544.00/242.17 Q DP problem: 544.00/242.17 The TRS P consists of the following rules: 544.00/242.17 544.00/242.17 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.17 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.17 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.17 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.17 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.17 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.17 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.17 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.17 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.17 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.17 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.17 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.17 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.17 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.17 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.17 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.17 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.17 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.17 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.17 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.17 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.17 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.17 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.17 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.17 544.00/242.17 The TRS R consists of the following rules: 544.00/242.17 544.00/242.17 down(a) -> up(f(a)) 544.00/242.17 down(b) -> up(g(b)) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.17 down(f(a)) -> f_flat(down(a)) 544.00/242.17 down(f(b)) -> f_flat(down(b)) 544.00/242.17 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.17 down(f(c)) -> f_flat(down(c)) 544.00/242.17 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.17 down(g(a)) -> g_flat(down(a)) 544.00/242.17 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.17 down(g(b)) -> g_flat(down(b)) 544.00/242.17 down(g(c)) -> g_flat(down(c)) 544.00/242.17 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.17 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.17 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.17 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.17 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.17 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.17 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.17 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.17 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.17 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.17 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.17 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.17 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.17 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.17 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.17 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.17 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.17 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.17 544.00/242.17 The set Q consists of the following terms: 544.00/242.17 544.00/242.17 down(a) 544.00/242.17 down(b) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.17 down(f(a)) 544.00/242.17 down(f(b)) 544.00/242.17 down(f(g(x0))) 544.00/242.17 down(f(c)) 544.00/242.17 down(f(fresh_constant)) 544.00/242.17 down(g(a)) 544.00/242.17 down(g(f(x0))) 544.00/242.17 down(g(b)) 544.00/242.17 down(g(c)) 544.00/242.17 down(g(fresh_constant)) 544.00/242.17 down(f(f(a))) 544.00/242.17 down(f(f(b))) 544.00/242.17 down(f(f(g(x0)))) 544.00/242.17 down(f(f(c))) 544.00/242.17 down(f(f(fresh_constant))) 544.00/242.17 down(g(g(a))) 544.00/242.17 down(g(g(f(x0)))) 544.00/242.17 down(g(g(b))) 544.00/242.17 down(g(g(c))) 544.00/242.17 down(g(g(fresh_constant))) 544.00/242.17 down(f(f(f(a)))) 544.00/242.17 down(f(f(f(b)))) 544.00/242.17 down(f(f(f(g(x0))))) 544.00/242.17 down(f(f(f(c)))) 544.00/242.17 down(f(f(f(fresh_constant)))) 544.00/242.17 down(g(g(g(a)))) 544.00/242.17 down(g(g(g(f(x0))))) 544.00/242.17 down(g(g(g(b)))) 544.00/242.17 down(g(g(g(c)))) 544.00/242.17 down(g(g(g(fresh_constant)))) 544.00/242.17 down(f(f(f(f(a))))) 544.00/242.17 down(f(f(f(f(b))))) 544.00/242.17 down(f(f(f(f(g(x0)))))) 544.00/242.17 down(f(f(f(f(c))))) 544.00/242.17 down(f(f(f(f(fresh_constant))))) 544.00/242.17 down(g(g(g(g(a))))) 544.00/242.17 down(g(g(g(g(f(x0)))))) 544.00/242.17 down(g(g(g(g(b))))) 544.00/242.17 down(g(g(g(g(c))))) 544.00/242.17 down(g(g(g(g(fresh_constant))))) 544.00/242.17 down(f(f(f(f(f(a)))))) 544.00/242.17 down(f(f(f(f(f(b)))))) 544.00/242.17 down(f(f(f(f(f(g(x0))))))) 544.00/242.17 down(f(f(f(f(f(c)))))) 544.00/242.17 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.17 down(g(g(g(g(g(a)))))) 544.00/242.17 down(g(g(g(g(g(f(x0))))))) 544.00/242.17 down(g(g(g(g(g(b)))))) 544.00/242.17 down(g(g(g(g(g(c)))))) 544.00/242.17 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.17 down(f(f(f(f(f(f(a))))))) 544.00/242.17 down(f(f(f(f(f(f(b))))))) 544.00/242.17 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.17 down(f(f(f(f(f(f(c))))))) 544.00/242.17 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.17 down(g(g(g(g(g(g(a))))))) 544.00/242.17 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.17 down(g(g(g(g(g(g(b))))))) 544.00/242.17 down(g(g(g(g(g(g(c))))))) 544.00/242.17 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.17 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.17 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.17 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.17 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.17 f_flat(up(x0)) 544.00/242.17 g_flat(up(x0)) 544.00/242.17 544.00/242.17 We have to consider all minimal (P,Q,R)-chains. 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1119) TransformationProof (EQUIVALENT) 544.00/242.17 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.17 544.00/242.17 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.17 544.00/242.17 544.00/242.17 ---------------------------------------- 544.00/242.17 544.00/242.17 (1120) 544.00/242.17 Obligation: 544.00/242.17 Q DP problem: 544.00/242.17 The TRS P consists of the following rules: 544.00/242.17 544.00/242.17 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.17 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.17 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.17 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.17 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.17 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.17 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.17 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.17 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.17 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.17 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.17 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.17 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.17 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.17 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.17 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.17 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.18 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.18 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.18 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.18 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.18 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.18 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.18 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.18 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.18 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.18 544.00/242.18 The TRS R consists of the following rules: 544.00/242.18 544.00/242.18 down(a) -> up(f(a)) 544.00/242.18 down(b) -> up(g(b)) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.18 down(f(a)) -> f_flat(down(a)) 544.00/242.18 down(f(b)) -> f_flat(down(b)) 544.00/242.18 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.18 down(f(c)) -> f_flat(down(c)) 544.00/242.18 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.18 down(g(a)) -> g_flat(down(a)) 544.00/242.18 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.18 down(g(b)) -> g_flat(down(b)) 544.00/242.18 down(g(c)) -> g_flat(down(c)) 544.00/242.18 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.18 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.18 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.18 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.18 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.18 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.18 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.18 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.18 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.18 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.18 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.18 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.18 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.18 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.18 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.18 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.18 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.18 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.18 544.00/242.18 The set Q consists of the following terms: 544.00/242.18 544.00/242.18 down(a) 544.00/242.18 down(b) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.18 down(f(a)) 544.00/242.18 down(f(b)) 544.00/242.18 down(f(g(x0))) 544.00/242.18 down(f(c)) 544.00/242.18 down(f(fresh_constant)) 544.00/242.18 down(g(a)) 544.00/242.18 down(g(f(x0))) 544.00/242.18 down(g(b)) 544.00/242.18 down(g(c)) 544.00/242.18 down(g(fresh_constant)) 544.00/242.18 down(f(f(a))) 544.00/242.18 down(f(f(b))) 544.00/242.18 down(f(f(g(x0)))) 544.00/242.18 down(f(f(c))) 544.00/242.18 down(f(f(fresh_constant))) 544.00/242.18 down(g(g(a))) 544.00/242.18 down(g(g(f(x0)))) 544.00/242.18 down(g(g(b))) 544.00/242.18 down(g(g(c))) 544.00/242.18 down(g(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) 544.00/242.18 down(f(f(f(g(x0))))) 544.00/242.18 down(f(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) 544.00/242.18 down(g(g(g(f(x0))))) 544.00/242.18 down(g(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(x0)))))) 544.00/242.18 down(f(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(x0)))))) 544.00/242.18 down(g(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(x0))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(x0))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 f_flat(up(x0)) 544.00/242.18 g_flat(up(x0)) 544.00/242.18 544.00/242.18 We have to consider all minimal (P,Q,R)-chains. 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1121) TransformationProof (EQUIVALENT) 544.00/242.18 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.18 544.00/242.18 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.18 544.00/242.18 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1122) 544.00/242.18 Obligation: 544.00/242.18 Q DP problem: 544.00/242.18 The TRS P consists of the following rules: 544.00/242.18 544.00/242.18 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.18 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.18 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.18 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.18 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.18 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.18 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.18 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.18 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.18 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.18 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.18 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.18 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.18 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.18 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.18 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.18 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.18 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.18 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.18 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.18 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.18 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.18 544.00/242.18 The TRS R consists of the following rules: 544.00/242.18 544.00/242.18 down(a) -> up(f(a)) 544.00/242.18 down(b) -> up(g(b)) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.18 down(f(a)) -> f_flat(down(a)) 544.00/242.18 down(f(b)) -> f_flat(down(b)) 544.00/242.18 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.18 down(f(c)) -> f_flat(down(c)) 544.00/242.18 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.18 down(g(a)) -> g_flat(down(a)) 544.00/242.18 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.18 down(g(b)) -> g_flat(down(b)) 544.00/242.18 down(g(c)) -> g_flat(down(c)) 544.00/242.18 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.18 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.18 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.18 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.18 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.18 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.18 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.18 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.18 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.18 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.18 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.18 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.18 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.18 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.18 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.18 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.18 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.18 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.18 544.00/242.18 The set Q consists of the following terms: 544.00/242.18 544.00/242.18 down(a) 544.00/242.18 down(b) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.18 down(f(a)) 544.00/242.18 down(f(b)) 544.00/242.18 down(f(g(x0))) 544.00/242.18 down(f(c)) 544.00/242.18 down(f(fresh_constant)) 544.00/242.18 down(g(a)) 544.00/242.18 down(g(f(x0))) 544.00/242.18 down(g(b)) 544.00/242.18 down(g(c)) 544.00/242.18 down(g(fresh_constant)) 544.00/242.18 down(f(f(a))) 544.00/242.18 down(f(f(b))) 544.00/242.18 down(f(f(g(x0)))) 544.00/242.18 down(f(f(c))) 544.00/242.18 down(f(f(fresh_constant))) 544.00/242.18 down(g(g(a))) 544.00/242.18 down(g(g(f(x0)))) 544.00/242.18 down(g(g(b))) 544.00/242.18 down(g(g(c))) 544.00/242.18 down(g(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) 544.00/242.18 down(f(f(f(g(x0))))) 544.00/242.18 down(f(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) 544.00/242.18 down(g(g(g(f(x0))))) 544.00/242.18 down(g(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(x0)))))) 544.00/242.18 down(f(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(x0)))))) 544.00/242.18 down(g(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(x0))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(x0))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 f_flat(up(x0)) 544.00/242.18 g_flat(up(x0)) 544.00/242.18 544.00/242.18 We have to consider all minimal (P,Q,R)-chains. 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1123) TransformationProof (EQUIVALENT) 544.00/242.18 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.18 544.00/242.18 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.18 544.00/242.18 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1124) 544.00/242.18 Obligation: 544.00/242.18 Q DP problem: 544.00/242.18 The TRS P consists of the following rules: 544.00/242.18 544.00/242.18 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.18 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.18 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.18 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.18 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.18 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.18 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.18 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.18 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.18 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.18 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.18 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.18 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.18 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.18 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.18 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.18 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.18 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.18 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.18 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.18 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.18 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.18 544.00/242.18 The TRS R consists of the following rules: 544.00/242.18 544.00/242.18 down(a) -> up(f(a)) 544.00/242.18 down(b) -> up(g(b)) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.18 down(f(a)) -> f_flat(down(a)) 544.00/242.18 down(f(b)) -> f_flat(down(b)) 544.00/242.18 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.18 down(f(c)) -> f_flat(down(c)) 544.00/242.18 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.18 down(g(a)) -> g_flat(down(a)) 544.00/242.18 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.18 down(g(b)) -> g_flat(down(b)) 544.00/242.18 down(g(c)) -> g_flat(down(c)) 544.00/242.18 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.18 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.18 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.18 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.18 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.18 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.18 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.18 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.18 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.18 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.18 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.18 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.18 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.18 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.18 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.18 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.18 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.18 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.18 544.00/242.18 The set Q consists of the following terms: 544.00/242.18 544.00/242.18 down(a) 544.00/242.18 down(b) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.18 down(f(a)) 544.00/242.18 down(f(b)) 544.00/242.18 down(f(g(x0))) 544.00/242.18 down(f(c)) 544.00/242.18 down(f(fresh_constant)) 544.00/242.18 down(g(a)) 544.00/242.18 down(g(f(x0))) 544.00/242.18 down(g(b)) 544.00/242.18 down(g(c)) 544.00/242.18 down(g(fresh_constant)) 544.00/242.18 down(f(f(a))) 544.00/242.18 down(f(f(b))) 544.00/242.18 down(f(f(g(x0)))) 544.00/242.18 down(f(f(c))) 544.00/242.18 down(f(f(fresh_constant))) 544.00/242.18 down(g(g(a))) 544.00/242.18 down(g(g(f(x0)))) 544.00/242.18 down(g(g(b))) 544.00/242.18 down(g(g(c))) 544.00/242.18 down(g(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) 544.00/242.18 down(f(f(f(g(x0))))) 544.00/242.18 down(f(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) 544.00/242.18 down(g(g(g(f(x0))))) 544.00/242.18 down(g(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(x0)))))) 544.00/242.18 down(f(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(x0)))))) 544.00/242.18 down(g(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(x0))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(x0))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 f_flat(up(x0)) 544.00/242.18 g_flat(up(x0)) 544.00/242.18 544.00/242.18 We have to consider all minimal (P,Q,R)-chains. 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1125) TransformationProof (EQUIVALENT) 544.00/242.18 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(a))))))))))) at position [0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.18 544.00/242.18 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a))))))))))))) 544.00/242.18 544.00/242.18 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1126) 544.00/242.18 Obligation: 544.00/242.18 Q DP problem: 544.00/242.18 The TRS P consists of the following rules: 544.00/242.18 544.00/242.18 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.18 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.18 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.18 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.18 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.18 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.18 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.18 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.18 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.18 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.18 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.18 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.18 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.18 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.18 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.18 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.18 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.18 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.18 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.18 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.18 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.18 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.18 544.00/242.18 The TRS R consists of the following rules: 544.00/242.18 544.00/242.18 down(a) -> up(f(a)) 544.00/242.18 down(b) -> up(g(b)) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.18 down(f(a)) -> f_flat(down(a)) 544.00/242.18 down(f(b)) -> f_flat(down(b)) 544.00/242.18 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.18 down(f(c)) -> f_flat(down(c)) 544.00/242.18 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.18 down(g(a)) -> g_flat(down(a)) 544.00/242.18 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.18 down(g(b)) -> g_flat(down(b)) 544.00/242.18 down(g(c)) -> g_flat(down(c)) 544.00/242.18 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.18 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.18 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.18 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.18 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.18 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.18 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.18 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.18 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.18 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.18 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.18 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.18 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.18 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.18 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.18 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.18 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.18 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.18 544.00/242.18 The set Q consists of the following terms: 544.00/242.18 544.00/242.18 down(a) 544.00/242.18 down(b) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.18 down(f(a)) 544.00/242.18 down(f(b)) 544.00/242.18 down(f(g(x0))) 544.00/242.18 down(f(c)) 544.00/242.18 down(f(fresh_constant)) 544.00/242.18 down(g(a)) 544.00/242.18 down(g(f(x0))) 544.00/242.18 down(g(b)) 544.00/242.18 down(g(c)) 544.00/242.18 down(g(fresh_constant)) 544.00/242.18 down(f(f(a))) 544.00/242.18 down(f(f(b))) 544.00/242.18 down(f(f(g(x0)))) 544.00/242.18 down(f(f(c))) 544.00/242.18 down(f(f(fresh_constant))) 544.00/242.18 down(g(g(a))) 544.00/242.18 down(g(g(f(x0)))) 544.00/242.18 down(g(g(b))) 544.00/242.18 down(g(g(c))) 544.00/242.18 down(g(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) 544.00/242.18 down(f(f(f(g(x0))))) 544.00/242.18 down(f(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) 544.00/242.18 down(g(g(g(f(x0))))) 544.00/242.18 down(g(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(x0)))))) 544.00/242.18 down(f(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(x0)))))) 544.00/242.18 down(g(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(x0))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(x0))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 f_flat(up(x0)) 544.00/242.18 g_flat(up(x0)) 544.00/242.18 544.00/242.18 We have to consider all minimal (P,Q,R)-chains. 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1127) TransformationProof (EQUIVALENT) 544.00/242.18 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(b))))))) -> TOP(f_flat(up(f(f(f(f(g(b)))))))) at position [0] we obtained the following new rules [LPAR04]: 544.00/242.18 544.00/242.18 (TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))),TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b))))))))) 544.00/242.18 544.00/242.18 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1128) 544.00/242.18 Obligation: 544.00/242.18 Q DP problem: 544.00/242.18 The TRS P consists of the following rules: 544.00/242.18 544.00/242.18 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.18 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.18 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.18 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.18 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.18 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.18 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.18 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.18 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.18 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.18 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.18 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.18 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.18 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.18 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.18 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.18 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.18 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.18 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.18 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.18 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.18 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.18 544.00/242.18 The TRS R consists of the following rules: 544.00/242.18 544.00/242.18 down(a) -> up(f(a)) 544.00/242.18 down(b) -> up(g(b)) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.18 down(f(a)) -> f_flat(down(a)) 544.00/242.18 down(f(b)) -> f_flat(down(b)) 544.00/242.18 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.18 down(f(c)) -> f_flat(down(c)) 544.00/242.18 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.18 down(g(a)) -> g_flat(down(a)) 544.00/242.18 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.18 down(g(b)) -> g_flat(down(b)) 544.00/242.18 down(g(c)) -> g_flat(down(c)) 544.00/242.18 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.18 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.18 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.18 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.18 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.18 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.18 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.18 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.18 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.18 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.18 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.18 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.18 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.18 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.18 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.18 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.18 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.18 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.18 544.00/242.18 The set Q consists of the following terms: 544.00/242.18 544.00/242.18 down(a) 544.00/242.18 down(b) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.18 down(f(a)) 544.00/242.18 down(f(b)) 544.00/242.18 down(f(g(x0))) 544.00/242.18 down(f(c)) 544.00/242.18 down(f(fresh_constant)) 544.00/242.18 down(g(a)) 544.00/242.18 down(g(f(x0))) 544.00/242.18 down(g(b)) 544.00/242.18 down(g(c)) 544.00/242.18 down(g(fresh_constant)) 544.00/242.18 down(f(f(a))) 544.00/242.18 down(f(f(b))) 544.00/242.18 down(f(f(g(x0)))) 544.00/242.18 down(f(f(c))) 544.00/242.18 down(f(f(fresh_constant))) 544.00/242.18 down(g(g(a))) 544.00/242.18 down(g(g(f(x0)))) 544.00/242.18 down(g(g(b))) 544.00/242.18 down(g(g(c))) 544.00/242.18 down(g(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) 544.00/242.18 down(f(f(f(g(x0))))) 544.00/242.18 down(f(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) 544.00/242.18 down(g(g(g(f(x0))))) 544.00/242.18 down(g(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(x0)))))) 544.00/242.18 down(f(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(x0)))))) 544.00/242.18 down(g(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(x0))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(x0))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 f_flat(up(x0)) 544.00/242.18 g_flat(up(x0)) 544.00/242.18 544.00/242.18 We have to consider all minimal (P,Q,R)-chains. 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1129) TransformationProof (EQUIVALENT) 544.00/242.18 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.18 544.00/242.18 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.18 544.00/242.18 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1130) 544.00/242.18 Obligation: 544.00/242.18 Q DP problem: 544.00/242.18 The TRS P consists of the following rules: 544.00/242.18 544.00/242.18 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.18 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.18 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.18 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.18 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.18 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.18 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.18 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.18 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.18 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.18 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.18 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.18 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.18 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.18 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.18 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.18 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.18 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.18 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.18 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.18 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.18 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.18 544.00/242.18 The TRS R consists of the following rules: 544.00/242.18 544.00/242.18 down(a) -> up(f(a)) 544.00/242.18 down(b) -> up(g(b)) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.18 down(f(a)) -> f_flat(down(a)) 544.00/242.18 down(f(b)) -> f_flat(down(b)) 544.00/242.18 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.18 down(f(c)) -> f_flat(down(c)) 544.00/242.18 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.18 down(g(a)) -> g_flat(down(a)) 544.00/242.18 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.18 down(g(b)) -> g_flat(down(b)) 544.00/242.18 down(g(c)) -> g_flat(down(c)) 544.00/242.18 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.18 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.18 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.18 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.18 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.18 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.18 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.18 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.18 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.18 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.18 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.18 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.18 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.18 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.18 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.18 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.18 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.18 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.18 544.00/242.18 The set Q consists of the following terms: 544.00/242.18 544.00/242.18 down(a) 544.00/242.18 down(b) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.18 down(f(a)) 544.00/242.18 down(f(b)) 544.00/242.18 down(f(g(x0))) 544.00/242.18 down(f(c)) 544.00/242.18 down(f(fresh_constant)) 544.00/242.18 down(g(a)) 544.00/242.18 down(g(f(x0))) 544.00/242.18 down(g(b)) 544.00/242.18 down(g(c)) 544.00/242.18 down(g(fresh_constant)) 544.00/242.18 down(f(f(a))) 544.00/242.18 down(f(f(b))) 544.00/242.18 down(f(f(g(x0)))) 544.00/242.18 down(f(f(c))) 544.00/242.18 down(f(f(fresh_constant))) 544.00/242.18 down(g(g(a))) 544.00/242.18 down(g(g(f(x0)))) 544.00/242.18 down(g(g(b))) 544.00/242.18 down(g(g(c))) 544.00/242.18 down(g(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) 544.00/242.18 down(f(f(f(g(x0))))) 544.00/242.18 down(f(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) 544.00/242.18 down(g(g(g(f(x0))))) 544.00/242.18 down(g(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(x0)))))) 544.00/242.18 down(f(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(x0)))))) 544.00/242.18 down(g(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(x0))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(x0))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 f_flat(up(x0)) 544.00/242.18 g_flat(up(x0)) 544.00/242.18 544.00/242.18 We have to consider all minimal (P,Q,R)-chains. 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1131) TransformationProof (EQUIVALENT) 544.00/242.18 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.18 544.00/242.18 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.18 544.00/242.18 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1132) 544.00/242.18 Obligation: 544.00/242.18 Q DP problem: 544.00/242.18 The TRS P consists of the following rules: 544.00/242.18 544.00/242.18 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.18 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.18 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.18 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.18 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.18 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.18 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.18 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.18 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.18 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.18 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.18 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.18 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.18 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.18 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.18 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.18 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.18 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.18 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.18 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.18 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.18 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.18 544.00/242.18 The TRS R consists of the following rules: 544.00/242.18 544.00/242.18 down(a) -> up(f(a)) 544.00/242.18 down(b) -> up(g(b)) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.18 down(f(a)) -> f_flat(down(a)) 544.00/242.18 down(f(b)) -> f_flat(down(b)) 544.00/242.18 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.18 down(f(c)) -> f_flat(down(c)) 544.00/242.18 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.18 down(g(a)) -> g_flat(down(a)) 544.00/242.18 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.18 down(g(b)) -> g_flat(down(b)) 544.00/242.18 down(g(c)) -> g_flat(down(c)) 544.00/242.18 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.18 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.18 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.18 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.18 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.18 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.18 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.18 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.18 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.18 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.18 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.18 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.18 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.18 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.18 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.18 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.18 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.18 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.18 544.00/242.18 The set Q consists of the following terms: 544.00/242.18 544.00/242.18 down(a) 544.00/242.18 down(b) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.18 down(f(a)) 544.00/242.18 down(f(b)) 544.00/242.18 down(f(g(x0))) 544.00/242.18 down(f(c)) 544.00/242.18 down(f(fresh_constant)) 544.00/242.18 down(g(a)) 544.00/242.18 down(g(f(x0))) 544.00/242.18 down(g(b)) 544.00/242.18 down(g(c)) 544.00/242.18 down(g(fresh_constant)) 544.00/242.18 down(f(f(a))) 544.00/242.18 down(f(f(b))) 544.00/242.18 down(f(f(g(x0)))) 544.00/242.18 down(f(f(c))) 544.00/242.18 down(f(f(fresh_constant))) 544.00/242.18 down(g(g(a))) 544.00/242.18 down(g(g(f(x0)))) 544.00/242.18 down(g(g(b))) 544.00/242.18 down(g(g(c))) 544.00/242.18 down(g(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) 544.00/242.18 down(f(f(f(g(x0))))) 544.00/242.18 down(f(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) 544.00/242.18 down(g(g(g(f(x0))))) 544.00/242.18 down(g(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(x0)))))) 544.00/242.18 down(f(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(x0)))))) 544.00/242.18 down(g(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(x0))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(x0))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 f_flat(up(x0)) 544.00/242.18 g_flat(up(x0)) 544.00/242.18 544.00/242.18 We have to consider all minimal (P,Q,R)-chains. 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1133) TransformationProof (EQUIVALENT) 544.00/242.18 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.18 544.00/242.18 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.18 544.00/242.18 544.00/242.18 ---------------------------------------- 544.00/242.18 544.00/242.18 (1134) 544.00/242.18 Obligation: 544.00/242.18 Q DP problem: 544.00/242.18 The TRS P consists of the following rules: 544.00/242.18 544.00/242.18 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.18 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.18 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.18 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.18 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.18 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.18 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.18 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.18 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.18 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.18 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.18 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.18 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.18 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.18 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.18 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.18 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.18 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.18 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.18 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.18 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.18 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.18 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.18 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.18 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.18 544.00/242.18 The TRS R consists of the following rules: 544.00/242.18 544.00/242.18 down(a) -> up(f(a)) 544.00/242.18 down(b) -> up(g(b)) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.18 down(f(a)) -> f_flat(down(a)) 544.00/242.18 down(f(b)) -> f_flat(down(b)) 544.00/242.18 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.18 down(f(c)) -> f_flat(down(c)) 544.00/242.18 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.18 down(g(a)) -> g_flat(down(a)) 544.00/242.18 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.18 down(g(b)) -> g_flat(down(b)) 544.00/242.18 down(g(c)) -> g_flat(down(c)) 544.00/242.18 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.18 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.18 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.18 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.18 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.18 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.18 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.18 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.18 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.18 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.18 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.18 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.18 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.18 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.18 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.18 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.18 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.18 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.18 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.18 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.18 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.18 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.18 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.18 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.18 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.18 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.18 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.18 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.18 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.18 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.18 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.18 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.18 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.18 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.18 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.18 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.18 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.18 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.18 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.18 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.18 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.18 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.18 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.18 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.18 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.18 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.18 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.18 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.18 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.18 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.18 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.18 544.00/242.18 The set Q consists of the following terms: 544.00/242.18 544.00/242.18 down(a) 544.00/242.18 down(b) 544.00/242.18 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.18 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.18 down(f(a)) 544.00/242.18 down(f(b)) 544.00/242.18 down(f(g(x0))) 544.00/242.18 down(f(c)) 544.00/242.18 down(f(fresh_constant)) 544.00/242.18 down(g(a)) 544.00/242.18 down(g(f(x0))) 544.00/242.18 down(g(b)) 544.00/242.18 down(g(c)) 544.00/242.18 down(g(fresh_constant)) 544.00/242.18 down(f(f(a))) 544.00/242.18 down(f(f(b))) 544.00/242.18 down(f(f(g(x0)))) 544.00/242.18 down(f(f(c))) 544.00/242.18 down(f(f(fresh_constant))) 544.00/242.18 down(g(g(a))) 544.00/242.18 down(g(g(f(x0)))) 544.00/242.18 down(g(g(b))) 544.00/242.18 down(g(g(c))) 544.00/242.18 down(g(g(fresh_constant))) 544.00/242.18 down(f(f(f(a)))) 544.00/242.18 down(f(f(f(b)))) 544.00/242.18 down(f(f(f(g(x0))))) 544.00/242.18 down(f(f(f(c)))) 544.00/242.18 down(f(f(f(fresh_constant)))) 544.00/242.18 down(g(g(g(a)))) 544.00/242.18 down(g(g(g(f(x0))))) 544.00/242.19 down(g(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(x0)))))) 544.00/242.19 down(f(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(x0)))))) 544.00/242.19 down(g(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(x0))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(x0))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 f_flat(up(x0)) 544.00/242.19 g_flat(up(x0)) 544.00/242.19 544.00/242.19 We have to consider all minimal (P,Q,R)-chains. 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1135) TransformationProof (EQUIVALENT) 544.00/242.19 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(a)))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.19 544.00/242.19 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a))))))))))))) 544.00/242.19 544.00/242.19 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1136) 544.00/242.19 Obligation: 544.00/242.19 Q DP problem: 544.00/242.19 The TRS P consists of the following rules: 544.00/242.19 544.00/242.19 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.19 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.19 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.19 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.19 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.19 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.19 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.19 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.19 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.19 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.19 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.19 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.19 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.19 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.19 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.19 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.19 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.19 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.19 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.19 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.19 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.19 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.19 544.00/242.19 The TRS R consists of the following rules: 544.00/242.19 544.00/242.19 down(a) -> up(f(a)) 544.00/242.19 down(b) -> up(g(b)) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.19 down(f(a)) -> f_flat(down(a)) 544.00/242.19 down(f(b)) -> f_flat(down(b)) 544.00/242.19 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.19 down(f(c)) -> f_flat(down(c)) 544.00/242.19 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.19 down(g(a)) -> g_flat(down(a)) 544.00/242.19 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.19 down(g(b)) -> g_flat(down(b)) 544.00/242.19 down(g(c)) -> g_flat(down(c)) 544.00/242.19 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.19 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.19 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.19 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.19 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.19 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.19 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.19 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.19 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.19 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.19 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.19 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.19 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.19 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.19 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.19 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.19 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.19 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.19 544.00/242.19 The set Q consists of the following terms: 544.00/242.19 544.00/242.19 down(a) 544.00/242.19 down(b) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.19 down(f(a)) 544.00/242.19 down(f(b)) 544.00/242.19 down(f(g(x0))) 544.00/242.19 down(f(c)) 544.00/242.19 down(f(fresh_constant)) 544.00/242.19 down(g(a)) 544.00/242.19 down(g(f(x0))) 544.00/242.19 down(g(b)) 544.00/242.19 down(g(c)) 544.00/242.19 down(g(fresh_constant)) 544.00/242.19 down(f(f(a))) 544.00/242.19 down(f(f(b))) 544.00/242.19 down(f(f(g(x0)))) 544.00/242.19 down(f(f(c))) 544.00/242.19 down(f(f(fresh_constant))) 544.00/242.19 down(g(g(a))) 544.00/242.19 down(g(g(f(x0)))) 544.00/242.19 down(g(g(b))) 544.00/242.19 down(g(g(c))) 544.00/242.19 down(g(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) 544.00/242.19 down(f(f(f(g(x0))))) 544.00/242.19 down(f(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) 544.00/242.19 down(g(g(g(f(x0))))) 544.00/242.19 down(g(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(x0)))))) 544.00/242.19 down(f(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(x0)))))) 544.00/242.19 down(g(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(x0))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(x0))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 f_flat(up(x0)) 544.00/242.19 g_flat(up(x0)) 544.00/242.19 544.00/242.19 We have to consider all minimal (P,Q,R)-chains. 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1137) TransformationProof (EQUIVALENT) 544.00/242.19 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(g(b)))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.19 544.00/242.19 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b))))))))))))) 544.00/242.19 544.00/242.19 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1138) 544.00/242.19 Obligation: 544.00/242.19 Q DP problem: 544.00/242.19 The TRS P consists of the following rules: 544.00/242.19 544.00/242.19 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.19 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.19 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.19 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.19 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.19 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.19 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.19 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.19 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.19 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.19 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.19 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.19 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.19 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.19 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.19 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.19 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.19 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.19 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.19 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.19 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.19 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.19 544.00/242.19 The TRS R consists of the following rules: 544.00/242.19 544.00/242.19 down(a) -> up(f(a)) 544.00/242.19 down(b) -> up(g(b)) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.19 down(f(a)) -> f_flat(down(a)) 544.00/242.19 down(f(b)) -> f_flat(down(b)) 544.00/242.19 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.19 down(f(c)) -> f_flat(down(c)) 544.00/242.19 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.19 down(g(a)) -> g_flat(down(a)) 544.00/242.19 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.19 down(g(b)) -> g_flat(down(b)) 544.00/242.19 down(g(c)) -> g_flat(down(c)) 544.00/242.19 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.19 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.19 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.19 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.19 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.19 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.19 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.19 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.19 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.19 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.19 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.19 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.19 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.19 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.19 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.19 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.19 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.19 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.19 544.00/242.19 The set Q consists of the following terms: 544.00/242.19 544.00/242.19 down(a) 544.00/242.19 down(b) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.19 down(f(a)) 544.00/242.19 down(f(b)) 544.00/242.19 down(f(g(x0))) 544.00/242.19 down(f(c)) 544.00/242.19 down(f(fresh_constant)) 544.00/242.19 down(g(a)) 544.00/242.19 down(g(f(x0))) 544.00/242.19 down(g(b)) 544.00/242.19 down(g(c)) 544.00/242.19 down(g(fresh_constant)) 544.00/242.19 down(f(f(a))) 544.00/242.19 down(f(f(b))) 544.00/242.19 down(f(f(g(x0)))) 544.00/242.19 down(f(f(c))) 544.00/242.19 down(f(f(fresh_constant))) 544.00/242.19 down(g(g(a))) 544.00/242.19 down(g(g(f(x0)))) 544.00/242.19 down(g(g(b))) 544.00/242.19 down(g(g(c))) 544.00/242.19 down(g(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) 544.00/242.19 down(f(f(f(g(x0))))) 544.00/242.19 down(f(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) 544.00/242.19 down(g(g(g(f(x0))))) 544.00/242.19 down(g(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(x0)))))) 544.00/242.19 down(f(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(x0)))))) 544.00/242.19 down(g(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(x0))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(x0))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 f_flat(up(x0)) 544.00/242.19 g_flat(up(x0)) 544.00/242.19 544.00/242.19 We have to consider all minimal (P,Q,R)-chains. 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1139) TransformationProof (EQUIVALENT) 544.00/242.19 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(b))))))))))) at position [0,0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.19 544.00/242.19 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b))))))))))))) 544.00/242.19 544.00/242.19 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1140) 544.00/242.19 Obligation: 544.00/242.19 Q DP problem: 544.00/242.19 The TRS P consists of the following rules: 544.00/242.19 544.00/242.19 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.19 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.19 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.19 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.19 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.19 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.19 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.19 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.19 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.19 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.19 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.19 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.19 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.19 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.19 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.19 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.19 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.19 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.19 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.19 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.19 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.19 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.19 544.00/242.19 The TRS R consists of the following rules: 544.00/242.19 544.00/242.19 down(a) -> up(f(a)) 544.00/242.19 down(b) -> up(g(b)) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.19 down(f(a)) -> f_flat(down(a)) 544.00/242.19 down(f(b)) -> f_flat(down(b)) 544.00/242.19 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.19 down(f(c)) -> f_flat(down(c)) 544.00/242.19 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.19 down(g(a)) -> g_flat(down(a)) 544.00/242.19 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.19 down(g(b)) -> g_flat(down(b)) 544.00/242.19 down(g(c)) -> g_flat(down(c)) 544.00/242.19 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.19 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.19 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.19 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.19 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.19 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.19 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.19 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.19 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.19 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.19 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.19 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.19 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.19 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.19 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.19 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.19 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.19 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.19 544.00/242.19 The set Q consists of the following terms: 544.00/242.19 544.00/242.19 down(a) 544.00/242.19 down(b) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.19 down(f(a)) 544.00/242.19 down(f(b)) 544.00/242.19 down(f(g(x0))) 544.00/242.19 down(f(c)) 544.00/242.19 down(f(fresh_constant)) 544.00/242.19 down(g(a)) 544.00/242.19 down(g(f(x0))) 544.00/242.19 down(g(b)) 544.00/242.19 down(g(c)) 544.00/242.19 down(g(fresh_constant)) 544.00/242.19 down(f(f(a))) 544.00/242.19 down(f(f(b))) 544.00/242.19 down(f(f(g(x0)))) 544.00/242.19 down(f(f(c))) 544.00/242.19 down(f(f(fresh_constant))) 544.00/242.19 down(g(g(a))) 544.00/242.19 down(g(g(f(x0)))) 544.00/242.19 down(g(g(b))) 544.00/242.19 down(g(g(c))) 544.00/242.19 down(g(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) 544.00/242.19 down(f(f(f(g(x0))))) 544.00/242.19 down(f(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) 544.00/242.19 down(g(g(g(f(x0))))) 544.00/242.19 down(g(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(x0)))))) 544.00/242.19 down(f(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(x0)))))) 544.00/242.19 down(g(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(x0))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(x0))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 f_flat(up(x0)) 544.00/242.19 g_flat(up(x0)) 544.00/242.19 544.00/242.19 We have to consider all minimal (P,Q,R)-chains. 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1141) TransformationProof (EQUIVALENT) 544.00/242.19 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.19 544.00/242.19 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.00/242.19 544.00/242.19 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1142) 544.00/242.19 Obligation: 544.00/242.19 Q DP problem: 544.00/242.19 The TRS P consists of the following rules: 544.00/242.19 544.00/242.19 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.19 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.19 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.19 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.19 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.19 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.19 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.19 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.19 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.19 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.19 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.19 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.19 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.19 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.19 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.19 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.19 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.19 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.19 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.19 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.19 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.19 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.19 544.00/242.19 The TRS R consists of the following rules: 544.00/242.19 544.00/242.19 down(a) -> up(f(a)) 544.00/242.19 down(b) -> up(g(b)) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.19 down(f(a)) -> f_flat(down(a)) 544.00/242.19 down(f(b)) -> f_flat(down(b)) 544.00/242.19 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.19 down(f(c)) -> f_flat(down(c)) 544.00/242.19 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.19 down(g(a)) -> g_flat(down(a)) 544.00/242.19 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.19 down(g(b)) -> g_flat(down(b)) 544.00/242.19 down(g(c)) -> g_flat(down(c)) 544.00/242.19 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.19 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.19 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.19 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.19 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.19 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.19 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.19 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.19 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.19 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.19 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.19 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.19 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.19 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.19 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.19 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.19 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.19 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.19 544.00/242.19 The set Q consists of the following terms: 544.00/242.19 544.00/242.19 down(a) 544.00/242.19 down(b) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.19 down(f(a)) 544.00/242.19 down(f(b)) 544.00/242.19 down(f(g(x0))) 544.00/242.19 down(f(c)) 544.00/242.19 down(f(fresh_constant)) 544.00/242.19 down(g(a)) 544.00/242.19 down(g(f(x0))) 544.00/242.19 down(g(b)) 544.00/242.19 down(g(c)) 544.00/242.19 down(g(fresh_constant)) 544.00/242.19 down(f(f(a))) 544.00/242.19 down(f(f(b))) 544.00/242.19 down(f(f(g(x0)))) 544.00/242.19 down(f(f(c))) 544.00/242.19 down(f(f(fresh_constant))) 544.00/242.19 down(g(g(a))) 544.00/242.19 down(g(g(f(x0)))) 544.00/242.19 down(g(g(b))) 544.00/242.19 down(g(g(c))) 544.00/242.19 down(g(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) 544.00/242.19 down(f(f(f(g(x0))))) 544.00/242.19 down(f(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) 544.00/242.19 down(g(g(g(f(x0))))) 544.00/242.19 down(g(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(x0)))))) 544.00/242.19 down(f(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(x0)))))) 544.00/242.19 down(g(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(x0))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(x0))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 f_flat(up(x0)) 544.00/242.19 g_flat(up(x0)) 544.00/242.19 544.00/242.19 We have to consider all minimal (P,Q,R)-chains. 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1143) TransformationProof (EQUIVALENT) 544.00/242.19 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.19 544.00/242.19 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.00/242.19 544.00/242.19 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1144) 544.00/242.19 Obligation: 544.00/242.19 Q DP problem: 544.00/242.19 The TRS P consists of the following rules: 544.00/242.19 544.00/242.19 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.19 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.19 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.19 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.19 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.19 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.19 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.19 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.19 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.19 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.19 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.19 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.19 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.19 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.19 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.19 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.19 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.19 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.19 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.19 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.19 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.19 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.19 544.00/242.19 The TRS R consists of the following rules: 544.00/242.19 544.00/242.19 down(a) -> up(f(a)) 544.00/242.19 down(b) -> up(g(b)) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.19 down(f(a)) -> f_flat(down(a)) 544.00/242.19 down(f(b)) -> f_flat(down(b)) 544.00/242.19 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.19 down(f(c)) -> f_flat(down(c)) 544.00/242.19 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.19 down(g(a)) -> g_flat(down(a)) 544.00/242.19 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.19 down(g(b)) -> g_flat(down(b)) 544.00/242.19 down(g(c)) -> g_flat(down(c)) 544.00/242.19 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.19 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.19 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.19 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.19 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.19 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.19 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.19 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.19 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.19 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.19 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.19 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.19 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.19 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.19 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.19 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.19 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.19 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.19 544.00/242.19 The set Q consists of the following terms: 544.00/242.19 544.00/242.19 down(a) 544.00/242.19 down(b) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.19 down(f(a)) 544.00/242.19 down(f(b)) 544.00/242.19 down(f(g(x0))) 544.00/242.19 down(f(c)) 544.00/242.19 down(f(fresh_constant)) 544.00/242.19 down(g(a)) 544.00/242.19 down(g(f(x0))) 544.00/242.19 down(g(b)) 544.00/242.19 down(g(c)) 544.00/242.19 down(g(fresh_constant)) 544.00/242.19 down(f(f(a))) 544.00/242.19 down(f(f(b))) 544.00/242.19 down(f(f(g(x0)))) 544.00/242.19 down(f(f(c))) 544.00/242.19 down(f(f(fresh_constant))) 544.00/242.19 down(g(g(a))) 544.00/242.19 down(g(g(f(x0)))) 544.00/242.19 down(g(g(b))) 544.00/242.19 down(g(g(c))) 544.00/242.19 down(g(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) 544.00/242.19 down(f(f(f(g(x0))))) 544.00/242.19 down(f(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) 544.00/242.19 down(g(g(g(f(x0))))) 544.00/242.19 down(g(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(x0)))))) 544.00/242.19 down(f(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(x0)))))) 544.00/242.19 down(g(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(x0))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(x0))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 f_flat(up(x0)) 544.00/242.19 g_flat(up(x0)) 544.00/242.19 544.00/242.19 We have to consider all minimal (P,Q,R)-chains. 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1145) TransformationProof (EQUIVALENT) 544.00/242.19 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(a))))))) -> TOP(g_flat(up(g(g(g(g(f(a)))))))) at position [0] we obtained the following new rules [LPAR04]: 544.00/242.19 544.00/242.19 (TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))),TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a))))))))) 544.00/242.19 544.00/242.19 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1146) 544.00/242.19 Obligation: 544.00/242.19 Q DP problem: 544.00/242.19 The TRS P consists of the following rules: 544.00/242.19 544.00/242.19 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.19 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.19 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.19 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.19 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.19 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.19 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.19 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.19 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.19 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.19 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.19 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.19 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.19 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.19 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.19 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.19 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.19 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.19 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.19 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.19 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.19 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.19 544.00/242.19 The TRS R consists of the following rules: 544.00/242.19 544.00/242.19 down(a) -> up(f(a)) 544.00/242.19 down(b) -> up(g(b)) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.19 down(f(a)) -> f_flat(down(a)) 544.00/242.19 down(f(b)) -> f_flat(down(b)) 544.00/242.19 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.19 down(f(c)) -> f_flat(down(c)) 544.00/242.19 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.19 down(g(a)) -> g_flat(down(a)) 544.00/242.19 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.19 down(g(b)) -> g_flat(down(b)) 544.00/242.19 down(g(c)) -> g_flat(down(c)) 544.00/242.19 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.19 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.19 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.19 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.19 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.19 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.19 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.19 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.19 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.19 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.19 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.19 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.19 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.19 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.19 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.19 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.19 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.19 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.19 544.00/242.19 The set Q consists of the following terms: 544.00/242.19 544.00/242.19 down(a) 544.00/242.19 down(b) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.19 down(f(a)) 544.00/242.19 down(f(b)) 544.00/242.19 down(f(g(x0))) 544.00/242.19 down(f(c)) 544.00/242.19 down(f(fresh_constant)) 544.00/242.19 down(g(a)) 544.00/242.19 down(g(f(x0))) 544.00/242.19 down(g(b)) 544.00/242.19 down(g(c)) 544.00/242.19 down(g(fresh_constant)) 544.00/242.19 down(f(f(a))) 544.00/242.19 down(f(f(b))) 544.00/242.19 down(f(f(g(x0)))) 544.00/242.19 down(f(f(c))) 544.00/242.19 down(f(f(fresh_constant))) 544.00/242.19 down(g(g(a))) 544.00/242.19 down(g(g(f(x0)))) 544.00/242.19 down(g(g(b))) 544.00/242.19 down(g(g(c))) 544.00/242.19 down(g(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) 544.00/242.19 down(f(f(f(g(x0))))) 544.00/242.19 down(f(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) 544.00/242.19 down(g(g(g(f(x0))))) 544.00/242.19 down(g(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(x0)))))) 544.00/242.19 down(f(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(x0)))))) 544.00/242.19 down(g(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(x0))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(x0))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 f_flat(up(x0)) 544.00/242.19 g_flat(up(x0)) 544.00/242.19 544.00/242.19 We have to consider all minimal (P,Q,R)-chains. 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1147) TransformationProof (EQUIVALENT) 544.00/242.19 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.19 544.00/242.19 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.00/242.19 544.00/242.19 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1148) 544.00/242.19 Obligation: 544.00/242.19 Q DP problem: 544.00/242.19 The TRS P consists of the following rules: 544.00/242.19 544.00/242.19 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.19 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.19 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.19 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.19 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.19 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.19 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.19 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.19 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.19 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.19 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.19 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.19 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.19 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.19 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.19 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.19 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.19 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.19 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.19 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.19 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.19 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.19 544.00/242.19 The TRS R consists of the following rules: 544.00/242.19 544.00/242.19 down(a) -> up(f(a)) 544.00/242.19 down(b) -> up(g(b)) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.19 down(f(a)) -> f_flat(down(a)) 544.00/242.19 down(f(b)) -> f_flat(down(b)) 544.00/242.19 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.19 down(f(c)) -> f_flat(down(c)) 544.00/242.19 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.19 down(g(a)) -> g_flat(down(a)) 544.00/242.19 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.19 down(g(b)) -> g_flat(down(b)) 544.00/242.19 down(g(c)) -> g_flat(down(c)) 544.00/242.19 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.19 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.19 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.19 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.19 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.19 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.19 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.19 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.19 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.19 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.19 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.19 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.19 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.19 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.19 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.19 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.19 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.19 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.19 544.00/242.19 The set Q consists of the following terms: 544.00/242.19 544.00/242.19 down(a) 544.00/242.19 down(b) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.19 down(f(a)) 544.00/242.19 down(f(b)) 544.00/242.19 down(f(g(x0))) 544.00/242.19 down(f(c)) 544.00/242.19 down(f(fresh_constant)) 544.00/242.19 down(g(a)) 544.00/242.19 down(g(f(x0))) 544.00/242.19 down(g(b)) 544.00/242.19 down(g(c)) 544.00/242.19 down(g(fresh_constant)) 544.00/242.19 down(f(f(a))) 544.00/242.19 down(f(f(b))) 544.00/242.19 down(f(f(g(x0)))) 544.00/242.19 down(f(f(c))) 544.00/242.19 down(f(f(fresh_constant))) 544.00/242.19 down(g(g(a))) 544.00/242.19 down(g(g(f(x0)))) 544.00/242.19 down(g(g(b))) 544.00/242.19 down(g(g(c))) 544.00/242.19 down(g(g(fresh_constant))) 544.00/242.19 down(f(f(f(a)))) 544.00/242.19 down(f(f(f(b)))) 544.00/242.19 down(f(f(f(g(x0))))) 544.00/242.19 down(f(f(f(c)))) 544.00/242.19 down(f(f(f(fresh_constant)))) 544.00/242.19 down(g(g(g(a)))) 544.00/242.19 down(g(g(g(f(x0))))) 544.00/242.19 down(g(g(g(b)))) 544.00/242.19 down(g(g(g(c)))) 544.00/242.19 down(g(g(g(fresh_constant)))) 544.00/242.19 down(f(f(f(f(a))))) 544.00/242.19 down(f(f(f(f(b))))) 544.00/242.19 down(f(f(f(f(g(x0)))))) 544.00/242.19 down(f(f(f(f(c))))) 544.00/242.19 down(f(f(f(f(fresh_constant))))) 544.00/242.19 down(g(g(g(g(a))))) 544.00/242.19 down(g(g(g(g(f(x0)))))) 544.00/242.19 down(g(g(g(g(b))))) 544.00/242.19 down(g(g(g(g(c))))) 544.00/242.19 down(g(g(g(g(fresh_constant))))) 544.00/242.19 down(f(f(f(f(f(a)))))) 544.00/242.19 down(f(f(f(f(f(b)))))) 544.00/242.19 down(f(f(f(f(f(g(x0))))))) 544.00/242.19 down(f(f(f(f(f(c)))))) 544.00/242.19 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.19 down(g(g(g(g(g(a)))))) 544.00/242.19 down(g(g(g(g(g(f(x0))))))) 544.00/242.19 down(g(g(g(g(g(b)))))) 544.00/242.19 down(g(g(g(g(g(c)))))) 544.00/242.19 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.19 down(f(f(f(f(f(f(a))))))) 544.00/242.19 down(f(f(f(f(f(f(b))))))) 544.00/242.19 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.19 down(f(f(f(f(f(f(c))))))) 544.00/242.19 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.19 down(g(g(g(g(g(g(a))))))) 544.00/242.19 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.19 down(g(g(g(g(g(g(b))))))) 544.00/242.19 down(g(g(g(g(g(g(c))))))) 544.00/242.19 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.19 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.19 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.19 f_flat(up(x0)) 544.00/242.19 g_flat(up(x0)) 544.00/242.19 544.00/242.19 We have to consider all minimal (P,Q,R)-chains. 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1149) TransformationProof (EQUIVALENT) 544.00/242.19 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.19 544.00/242.19 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.00/242.19 544.00/242.19 544.00/242.19 ---------------------------------------- 544.00/242.19 544.00/242.19 (1150) 544.00/242.19 Obligation: 544.00/242.19 Q DP problem: 544.00/242.19 The TRS P consists of the following rules: 544.00/242.19 544.00/242.19 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.19 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.19 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.19 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.19 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.19 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.19 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.19 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.19 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.19 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.19 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.19 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.19 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.19 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.19 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.19 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.19 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.19 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.19 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.19 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.19 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.19 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.19 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.19 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.19 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.19 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.19 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.19 544.00/242.19 The TRS R consists of the following rules: 544.00/242.19 544.00/242.19 down(a) -> up(f(a)) 544.00/242.19 down(b) -> up(g(b)) 544.00/242.19 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.19 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.19 down(f(a)) -> f_flat(down(a)) 544.00/242.19 down(f(b)) -> f_flat(down(b)) 544.00/242.19 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.19 down(f(c)) -> f_flat(down(c)) 544.00/242.19 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.19 down(g(a)) -> g_flat(down(a)) 544.00/242.19 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.19 down(g(b)) -> g_flat(down(b)) 544.00/242.19 down(g(c)) -> g_flat(down(c)) 544.00/242.19 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.19 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.19 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.19 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.19 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.19 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.19 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.19 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.19 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.19 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.19 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.20 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.20 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.20 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.20 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.20 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.20 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.20 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.20 544.00/242.20 The set Q consists of the following terms: 544.00/242.20 544.00/242.20 down(a) 544.00/242.20 down(b) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.20 down(f(a)) 544.00/242.20 down(f(b)) 544.00/242.20 down(f(g(x0))) 544.00/242.20 down(f(c)) 544.00/242.20 down(f(fresh_constant)) 544.00/242.20 down(g(a)) 544.00/242.20 down(g(f(x0))) 544.00/242.20 down(g(b)) 544.00/242.20 down(g(c)) 544.00/242.20 down(g(fresh_constant)) 544.00/242.20 down(f(f(a))) 544.00/242.20 down(f(f(b))) 544.00/242.20 down(f(f(g(x0)))) 544.00/242.20 down(f(f(c))) 544.00/242.20 down(f(f(fresh_constant))) 544.00/242.20 down(g(g(a))) 544.00/242.20 down(g(g(f(x0)))) 544.00/242.20 down(g(g(b))) 544.00/242.20 down(g(g(c))) 544.00/242.20 down(g(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) 544.00/242.20 down(f(f(f(g(x0))))) 544.00/242.20 down(f(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) 544.00/242.20 down(g(g(g(f(x0))))) 544.00/242.20 down(g(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(x0)))))) 544.00/242.20 down(f(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(x0)))))) 544.00/242.20 down(g(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(x0))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(x0))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 f_flat(up(x0)) 544.00/242.20 g_flat(up(x0)) 544.00/242.20 544.00/242.20 We have to consider all minimal (P,Q,R)-chains. 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1151) TransformationProof (EQUIVALENT) 544.00/242.20 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.20 544.00/242.20 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.00/242.20 544.00/242.20 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1152) 544.00/242.20 Obligation: 544.00/242.20 Q DP problem: 544.00/242.20 The TRS P consists of the following rules: 544.00/242.20 544.00/242.20 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.20 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.20 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.20 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.20 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.20 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.20 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.20 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.20 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.20 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.20 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.20 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.20 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.20 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.20 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.20 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.20 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.20 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.20 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.20 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.20 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.20 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.20 544.00/242.20 The TRS R consists of the following rules: 544.00/242.20 544.00/242.20 down(a) -> up(f(a)) 544.00/242.20 down(b) -> up(g(b)) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.20 down(f(a)) -> f_flat(down(a)) 544.00/242.20 down(f(b)) -> f_flat(down(b)) 544.00/242.20 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.20 down(f(c)) -> f_flat(down(c)) 544.00/242.20 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.20 down(g(a)) -> g_flat(down(a)) 544.00/242.20 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.20 down(g(b)) -> g_flat(down(b)) 544.00/242.20 down(g(c)) -> g_flat(down(c)) 544.00/242.20 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.20 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.20 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.20 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.20 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.20 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.20 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.20 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.20 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.20 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.20 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.20 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.20 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.20 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.20 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.20 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.20 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.20 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.20 544.00/242.20 The set Q consists of the following terms: 544.00/242.20 544.00/242.20 down(a) 544.00/242.20 down(b) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.20 down(f(a)) 544.00/242.20 down(f(b)) 544.00/242.20 down(f(g(x0))) 544.00/242.20 down(f(c)) 544.00/242.20 down(f(fresh_constant)) 544.00/242.20 down(g(a)) 544.00/242.20 down(g(f(x0))) 544.00/242.20 down(g(b)) 544.00/242.20 down(g(c)) 544.00/242.20 down(g(fresh_constant)) 544.00/242.20 down(f(f(a))) 544.00/242.20 down(f(f(b))) 544.00/242.20 down(f(f(g(x0)))) 544.00/242.20 down(f(f(c))) 544.00/242.20 down(f(f(fresh_constant))) 544.00/242.20 down(g(g(a))) 544.00/242.20 down(g(g(f(x0)))) 544.00/242.20 down(g(g(b))) 544.00/242.20 down(g(g(c))) 544.00/242.20 down(g(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) 544.00/242.20 down(f(f(f(g(x0))))) 544.00/242.20 down(f(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) 544.00/242.20 down(g(g(g(f(x0))))) 544.00/242.20 down(g(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(x0)))))) 544.00/242.20 down(f(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(x0)))))) 544.00/242.20 down(g(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(x0))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(x0))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 f_flat(up(x0)) 544.00/242.20 g_flat(up(x0)) 544.00/242.20 544.00/242.20 We have to consider all minimal (P,Q,R)-chains. 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1153) TransformationProof (EQUIVALENT) 544.00/242.20 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(f(a)))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.20 544.00/242.20 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a))))))))))))) 544.00/242.20 544.00/242.20 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1154) 544.00/242.20 Obligation: 544.00/242.20 Q DP problem: 544.00/242.20 The TRS P consists of the following rules: 544.00/242.20 544.00/242.20 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.20 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.20 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.20 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.20 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.20 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.20 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.20 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.20 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.20 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.20 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.20 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.20 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.20 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.20 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.20 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.20 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.20 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.20 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.20 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.20 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.20 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.20 544.00/242.20 The TRS R consists of the following rules: 544.00/242.20 544.00/242.20 down(a) -> up(f(a)) 544.00/242.20 down(b) -> up(g(b)) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.20 down(f(a)) -> f_flat(down(a)) 544.00/242.20 down(f(b)) -> f_flat(down(b)) 544.00/242.20 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.20 down(f(c)) -> f_flat(down(c)) 544.00/242.20 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.20 down(g(a)) -> g_flat(down(a)) 544.00/242.20 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.20 down(g(b)) -> g_flat(down(b)) 544.00/242.20 down(g(c)) -> g_flat(down(c)) 544.00/242.20 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.20 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.20 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.20 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.20 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.20 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.20 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.20 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.20 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.20 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.20 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.20 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.20 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.20 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.20 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.20 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.20 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.20 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.20 544.00/242.20 The set Q consists of the following terms: 544.00/242.20 544.00/242.20 down(a) 544.00/242.20 down(b) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.20 down(f(a)) 544.00/242.20 down(f(b)) 544.00/242.20 down(f(g(x0))) 544.00/242.20 down(f(c)) 544.00/242.20 down(f(fresh_constant)) 544.00/242.20 down(g(a)) 544.00/242.20 down(g(f(x0))) 544.00/242.20 down(g(b)) 544.00/242.20 down(g(c)) 544.00/242.20 down(g(fresh_constant)) 544.00/242.20 down(f(f(a))) 544.00/242.20 down(f(f(b))) 544.00/242.20 down(f(f(g(x0)))) 544.00/242.20 down(f(f(c))) 544.00/242.20 down(f(f(fresh_constant))) 544.00/242.20 down(g(g(a))) 544.00/242.20 down(g(g(f(x0)))) 544.00/242.20 down(g(g(b))) 544.00/242.20 down(g(g(c))) 544.00/242.20 down(g(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) 544.00/242.20 down(f(f(f(g(x0))))) 544.00/242.20 down(f(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) 544.00/242.20 down(g(g(g(f(x0))))) 544.00/242.20 down(g(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(x0)))))) 544.00/242.20 down(f(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(x0)))))) 544.00/242.20 down(g(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(x0))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(x0))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 f_flat(up(x0)) 544.00/242.20 g_flat(up(x0)) 544.00/242.20 544.00/242.20 We have to consider all minimal (P,Q,R)-chains. 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1155) TransformationProof (EQUIVALENT) 544.00/242.20 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(g(b))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.00/242.20 544.00/242.20 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.00/242.20 544.00/242.20 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1156) 544.00/242.20 Obligation: 544.00/242.20 Q DP problem: 544.00/242.20 The TRS P consists of the following rules: 544.00/242.20 544.00/242.20 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.20 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.20 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.20 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.20 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.20 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.20 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.20 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.20 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.20 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.20 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.20 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.20 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.20 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.20 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.20 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.20 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.20 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.20 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.20 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.20 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.20 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.20 544.00/242.20 The TRS R consists of the following rules: 544.00/242.20 544.00/242.20 down(a) -> up(f(a)) 544.00/242.20 down(b) -> up(g(b)) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.20 down(f(a)) -> f_flat(down(a)) 544.00/242.20 down(f(b)) -> f_flat(down(b)) 544.00/242.20 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.20 down(f(c)) -> f_flat(down(c)) 544.00/242.20 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.20 down(g(a)) -> g_flat(down(a)) 544.00/242.20 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.20 down(g(b)) -> g_flat(down(b)) 544.00/242.20 down(g(c)) -> g_flat(down(c)) 544.00/242.20 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.20 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.20 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.20 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.20 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.20 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.20 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.20 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.20 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.20 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.20 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.20 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.20 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.20 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.20 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.20 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.20 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.20 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.20 544.00/242.20 The set Q consists of the following terms: 544.00/242.20 544.00/242.20 down(a) 544.00/242.20 down(b) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.20 down(f(a)) 544.00/242.20 down(f(b)) 544.00/242.20 down(f(g(x0))) 544.00/242.20 down(f(c)) 544.00/242.20 down(f(fresh_constant)) 544.00/242.20 down(g(a)) 544.00/242.20 down(g(f(x0))) 544.00/242.20 down(g(b)) 544.00/242.20 down(g(c)) 544.00/242.20 down(g(fresh_constant)) 544.00/242.20 down(f(f(a))) 544.00/242.20 down(f(f(b))) 544.00/242.20 down(f(f(g(x0)))) 544.00/242.20 down(f(f(c))) 544.00/242.20 down(f(f(fresh_constant))) 544.00/242.20 down(g(g(a))) 544.00/242.20 down(g(g(f(x0)))) 544.00/242.20 down(g(g(b))) 544.00/242.20 down(g(g(c))) 544.00/242.20 down(g(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) 544.00/242.20 down(f(f(f(g(x0))))) 544.00/242.20 down(f(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) 544.00/242.20 down(g(g(g(f(x0))))) 544.00/242.20 down(g(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(x0)))))) 544.00/242.20 down(f(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(x0)))))) 544.00/242.20 down(g(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(x0))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(x0))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 f_flat(up(x0)) 544.00/242.20 g_flat(up(x0)) 544.00/242.20 544.00/242.20 We have to consider all minimal (P,Q,R)-chains. 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1157) TransformationProof (EQUIVALENT) 544.00/242.20 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.20 544.00/242.20 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.00/242.20 544.00/242.20 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1158) 544.00/242.20 Obligation: 544.00/242.20 Q DP problem: 544.00/242.20 The TRS P consists of the following rules: 544.00/242.20 544.00/242.20 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.20 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.20 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.20 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.20 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.20 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.20 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.20 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.20 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.20 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.20 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.20 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.20 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.20 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.20 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.20 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.20 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.20 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.20 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.20 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.20 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.20 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.20 544.00/242.20 The TRS R consists of the following rules: 544.00/242.20 544.00/242.20 down(a) -> up(f(a)) 544.00/242.20 down(b) -> up(g(b)) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.20 down(f(a)) -> f_flat(down(a)) 544.00/242.20 down(f(b)) -> f_flat(down(b)) 544.00/242.20 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.20 down(f(c)) -> f_flat(down(c)) 544.00/242.20 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.20 down(g(a)) -> g_flat(down(a)) 544.00/242.20 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.20 down(g(b)) -> g_flat(down(b)) 544.00/242.20 down(g(c)) -> g_flat(down(c)) 544.00/242.20 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.20 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.20 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.20 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.20 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.20 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.20 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.20 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.20 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.20 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.20 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.20 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.20 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.20 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.20 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.20 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.20 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.20 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.20 544.00/242.20 The set Q consists of the following terms: 544.00/242.20 544.00/242.20 down(a) 544.00/242.20 down(b) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.20 down(f(a)) 544.00/242.20 down(f(b)) 544.00/242.20 down(f(g(x0))) 544.00/242.20 down(f(c)) 544.00/242.20 down(f(fresh_constant)) 544.00/242.20 down(g(a)) 544.00/242.20 down(g(f(x0))) 544.00/242.20 down(g(b)) 544.00/242.20 down(g(c)) 544.00/242.20 down(g(fresh_constant)) 544.00/242.20 down(f(f(a))) 544.00/242.20 down(f(f(b))) 544.00/242.20 down(f(f(g(x0)))) 544.00/242.20 down(f(f(c))) 544.00/242.20 down(f(f(fresh_constant))) 544.00/242.20 down(g(g(a))) 544.00/242.20 down(g(g(f(x0)))) 544.00/242.20 down(g(g(b))) 544.00/242.20 down(g(g(c))) 544.00/242.20 down(g(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) 544.00/242.20 down(f(f(f(g(x0))))) 544.00/242.20 down(f(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) 544.00/242.20 down(g(g(g(f(x0))))) 544.00/242.20 down(g(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(x0)))))) 544.00/242.20 down(f(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(x0)))))) 544.00/242.20 down(g(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(x0))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(x0))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 f_flat(up(x0)) 544.00/242.20 g_flat(up(x0)) 544.00/242.20 544.00/242.20 We have to consider all minimal (P,Q,R)-chains. 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1159) TransformationProof (EQUIVALENT) 544.00/242.20 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.20 544.00/242.20 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.00/242.20 544.00/242.20 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1160) 544.00/242.20 Obligation: 544.00/242.20 Q DP problem: 544.00/242.20 The TRS P consists of the following rules: 544.00/242.20 544.00/242.20 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.20 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.20 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.20 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.20 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.20 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.20 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.20 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.20 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.20 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.20 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.20 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.20 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.20 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.20 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.20 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.20 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.20 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.20 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.20 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.20 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.20 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.20 544.00/242.20 The TRS R consists of the following rules: 544.00/242.20 544.00/242.20 down(a) -> up(f(a)) 544.00/242.20 down(b) -> up(g(b)) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.20 down(f(a)) -> f_flat(down(a)) 544.00/242.20 down(f(b)) -> f_flat(down(b)) 544.00/242.20 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.20 down(f(c)) -> f_flat(down(c)) 544.00/242.20 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.20 down(g(a)) -> g_flat(down(a)) 544.00/242.20 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.20 down(g(b)) -> g_flat(down(b)) 544.00/242.20 down(g(c)) -> g_flat(down(c)) 544.00/242.20 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.20 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.20 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.20 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.20 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.20 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.20 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.20 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.20 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.20 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.20 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.20 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.20 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.20 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.20 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.20 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.20 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.20 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.20 544.00/242.20 The set Q consists of the following terms: 544.00/242.20 544.00/242.20 down(a) 544.00/242.20 down(b) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.20 down(f(a)) 544.00/242.20 down(f(b)) 544.00/242.20 down(f(g(x0))) 544.00/242.20 down(f(c)) 544.00/242.20 down(f(fresh_constant)) 544.00/242.20 down(g(a)) 544.00/242.20 down(g(f(x0))) 544.00/242.20 down(g(b)) 544.00/242.20 down(g(c)) 544.00/242.20 down(g(fresh_constant)) 544.00/242.20 down(f(f(a))) 544.00/242.20 down(f(f(b))) 544.00/242.20 down(f(f(g(x0)))) 544.00/242.20 down(f(f(c))) 544.00/242.20 down(f(f(fresh_constant))) 544.00/242.20 down(g(g(a))) 544.00/242.20 down(g(g(f(x0)))) 544.00/242.20 down(g(g(b))) 544.00/242.20 down(g(g(c))) 544.00/242.20 down(g(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) 544.00/242.20 down(f(f(f(g(x0))))) 544.00/242.20 down(f(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) 544.00/242.20 down(g(g(g(f(x0))))) 544.00/242.20 down(g(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(x0)))))) 544.00/242.20 down(f(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(x0)))))) 544.00/242.20 down(g(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(x0))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(x0))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 f_flat(up(x0)) 544.00/242.20 g_flat(up(x0)) 544.00/242.20 544.00/242.20 We have to consider all minimal (P,Q,R)-chains. 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1161) TransformationProof (EQUIVALENT) 544.00/242.20 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(a)))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.20 544.00/242.20 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a))))))))))))) 544.00/242.20 544.00/242.20 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1162) 544.00/242.20 Obligation: 544.00/242.20 Q DP problem: 544.00/242.20 The TRS P consists of the following rules: 544.00/242.20 544.00/242.20 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.20 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.20 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.20 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.20 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.20 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.20 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.20 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.20 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.20 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.20 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.20 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.20 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.20 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.20 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.20 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.20 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.20 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.20 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.20 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.20 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.20 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.20 544.00/242.20 The TRS R consists of the following rules: 544.00/242.20 544.00/242.20 down(a) -> up(f(a)) 544.00/242.20 down(b) -> up(g(b)) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.20 down(f(a)) -> f_flat(down(a)) 544.00/242.20 down(f(b)) -> f_flat(down(b)) 544.00/242.20 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.20 down(f(c)) -> f_flat(down(c)) 544.00/242.20 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.20 down(g(a)) -> g_flat(down(a)) 544.00/242.20 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.20 down(g(b)) -> g_flat(down(b)) 544.00/242.20 down(g(c)) -> g_flat(down(c)) 544.00/242.20 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.20 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.20 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.20 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.20 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.20 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.20 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.20 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.20 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.20 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.20 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.20 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.20 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.20 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.20 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.20 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.20 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.20 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.20 544.00/242.20 The set Q consists of the following terms: 544.00/242.20 544.00/242.20 down(a) 544.00/242.20 down(b) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.20 down(f(a)) 544.00/242.20 down(f(b)) 544.00/242.20 down(f(g(x0))) 544.00/242.20 down(f(c)) 544.00/242.20 down(f(fresh_constant)) 544.00/242.20 down(g(a)) 544.00/242.20 down(g(f(x0))) 544.00/242.20 down(g(b)) 544.00/242.20 down(g(c)) 544.00/242.20 down(g(fresh_constant)) 544.00/242.20 down(f(f(a))) 544.00/242.20 down(f(f(b))) 544.00/242.20 down(f(f(g(x0)))) 544.00/242.20 down(f(f(c))) 544.00/242.20 down(f(f(fresh_constant))) 544.00/242.20 down(g(g(a))) 544.00/242.20 down(g(g(f(x0)))) 544.00/242.20 down(g(g(b))) 544.00/242.20 down(g(g(c))) 544.00/242.20 down(g(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) 544.00/242.20 down(f(f(f(g(x0))))) 544.00/242.20 down(f(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) 544.00/242.20 down(g(g(g(f(x0))))) 544.00/242.20 down(g(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(x0)))))) 544.00/242.20 down(f(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(x0)))))) 544.00/242.20 down(g(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(x0))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(x0))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 f_flat(up(x0)) 544.00/242.20 g_flat(up(x0)) 544.00/242.20 544.00/242.20 We have to consider all minimal (P,Q,R)-chains. 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1163) TransformationProof (EQUIVALENT) 544.00/242.20 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(g(b)))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.20 544.00/242.20 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b))))))))))))) 544.00/242.20 544.00/242.20 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1164) 544.00/242.20 Obligation: 544.00/242.20 Q DP problem: 544.00/242.20 The TRS P consists of the following rules: 544.00/242.20 544.00/242.20 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.20 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.20 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.20 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.20 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.20 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.20 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.20 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.20 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.20 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.20 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.20 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.20 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.20 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.20 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.20 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.20 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.20 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.20 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.20 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.20 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.20 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.20 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.20 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.20 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.20 544.00/242.20 The TRS R consists of the following rules: 544.00/242.20 544.00/242.20 down(a) -> up(f(a)) 544.00/242.20 down(b) -> up(g(b)) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.20 down(f(a)) -> f_flat(down(a)) 544.00/242.20 down(f(b)) -> f_flat(down(b)) 544.00/242.20 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.20 down(f(c)) -> f_flat(down(c)) 544.00/242.20 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.20 down(g(a)) -> g_flat(down(a)) 544.00/242.20 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.20 down(g(b)) -> g_flat(down(b)) 544.00/242.20 down(g(c)) -> g_flat(down(c)) 544.00/242.20 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.20 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.20 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.20 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.20 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.20 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.20 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.20 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.20 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.20 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.20 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.20 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.20 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.20 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.20 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.20 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.20 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.20 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.20 544.00/242.20 The set Q consists of the following terms: 544.00/242.20 544.00/242.20 down(a) 544.00/242.20 down(b) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.20 down(f(a)) 544.00/242.20 down(f(b)) 544.00/242.20 down(f(g(x0))) 544.00/242.20 down(f(c)) 544.00/242.20 down(f(fresh_constant)) 544.00/242.20 down(g(a)) 544.00/242.20 down(g(f(x0))) 544.00/242.20 down(g(b)) 544.00/242.20 down(g(c)) 544.00/242.20 down(g(fresh_constant)) 544.00/242.20 down(f(f(a))) 544.00/242.20 down(f(f(b))) 544.00/242.20 down(f(f(g(x0)))) 544.00/242.20 down(f(f(c))) 544.00/242.20 down(f(f(fresh_constant))) 544.00/242.20 down(g(g(a))) 544.00/242.20 down(g(g(f(x0)))) 544.00/242.20 down(g(g(b))) 544.00/242.20 down(g(g(c))) 544.00/242.20 down(g(g(fresh_constant))) 544.00/242.20 down(f(f(f(a)))) 544.00/242.20 down(f(f(f(b)))) 544.00/242.20 down(f(f(f(g(x0))))) 544.00/242.20 down(f(f(f(c)))) 544.00/242.20 down(f(f(f(fresh_constant)))) 544.00/242.20 down(g(g(g(a)))) 544.00/242.20 down(g(g(g(f(x0))))) 544.00/242.20 down(g(g(g(b)))) 544.00/242.20 down(g(g(g(c)))) 544.00/242.20 down(g(g(g(fresh_constant)))) 544.00/242.20 down(f(f(f(f(a))))) 544.00/242.20 down(f(f(f(f(b))))) 544.00/242.20 down(f(f(f(f(g(x0)))))) 544.00/242.20 down(f(f(f(f(c))))) 544.00/242.20 down(f(f(f(f(fresh_constant))))) 544.00/242.20 down(g(g(g(g(a))))) 544.00/242.20 down(g(g(g(g(f(x0)))))) 544.00/242.20 down(g(g(g(g(b))))) 544.00/242.20 down(g(g(g(g(c))))) 544.00/242.20 down(g(g(g(g(fresh_constant))))) 544.00/242.20 down(f(f(f(f(f(a)))))) 544.00/242.20 down(f(f(f(f(f(b)))))) 544.00/242.20 down(f(f(f(f(f(g(x0))))))) 544.00/242.20 down(f(f(f(f(f(c)))))) 544.00/242.20 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.20 down(g(g(g(g(g(a)))))) 544.00/242.20 down(g(g(g(g(g(f(x0))))))) 544.00/242.20 down(g(g(g(g(g(b)))))) 544.00/242.20 down(g(g(g(g(g(c)))))) 544.00/242.20 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.20 down(f(f(f(f(f(f(a))))))) 544.00/242.20 down(f(f(f(f(f(f(b))))))) 544.00/242.20 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.20 down(f(f(f(f(f(f(c))))))) 544.00/242.20 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.20 down(g(g(g(g(g(g(a))))))) 544.00/242.20 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.20 down(g(g(g(g(g(g(b))))))) 544.00/242.20 down(g(g(g(g(g(g(c))))))) 544.00/242.20 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.20 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.20 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.20 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.20 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.20 f_flat(up(x0)) 544.00/242.20 g_flat(up(x0)) 544.00/242.20 544.00/242.20 We have to consider all minimal (P,Q,R)-chains. 544.00/242.20 ---------------------------------------- 544.00/242.20 544.00/242.20 (1165) TransformationProof (EQUIVALENT) 544.00/242.20 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(b)))))))))))) at position [0,0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.20 544.00/242.20 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b))))))))))))) 544.00/242.21 544.00/242.21 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1166) 544.00/242.21 Obligation: 544.00/242.21 Q DP problem: 544.00/242.21 The TRS P consists of the following rules: 544.00/242.21 544.00/242.21 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.21 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.21 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.21 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.21 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.21 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.21 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.21 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.21 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.21 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.21 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.21 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.21 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.21 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.21 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.21 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.21 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.21 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.21 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.21 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.21 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.21 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.00/242.21 544.00/242.21 The TRS R consists of the following rules: 544.00/242.21 544.00/242.21 down(a) -> up(f(a)) 544.00/242.21 down(b) -> up(g(b)) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.21 down(f(a)) -> f_flat(down(a)) 544.00/242.21 down(f(b)) -> f_flat(down(b)) 544.00/242.21 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.21 down(f(c)) -> f_flat(down(c)) 544.00/242.21 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.21 down(g(a)) -> g_flat(down(a)) 544.00/242.21 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.21 down(g(b)) -> g_flat(down(b)) 544.00/242.21 down(g(c)) -> g_flat(down(c)) 544.00/242.21 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.21 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.21 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.21 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.21 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.21 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.21 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.21 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.21 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.21 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.21 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.21 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.21 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.21 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.21 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.21 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.21 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.21 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.21 544.00/242.21 The set Q consists of the following terms: 544.00/242.21 544.00/242.21 down(a) 544.00/242.21 down(b) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.21 down(f(a)) 544.00/242.21 down(f(b)) 544.00/242.21 down(f(g(x0))) 544.00/242.21 down(f(c)) 544.00/242.21 down(f(fresh_constant)) 544.00/242.21 down(g(a)) 544.00/242.21 down(g(f(x0))) 544.00/242.21 down(g(b)) 544.00/242.21 down(g(c)) 544.00/242.21 down(g(fresh_constant)) 544.00/242.21 down(f(f(a))) 544.00/242.21 down(f(f(b))) 544.00/242.21 down(f(f(g(x0)))) 544.00/242.21 down(f(f(c))) 544.00/242.21 down(f(f(fresh_constant))) 544.00/242.21 down(g(g(a))) 544.00/242.21 down(g(g(f(x0)))) 544.00/242.21 down(g(g(b))) 544.00/242.21 down(g(g(c))) 544.00/242.21 down(g(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) 544.00/242.21 down(f(f(f(g(x0))))) 544.00/242.21 down(f(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) 544.00/242.21 down(g(g(g(f(x0))))) 544.00/242.21 down(g(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(x0)))))) 544.00/242.21 down(f(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(x0)))))) 544.00/242.21 down(g(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(x0))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(x0))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 f_flat(up(x0)) 544.00/242.21 g_flat(up(x0)) 544.00/242.21 544.00/242.21 We have to consider all minimal (P,Q,R)-chains. 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1167) TransformationProof (EQUIVALENT) 544.00/242.21 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.21 544.00/242.21 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.00/242.21 544.00/242.21 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1168) 544.00/242.21 Obligation: 544.00/242.21 Q DP problem: 544.00/242.21 The TRS P consists of the following rules: 544.00/242.21 544.00/242.21 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.21 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.21 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.21 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.21 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.21 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.21 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.21 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.21 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.21 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.21 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.21 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.21 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.21 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.21 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.21 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.21 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.21 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.21 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.21 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.21 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.21 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.00/242.21 544.00/242.21 The TRS R consists of the following rules: 544.00/242.21 544.00/242.21 down(a) -> up(f(a)) 544.00/242.21 down(b) -> up(g(b)) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.21 down(f(a)) -> f_flat(down(a)) 544.00/242.21 down(f(b)) -> f_flat(down(b)) 544.00/242.21 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.21 down(f(c)) -> f_flat(down(c)) 544.00/242.21 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.21 down(g(a)) -> g_flat(down(a)) 544.00/242.21 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.21 down(g(b)) -> g_flat(down(b)) 544.00/242.21 down(g(c)) -> g_flat(down(c)) 544.00/242.21 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.21 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.21 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.21 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.21 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.21 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.21 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.21 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.21 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.21 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.21 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.21 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.21 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.21 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.21 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.21 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.21 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.21 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.21 544.00/242.21 The set Q consists of the following terms: 544.00/242.21 544.00/242.21 down(a) 544.00/242.21 down(b) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.21 down(f(a)) 544.00/242.21 down(f(b)) 544.00/242.21 down(f(g(x0))) 544.00/242.21 down(f(c)) 544.00/242.21 down(f(fresh_constant)) 544.00/242.21 down(g(a)) 544.00/242.21 down(g(f(x0))) 544.00/242.21 down(g(b)) 544.00/242.21 down(g(c)) 544.00/242.21 down(g(fresh_constant)) 544.00/242.21 down(f(f(a))) 544.00/242.21 down(f(f(b))) 544.00/242.21 down(f(f(g(x0)))) 544.00/242.21 down(f(f(c))) 544.00/242.21 down(f(f(fresh_constant))) 544.00/242.21 down(g(g(a))) 544.00/242.21 down(g(g(f(x0)))) 544.00/242.21 down(g(g(b))) 544.00/242.21 down(g(g(c))) 544.00/242.21 down(g(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) 544.00/242.21 down(f(f(f(g(x0))))) 544.00/242.21 down(f(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) 544.00/242.21 down(g(g(g(f(x0))))) 544.00/242.21 down(g(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(x0)))))) 544.00/242.21 down(f(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(x0)))))) 544.00/242.21 down(g(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(x0))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(x0))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 f_flat(up(x0)) 544.00/242.21 g_flat(up(x0)) 544.00/242.21 544.00/242.21 We have to consider all minimal (P,Q,R)-chains. 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1169) TransformationProof (EQUIVALENT) 544.00/242.21 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.21 544.00/242.21 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.00/242.21 544.00/242.21 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1170) 544.00/242.21 Obligation: 544.00/242.21 Q DP problem: 544.00/242.21 The TRS P consists of the following rules: 544.00/242.21 544.00/242.21 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.21 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.21 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.21 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.21 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.21 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.21 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.21 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.21 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.21 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.21 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.21 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.21 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.21 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.21 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.21 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.21 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.21 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.21 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.21 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.21 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.21 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.00/242.21 544.00/242.21 The TRS R consists of the following rules: 544.00/242.21 544.00/242.21 down(a) -> up(f(a)) 544.00/242.21 down(b) -> up(g(b)) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.21 down(f(a)) -> f_flat(down(a)) 544.00/242.21 down(f(b)) -> f_flat(down(b)) 544.00/242.21 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.21 down(f(c)) -> f_flat(down(c)) 544.00/242.21 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.21 down(g(a)) -> g_flat(down(a)) 544.00/242.21 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.21 down(g(b)) -> g_flat(down(b)) 544.00/242.21 down(g(c)) -> g_flat(down(c)) 544.00/242.21 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.21 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.21 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.21 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.21 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.21 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.21 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.21 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.21 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.21 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.21 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.21 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.21 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.21 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.21 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.21 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.21 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.21 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.21 544.00/242.21 The set Q consists of the following terms: 544.00/242.21 544.00/242.21 down(a) 544.00/242.21 down(b) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.21 down(f(a)) 544.00/242.21 down(f(b)) 544.00/242.21 down(f(g(x0))) 544.00/242.21 down(f(c)) 544.00/242.21 down(f(fresh_constant)) 544.00/242.21 down(g(a)) 544.00/242.21 down(g(f(x0))) 544.00/242.21 down(g(b)) 544.00/242.21 down(g(c)) 544.00/242.21 down(g(fresh_constant)) 544.00/242.21 down(f(f(a))) 544.00/242.21 down(f(f(b))) 544.00/242.21 down(f(f(g(x0)))) 544.00/242.21 down(f(f(c))) 544.00/242.21 down(f(f(fresh_constant))) 544.00/242.21 down(g(g(a))) 544.00/242.21 down(g(g(f(x0)))) 544.00/242.21 down(g(g(b))) 544.00/242.21 down(g(g(c))) 544.00/242.21 down(g(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) 544.00/242.21 down(f(f(f(g(x0))))) 544.00/242.21 down(f(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) 544.00/242.21 down(g(g(g(f(x0))))) 544.00/242.21 down(g(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(x0)))))) 544.00/242.21 down(f(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(x0)))))) 544.00/242.21 down(g(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(x0))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(x0))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 f_flat(up(x0)) 544.00/242.21 g_flat(up(x0)) 544.00/242.21 544.00/242.21 We have to consider all minimal (P,Q,R)-chains. 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1171) TransformationProof (EQUIVALENT) 544.00/242.21 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(f(a))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.00/242.21 544.00/242.21 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.00/242.21 544.00/242.21 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1172) 544.00/242.21 Obligation: 544.00/242.21 Q DP problem: 544.00/242.21 The TRS P consists of the following rules: 544.00/242.21 544.00/242.21 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.21 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.21 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.21 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.21 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.21 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.21 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.21 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.21 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.21 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.21 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.21 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.21 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.21 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.21 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.21 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.21 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.21 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.21 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.21 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.21 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.21 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.00/242.21 544.00/242.21 The TRS R consists of the following rules: 544.00/242.21 544.00/242.21 down(a) -> up(f(a)) 544.00/242.21 down(b) -> up(g(b)) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.21 down(f(a)) -> f_flat(down(a)) 544.00/242.21 down(f(b)) -> f_flat(down(b)) 544.00/242.21 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.21 down(f(c)) -> f_flat(down(c)) 544.00/242.21 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.21 down(g(a)) -> g_flat(down(a)) 544.00/242.21 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.21 down(g(b)) -> g_flat(down(b)) 544.00/242.21 down(g(c)) -> g_flat(down(c)) 544.00/242.21 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.21 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.21 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.21 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.21 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.21 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.21 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.21 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.21 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.21 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.21 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.21 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.21 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.21 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.21 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.21 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.21 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.21 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.21 544.00/242.21 The set Q consists of the following terms: 544.00/242.21 544.00/242.21 down(a) 544.00/242.21 down(b) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.21 down(f(a)) 544.00/242.21 down(f(b)) 544.00/242.21 down(f(g(x0))) 544.00/242.21 down(f(c)) 544.00/242.21 down(f(fresh_constant)) 544.00/242.21 down(g(a)) 544.00/242.21 down(g(f(x0))) 544.00/242.21 down(g(b)) 544.00/242.21 down(g(c)) 544.00/242.21 down(g(fresh_constant)) 544.00/242.21 down(f(f(a))) 544.00/242.21 down(f(f(b))) 544.00/242.21 down(f(f(g(x0)))) 544.00/242.21 down(f(f(c))) 544.00/242.21 down(f(f(fresh_constant))) 544.00/242.21 down(g(g(a))) 544.00/242.21 down(g(g(f(x0)))) 544.00/242.21 down(g(g(b))) 544.00/242.21 down(g(g(c))) 544.00/242.21 down(g(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) 544.00/242.21 down(f(f(f(g(x0))))) 544.00/242.21 down(f(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) 544.00/242.21 down(g(g(g(f(x0))))) 544.00/242.21 down(g(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(x0)))))) 544.00/242.21 down(f(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(x0)))))) 544.00/242.21 down(g(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(x0))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(x0))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 f_flat(up(x0)) 544.00/242.21 g_flat(up(x0)) 544.00/242.21 544.00/242.21 We have to consider all minimal (P,Q,R)-chains. 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1173) TransformationProof (EQUIVALENT) 544.00/242.21 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.21 544.00/242.21 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.00/242.21 544.00/242.21 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1174) 544.00/242.21 Obligation: 544.00/242.21 Q DP problem: 544.00/242.21 The TRS P consists of the following rules: 544.00/242.21 544.00/242.21 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.21 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.21 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.21 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.21 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.21 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.21 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.21 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.21 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.21 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.21 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.21 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.21 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.21 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.21 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.21 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.21 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.21 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.21 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.21 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.21 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.21 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.00/242.21 544.00/242.21 The TRS R consists of the following rules: 544.00/242.21 544.00/242.21 down(a) -> up(f(a)) 544.00/242.21 down(b) -> up(g(b)) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.21 down(f(a)) -> f_flat(down(a)) 544.00/242.21 down(f(b)) -> f_flat(down(b)) 544.00/242.21 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.21 down(f(c)) -> f_flat(down(c)) 544.00/242.21 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.21 down(g(a)) -> g_flat(down(a)) 544.00/242.21 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.21 down(g(b)) -> g_flat(down(b)) 544.00/242.21 down(g(c)) -> g_flat(down(c)) 544.00/242.21 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.21 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.21 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.21 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.21 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.21 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.21 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.21 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.21 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.21 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.21 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.21 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.21 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.21 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.21 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.21 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.21 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.21 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.21 544.00/242.21 The set Q consists of the following terms: 544.00/242.21 544.00/242.21 down(a) 544.00/242.21 down(b) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.21 down(f(a)) 544.00/242.21 down(f(b)) 544.00/242.21 down(f(g(x0))) 544.00/242.21 down(f(c)) 544.00/242.21 down(f(fresh_constant)) 544.00/242.21 down(g(a)) 544.00/242.21 down(g(f(x0))) 544.00/242.21 down(g(b)) 544.00/242.21 down(g(c)) 544.00/242.21 down(g(fresh_constant)) 544.00/242.21 down(f(f(a))) 544.00/242.21 down(f(f(b))) 544.00/242.21 down(f(f(g(x0)))) 544.00/242.21 down(f(f(c))) 544.00/242.21 down(f(f(fresh_constant))) 544.00/242.21 down(g(g(a))) 544.00/242.21 down(g(g(f(x0)))) 544.00/242.21 down(g(g(b))) 544.00/242.21 down(g(g(c))) 544.00/242.21 down(g(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) 544.00/242.21 down(f(f(f(g(x0))))) 544.00/242.21 down(f(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) 544.00/242.21 down(g(g(g(f(x0))))) 544.00/242.21 down(g(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(x0)))))) 544.00/242.21 down(f(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(x0)))))) 544.00/242.21 down(g(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(x0))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(x0))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 f_flat(up(x0)) 544.00/242.21 g_flat(up(x0)) 544.00/242.21 544.00/242.21 We have to consider all minimal (P,Q,R)-chains. 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1175) TransformationProof (EQUIVALENT) 544.00/242.21 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.21 544.00/242.21 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.00/242.21 544.00/242.21 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1176) 544.00/242.21 Obligation: 544.00/242.21 Q DP problem: 544.00/242.21 The TRS P consists of the following rules: 544.00/242.21 544.00/242.21 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.21 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.21 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.21 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.21 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.21 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.21 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.21 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.21 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.21 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.21 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.21 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.21 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.21 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.21 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.21 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.21 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.21 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.21 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.21 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.21 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.21 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.00/242.21 544.00/242.21 The TRS R consists of the following rules: 544.00/242.21 544.00/242.21 down(a) -> up(f(a)) 544.00/242.21 down(b) -> up(g(b)) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.21 down(f(a)) -> f_flat(down(a)) 544.00/242.21 down(f(b)) -> f_flat(down(b)) 544.00/242.21 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.21 down(f(c)) -> f_flat(down(c)) 544.00/242.21 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.21 down(g(a)) -> g_flat(down(a)) 544.00/242.21 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.21 down(g(b)) -> g_flat(down(b)) 544.00/242.21 down(g(c)) -> g_flat(down(c)) 544.00/242.21 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.21 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.21 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.21 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.21 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.21 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.21 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.21 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.21 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.21 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.21 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.21 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.21 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.21 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.21 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.21 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.21 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.21 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.21 544.00/242.21 The set Q consists of the following terms: 544.00/242.21 544.00/242.21 down(a) 544.00/242.21 down(b) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.21 down(f(a)) 544.00/242.21 down(f(b)) 544.00/242.21 down(f(g(x0))) 544.00/242.21 down(f(c)) 544.00/242.21 down(f(fresh_constant)) 544.00/242.21 down(g(a)) 544.00/242.21 down(g(f(x0))) 544.00/242.21 down(g(b)) 544.00/242.21 down(g(c)) 544.00/242.21 down(g(fresh_constant)) 544.00/242.21 down(f(f(a))) 544.00/242.21 down(f(f(b))) 544.00/242.21 down(f(f(g(x0)))) 544.00/242.21 down(f(f(c))) 544.00/242.21 down(f(f(fresh_constant))) 544.00/242.21 down(g(g(a))) 544.00/242.21 down(g(g(f(x0)))) 544.00/242.21 down(g(g(b))) 544.00/242.21 down(g(g(c))) 544.00/242.21 down(g(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) 544.00/242.21 down(f(f(f(g(x0))))) 544.00/242.21 down(f(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) 544.00/242.21 down(g(g(g(f(x0))))) 544.00/242.21 down(g(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(x0)))))) 544.00/242.21 down(f(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(x0)))))) 544.00/242.21 down(g(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(x0))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(x0))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 f_flat(up(x0)) 544.00/242.21 g_flat(up(x0)) 544.00/242.21 544.00/242.21 We have to consider all minimal (P,Q,R)-chains. 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1177) TransformationProof (EQUIVALENT) 544.00/242.21 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(f(a)))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.00/242.21 544.00/242.21 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a))))))))))))) 544.00/242.21 544.00/242.21 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1178) 544.00/242.21 Obligation: 544.00/242.21 Q DP problem: 544.00/242.21 The TRS P consists of the following rules: 544.00/242.21 544.00/242.21 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.21 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.21 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.21 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.21 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.21 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.21 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.21 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.21 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.21 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.21 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.21 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.21 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.21 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.21 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.21 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.21 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.21 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.21 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.21 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.21 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.21 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.00/242.21 544.00/242.21 The TRS R consists of the following rules: 544.00/242.21 544.00/242.21 down(a) -> up(f(a)) 544.00/242.21 down(b) -> up(g(b)) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.21 down(f(a)) -> f_flat(down(a)) 544.00/242.21 down(f(b)) -> f_flat(down(b)) 544.00/242.21 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.21 down(f(c)) -> f_flat(down(c)) 544.00/242.21 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.21 down(g(a)) -> g_flat(down(a)) 544.00/242.21 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.21 down(g(b)) -> g_flat(down(b)) 544.00/242.21 down(g(c)) -> g_flat(down(c)) 544.00/242.21 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.21 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.21 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.21 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.21 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.21 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.21 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.21 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.21 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.21 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.21 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.21 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.21 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.21 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.21 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.21 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.21 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.21 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.21 544.00/242.21 The set Q consists of the following terms: 544.00/242.21 544.00/242.21 down(a) 544.00/242.21 down(b) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.21 down(f(a)) 544.00/242.21 down(f(b)) 544.00/242.21 down(f(g(x0))) 544.00/242.21 down(f(c)) 544.00/242.21 down(f(fresh_constant)) 544.00/242.21 down(g(a)) 544.00/242.21 down(g(f(x0))) 544.00/242.21 down(g(b)) 544.00/242.21 down(g(c)) 544.00/242.21 down(g(fresh_constant)) 544.00/242.21 down(f(f(a))) 544.00/242.21 down(f(f(b))) 544.00/242.21 down(f(f(g(x0)))) 544.00/242.21 down(f(f(c))) 544.00/242.21 down(f(f(fresh_constant))) 544.00/242.21 down(g(g(a))) 544.00/242.21 down(g(g(f(x0)))) 544.00/242.21 down(g(g(b))) 544.00/242.21 down(g(g(c))) 544.00/242.21 down(g(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) 544.00/242.21 down(f(f(f(g(x0))))) 544.00/242.21 down(f(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) 544.00/242.21 down(g(g(g(f(x0))))) 544.00/242.21 down(g(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(x0)))))) 544.00/242.21 down(f(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(x0)))))) 544.00/242.21 down(g(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(x0))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(x0))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(x0)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(x0)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(x0))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(x0))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(c))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(a))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(c))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.21 f_flat(up(x0)) 544.00/242.21 g_flat(up(x0)) 544.00/242.21 544.00/242.21 We have to consider all minimal (P,Q,R)-chains. 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1179) TransformationProof (EQUIVALENT) 544.00/242.21 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(f_flat(up(f(f(f(f(f(g(b))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.00/242.21 544.00/242.21 (TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))),TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b)))))))))) 544.00/242.21 544.00/242.21 544.00/242.21 ---------------------------------------- 544.00/242.21 544.00/242.21 (1180) 544.00/242.21 Obligation: 544.00/242.21 Q DP problem: 544.00/242.21 The TRS P consists of the following rules: 544.00/242.21 544.00/242.21 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.00/242.21 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.00/242.21 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.00/242.21 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.00/242.21 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.00/242.21 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.00/242.21 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.00/242.21 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.21 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.00/242.21 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.00/242.21 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.00/242.21 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.00/242.21 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.00/242.21 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.21 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.00/242.21 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.00/242.21 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.00/242.21 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.00/242.21 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.00/242.21 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.00/242.21 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.00/242.21 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.00/242.21 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.00/242.21 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.00/242.21 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.00/242.21 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.00/242.21 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.00/242.21 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.00/242.21 544.00/242.21 The TRS R consists of the following rules: 544.00/242.21 544.00/242.21 down(a) -> up(f(a)) 544.00/242.21 down(b) -> up(g(b)) 544.00/242.21 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.00/242.21 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.00/242.21 down(f(a)) -> f_flat(down(a)) 544.00/242.21 down(f(b)) -> f_flat(down(b)) 544.00/242.21 down(f(g(y4))) -> f_flat(down(g(y4))) 544.00/242.21 down(f(c)) -> f_flat(down(c)) 544.00/242.21 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.00/242.21 down(g(a)) -> g_flat(down(a)) 544.00/242.21 down(g(f(y6))) -> g_flat(down(f(y6))) 544.00/242.21 down(g(b)) -> g_flat(down(b)) 544.00/242.21 down(g(c)) -> g_flat(down(c)) 544.00/242.21 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.00/242.21 down(f(f(a))) -> f_flat(down(f(a))) 544.00/242.21 down(f(f(b))) -> f_flat(down(f(b))) 544.00/242.21 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.00/242.21 down(f(f(c))) -> f_flat(down(f(c))) 544.00/242.21 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.00/242.21 down(g(g(a))) -> g_flat(down(g(a))) 544.00/242.21 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.00/242.21 down(g(g(b))) -> g_flat(down(g(b))) 544.00/242.21 down(g(g(c))) -> g_flat(down(g(c))) 544.00/242.21 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.00/242.21 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.00/242.21 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.00/242.21 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.00/242.21 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.00/242.21 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.00/242.21 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.00/242.21 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.00/242.21 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.00/242.21 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.00/242.21 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.00/242.21 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.00/242.21 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.00/242.21 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.00/242.21 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.00/242.21 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.00/242.21 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.00/242.21 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.00/242.21 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.00/242.21 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.00/242.21 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.00/242.21 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.00/242.21 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.00/242.21 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.00/242.21 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.00/242.21 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.00/242.21 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.00/242.21 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.00/242.21 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.00/242.21 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.00/242.21 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.00/242.21 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.00/242.21 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.00/242.21 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.00/242.21 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.00/242.21 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.00/242.21 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.00/242.21 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.00/242.21 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.00/242.21 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.00/242.21 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.00/242.21 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.00/242.21 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.00/242.21 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.00/242.21 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.00/242.22 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.00/242.22 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.00/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.00/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.00/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.00/242.22 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.00/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.00/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.00/242.22 g_flat(up(x_1)) -> up(g(x_1)) 544.00/242.22 f_flat(up(x_1)) -> up(f(x_1)) 544.00/242.22 544.00/242.22 The set Q consists of the following terms: 544.00/242.22 544.00/242.22 down(a) 544.00/242.22 down(b) 544.00/242.22 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.00/242.22 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.00/242.22 down(f(a)) 544.00/242.22 down(f(b)) 544.00/242.22 down(f(g(x0))) 544.00/242.22 down(f(c)) 544.00/242.22 down(f(fresh_constant)) 544.00/242.22 down(g(a)) 544.00/242.22 down(g(f(x0))) 544.00/242.22 down(g(b)) 544.00/242.22 down(g(c)) 544.00/242.22 down(g(fresh_constant)) 544.00/242.22 down(f(f(a))) 544.00/242.22 down(f(f(b))) 544.00/242.22 down(f(f(g(x0)))) 544.00/242.22 down(f(f(c))) 544.09/242.22 down(f(f(fresh_constant))) 544.09/242.22 down(g(g(a))) 544.09/242.22 down(g(g(f(x0)))) 544.09/242.22 down(g(g(b))) 544.09/242.22 down(g(g(c))) 544.09/242.22 down(g(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) 544.09/242.22 down(f(f(f(g(x0))))) 544.09/242.22 down(f(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) 544.09/242.22 down(g(g(g(f(x0))))) 544.09/242.22 down(g(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(x0)))))) 544.09/242.22 down(f(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(x0)))))) 544.09/242.22 down(g(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(x0))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(x0))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 f_flat(up(x0)) 544.09/242.22 g_flat(up(x0)) 544.09/242.22 544.09/242.22 We have to consider all minimal (P,Q,R)-chains. 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1181) TransformationProof (EQUIVALENT) 544.09/242.22 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.22 544.09/242.22 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.22 544.09/242.22 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1182) 544.09/242.22 Obligation: 544.09/242.22 Q DP problem: 544.09/242.22 The TRS P consists of the following rules: 544.09/242.22 544.09/242.22 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.22 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.22 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.22 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.22 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.22 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.22 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.22 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.22 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.22 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.22 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.22 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.22 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.22 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.22 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.22 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.22 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.22 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.22 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.22 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.22 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.22 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.22 544.09/242.22 The TRS R consists of the following rules: 544.09/242.22 544.09/242.22 down(a) -> up(f(a)) 544.09/242.22 down(b) -> up(g(b)) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.22 down(f(a)) -> f_flat(down(a)) 544.09/242.22 down(f(b)) -> f_flat(down(b)) 544.09/242.22 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.22 down(f(c)) -> f_flat(down(c)) 544.09/242.22 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.22 down(g(a)) -> g_flat(down(a)) 544.09/242.22 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.22 down(g(b)) -> g_flat(down(b)) 544.09/242.22 down(g(c)) -> g_flat(down(c)) 544.09/242.22 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.22 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.22 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.22 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.22 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.22 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.22 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.22 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.22 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.22 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.22 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.22 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.22 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.22 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.22 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.22 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.22 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.22 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.22 544.09/242.22 The set Q consists of the following terms: 544.09/242.22 544.09/242.22 down(a) 544.09/242.22 down(b) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.22 down(f(a)) 544.09/242.22 down(f(b)) 544.09/242.22 down(f(g(x0))) 544.09/242.22 down(f(c)) 544.09/242.22 down(f(fresh_constant)) 544.09/242.22 down(g(a)) 544.09/242.22 down(g(f(x0))) 544.09/242.22 down(g(b)) 544.09/242.22 down(g(c)) 544.09/242.22 down(g(fresh_constant)) 544.09/242.22 down(f(f(a))) 544.09/242.22 down(f(f(b))) 544.09/242.22 down(f(f(g(x0)))) 544.09/242.22 down(f(f(c))) 544.09/242.22 down(f(f(fresh_constant))) 544.09/242.22 down(g(g(a))) 544.09/242.22 down(g(g(f(x0)))) 544.09/242.22 down(g(g(b))) 544.09/242.22 down(g(g(c))) 544.09/242.22 down(g(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) 544.09/242.22 down(f(f(f(g(x0))))) 544.09/242.22 down(f(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) 544.09/242.22 down(g(g(g(f(x0))))) 544.09/242.22 down(g(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(x0)))))) 544.09/242.22 down(f(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(x0)))))) 544.09/242.22 down(g(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(x0))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(x0))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 f_flat(up(x0)) 544.09/242.22 g_flat(up(x0)) 544.09/242.22 544.09/242.22 We have to consider all minimal (P,Q,R)-chains. 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1183) TransformationProof (EQUIVALENT) 544.09/242.22 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.22 544.09/242.22 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.22 544.09/242.22 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1184) 544.09/242.22 Obligation: 544.09/242.22 Q DP problem: 544.09/242.22 The TRS P consists of the following rules: 544.09/242.22 544.09/242.22 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.22 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.22 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.22 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.22 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.22 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.22 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.22 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.22 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.22 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.22 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.22 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.22 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.22 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.22 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.22 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.22 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.22 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.22 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.22 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.22 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.22 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.22 544.09/242.22 The TRS R consists of the following rules: 544.09/242.22 544.09/242.22 down(a) -> up(f(a)) 544.09/242.22 down(b) -> up(g(b)) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.22 down(f(a)) -> f_flat(down(a)) 544.09/242.22 down(f(b)) -> f_flat(down(b)) 544.09/242.22 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.22 down(f(c)) -> f_flat(down(c)) 544.09/242.22 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.22 down(g(a)) -> g_flat(down(a)) 544.09/242.22 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.22 down(g(b)) -> g_flat(down(b)) 544.09/242.22 down(g(c)) -> g_flat(down(c)) 544.09/242.22 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.22 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.22 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.22 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.22 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.22 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.22 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.22 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.22 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.22 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.22 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.22 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.22 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.22 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.22 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.22 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.22 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.22 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.22 544.09/242.22 The set Q consists of the following terms: 544.09/242.22 544.09/242.22 down(a) 544.09/242.22 down(b) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.22 down(f(a)) 544.09/242.22 down(f(b)) 544.09/242.22 down(f(g(x0))) 544.09/242.22 down(f(c)) 544.09/242.22 down(f(fresh_constant)) 544.09/242.22 down(g(a)) 544.09/242.22 down(g(f(x0))) 544.09/242.22 down(g(b)) 544.09/242.22 down(g(c)) 544.09/242.22 down(g(fresh_constant)) 544.09/242.22 down(f(f(a))) 544.09/242.22 down(f(f(b))) 544.09/242.22 down(f(f(g(x0)))) 544.09/242.22 down(f(f(c))) 544.09/242.22 down(f(f(fresh_constant))) 544.09/242.22 down(g(g(a))) 544.09/242.22 down(g(g(f(x0)))) 544.09/242.22 down(g(g(b))) 544.09/242.22 down(g(g(c))) 544.09/242.22 down(g(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) 544.09/242.22 down(f(f(f(g(x0))))) 544.09/242.22 down(f(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) 544.09/242.22 down(g(g(g(f(x0))))) 544.09/242.22 down(g(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(x0)))))) 544.09/242.22 down(f(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(x0)))))) 544.09/242.22 down(g(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(x0))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(x0))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 f_flat(up(x0)) 544.09/242.22 g_flat(up(x0)) 544.09/242.22 544.09/242.22 We have to consider all minimal (P,Q,R)-chains. 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1185) TransformationProof (EQUIVALENT) 544.09/242.22 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(a)))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.22 544.09/242.22 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a))))))))))))) 544.09/242.22 544.09/242.22 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1186) 544.09/242.22 Obligation: 544.09/242.22 Q DP problem: 544.09/242.22 The TRS P consists of the following rules: 544.09/242.22 544.09/242.22 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.22 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.22 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.22 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.22 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.22 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.22 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.22 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.22 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.22 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.22 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.22 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.22 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.22 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.22 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.22 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.22 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.22 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.22 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.22 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.22 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.22 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.22 544.09/242.22 The TRS R consists of the following rules: 544.09/242.22 544.09/242.22 down(a) -> up(f(a)) 544.09/242.22 down(b) -> up(g(b)) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.22 down(f(a)) -> f_flat(down(a)) 544.09/242.22 down(f(b)) -> f_flat(down(b)) 544.09/242.22 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.22 down(f(c)) -> f_flat(down(c)) 544.09/242.22 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.22 down(g(a)) -> g_flat(down(a)) 544.09/242.22 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.22 down(g(b)) -> g_flat(down(b)) 544.09/242.22 down(g(c)) -> g_flat(down(c)) 544.09/242.22 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.22 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.22 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.22 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.22 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.22 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.22 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.22 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.22 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.22 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.22 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.22 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.22 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.22 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.22 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.22 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.22 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.22 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.22 544.09/242.22 The set Q consists of the following terms: 544.09/242.22 544.09/242.22 down(a) 544.09/242.22 down(b) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.22 down(f(a)) 544.09/242.22 down(f(b)) 544.09/242.22 down(f(g(x0))) 544.09/242.22 down(f(c)) 544.09/242.22 down(f(fresh_constant)) 544.09/242.22 down(g(a)) 544.09/242.22 down(g(f(x0))) 544.09/242.22 down(g(b)) 544.09/242.22 down(g(c)) 544.09/242.22 down(g(fresh_constant)) 544.09/242.22 down(f(f(a))) 544.09/242.22 down(f(f(b))) 544.09/242.22 down(f(f(g(x0)))) 544.09/242.22 down(f(f(c))) 544.09/242.22 down(f(f(fresh_constant))) 544.09/242.22 down(g(g(a))) 544.09/242.22 down(g(g(f(x0)))) 544.09/242.22 down(g(g(b))) 544.09/242.22 down(g(g(c))) 544.09/242.22 down(g(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) 544.09/242.22 down(f(f(f(g(x0))))) 544.09/242.22 down(f(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) 544.09/242.22 down(g(g(g(f(x0))))) 544.09/242.22 down(g(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(x0)))))) 544.09/242.22 down(f(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(x0)))))) 544.09/242.22 down(g(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(x0))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(x0))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 f_flat(up(x0)) 544.09/242.22 g_flat(up(x0)) 544.09/242.22 544.09/242.22 We have to consider all minimal (P,Q,R)-chains. 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1187) TransformationProof (EQUIVALENT) 544.09/242.22 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(g(b)))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.22 544.09/242.22 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b))))))))))))) 544.09/242.22 544.09/242.22 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1188) 544.09/242.22 Obligation: 544.09/242.22 Q DP problem: 544.09/242.22 The TRS P consists of the following rules: 544.09/242.22 544.09/242.22 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.22 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.22 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.22 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.22 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.22 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.22 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.22 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.22 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.22 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.22 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.22 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.22 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.22 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.22 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.22 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.22 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.22 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.22 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.22 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.22 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.22 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.22 544.09/242.22 The TRS R consists of the following rules: 544.09/242.22 544.09/242.22 down(a) -> up(f(a)) 544.09/242.22 down(b) -> up(g(b)) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.22 down(f(a)) -> f_flat(down(a)) 544.09/242.22 down(f(b)) -> f_flat(down(b)) 544.09/242.22 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.22 down(f(c)) -> f_flat(down(c)) 544.09/242.22 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.22 down(g(a)) -> g_flat(down(a)) 544.09/242.22 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.22 down(g(b)) -> g_flat(down(b)) 544.09/242.22 down(g(c)) -> g_flat(down(c)) 544.09/242.22 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.22 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.22 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.22 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.22 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.22 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.22 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.22 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.22 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.22 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.22 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.22 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.22 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.22 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.22 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.22 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.22 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.22 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.22 544.09/242.22 The set Q consists of the following terms: 544.09/242.22 544.09/242.22 down(a) 544.09/242.22 down(b) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.22 down(f(a)) 544.09/242.22 down(f(b)) 544.09/242.22 down(f(g(x0))) 544.09/242.22 down(f(c)) 544.09/242.22 down(f(fresh_constant)) 544.09/242.22 down(g(a)) 544.09/242.22 down(g(f(x0))) 544.09/242.22 down(g(b)) 544.09/242.22 down(g(c)) 544.09/242.22 down(g(fresh_constant)) 544.09/242.22 down(f(f(a))) 544.09/242.22 down(f(f(b))) 544.09/242.22 down(f(f(g(x0)))) 544.09/242.22 down(f(f(c))) 544.09/242.22 down(f(f(fresh_constant))) 544.09/242.22 down(g(g(a))) 544.09/242.22 down(g(g(f(x0)))) 544.09/242.22 down(g(g(b))) 544.09/242.22 down(g(g(c))) 544.09/242.22 down(g(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) 544.09/242.22 down(f(f(f(g(x0))))) 544.09/242.22 down(f(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) 544.09/242.22 down(g(g(g(f(x0))))) 544.09/242.22 down(g(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(x0)))))) 544.09/242.22 down(f(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(x0)))))) 544.09/242.22 down(g(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(x0))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(x0))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 f_flat(up(x0)) 544.09/242.22 g_flat(up(x0)) 544.09/242.22 544.09/242.22 We have to consider all minimal (P,Q,R)-chains. 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1189) TransformationProof (EQUIVALENT) 544.09/242.22 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(b)))))))))))) at position [0,0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.22 544.09/242.22 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b))))))))))))) 544.09/242.22 544.09/242.22 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1190) 544.09/242.22 Obligation: 544.09/242.22 Q DP problem: 544.09/242.22 The TRS P consists of the following rules: 544.09/242.22 544.09/242.22 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.22 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.22 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.22 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.22 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.22 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.22 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.22 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.22 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.22 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.22 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.22 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.22 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.22 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.22 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.22 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.22 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.22 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.22 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.22 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.22 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.22 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.22 544.09/242.22 The TRS R consists of the following rules: 544.09/242.22 544.09/242.22 down(a) -> up(f(a)) 544.09/242.22 down(b) -> up(g(b)) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.22 down(f(a)) -> f_flat(down(a)) 544.09/242.22 down(f(b)) -> f_flat(down(b)) 544.09/242.22 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.22 down(f(c)) -> f_flat(down(c)) 544.09/242.22 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.22 down(g(a)) -> g_flat(down(a)) 544.09/242.22 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.22 down(g(b)) -> g_flat(down(b)) 544.09/242.22 down(g(c)) -> g_flat(down(c)) 544.09/242.22 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.22 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.22 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.22 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.22 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.22 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.22 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.22 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.22 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.22 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.22 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.22 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.22 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.22 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.22 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.22 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.22 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.22 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.22 544.09/242.22 The set Q consists of the following terms: 544.09/242.22 544.09/242.22 down(a) 544.09/242.22 down(b) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.22 down(f(a)) 544.09/242.22 down(f(b)) 544.09/242.22 down(f(g(x0))) 544.09/242.22 down(f(c)) 544.09/242.22 down(f(fresh_constant)) 544.09/242.22 down(g(a)) 544.09/242.22 down(g(f(x0))) 544.09/242.22 down(g(b)) 544.09/242.22 down(g(c)) 544.09/242.22 down(g(fresh_constant)) 544.09/242.22 down(f(f(a))) 544.09/242.22 down(f(f(b))) 544.09/242.22 down(f(f(g(x0)))) 544.09/242.22 down(f(f(c))) 544.09/242.22 down(f(f(fresh_constant))) 544.09/242.22 down(g(g(a))) 544.09/242.22 down(g(g(f(x0)))) 544.09/242.22 down(g(g(b))) 544.09/242.22 down(g(g(c))) 544.09/242.22 down(g(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) 544.09/242.22 down(f(f(f(g(x0))))) 544.09/242.22 down(f(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) 544.09/242.22 down(g(g(g(f(x0))))) 544.09/242.22 down(g(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(x0)))))) 544.09/242.22 down(f(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(x0)))))) 544.09/242.22 down(g(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(x0))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(x0))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 f_flat(up(x0)) 544.09/242.22 g_flat(up(x0)) 544.09/242.22 544.09/242.22 We have to consider all minimal (P,Q,R)-chains. 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1191) TransformationProof (EQUIVALENT) 544.09/242.22 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.22 544.09/242.22 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.22 544.09/242.22 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1192) 544.09/242.22 Obligation: 544.09/242.22 Q DP problem: 544.09/242.22 The TRS P consists of the following rules: 544.09/242.22 544.09/242.22 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.22 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.22 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.22 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.22 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.22 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.22 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.22 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.22 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.22 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.22 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.22 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.22 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.22 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.22 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.22 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.22 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.22 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.22 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.22 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.22 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.22 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.22 544.09/242.22 The TRS R consists of the following rules: 544.09/242.22 544.09/242.22 down(a) -> up(f(a)) 544.09/242.22 down(b) -> up(g(b)) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.22 down(f(a)) -> f_flat(down(a)) 544.09/242.22 down(f(b)) -> f_flat(down(b)) 544.09/242.22 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.22 down(f(c)) -> f_flat(down(c)) 544.09/242.22 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.22 down(g(a)) -> g_flat(down(a)) 544.09/242.22 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.22 down(g(b)) -> g_flat(down(b)) 544.09/242.22 down(g(c)) -> g_flat(down(c)) 544.09/242.22 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.22 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.22 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.22 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.22 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.22 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.22 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.22 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.22 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.22 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.22 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.22 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.22 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.22 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.22 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.22 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.22 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.22 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.22 544.09/242.22 The set Q consists of the following terms: 544.09/242.22 544.09/242.22 down(a) 544.09/242.22 down(b) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.22 down(f(a)) 544.09/242.22 down(f(b)) 544.09/242.22 down(f(g(x0))) 544.09/242.22 down(f(c)) 544.09/242.22 down(f(fresh_constant)) 544.09/242.22 down(g(a)) 544.09/242.22 down(g(f(x0))) 544.09/242.22 down(g(b)) 544.09/242.22 down(g(c)) 544.09/242.22 down(g(fresh_constant)) 544.09/242.22 down(f(f(a))) 544.09/242.22 down(f(f(b))) 544.09/242.22 down(f(f(g(x0)))) 544.09/242.22 down(f(f(c))) 544.09/242.22 down(f(f(fresh_constant))) 544.09/242.22 down(g(g(a))) 544.09/242.22 down(g(g(f(x0)))) 544.09/242.22 down(g(g(b))) 544.09/242.22 down(g(g(c))) 544.09/242.22 down(g(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) 544.09/242.22 down(f(f(f(g(x0))))) 544.09/242.22 down(f(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) 544.09/242.22 down(g(g(g(f(x0))))) 544.09/242.22 down(g(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(x0)))))) 544.09/242.22 down(f(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(x0)))))) 544.09/242.22 down(g(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(x0))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(x0))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 f_flat(up(x0)) 544.09/242.22 g_flat(up(x0)) 544.09/242.22 544.09/242.22 We have to consider all minimal (P,Q,R)-chains. 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1193) TransformationProof (EQUIVALENT) 544.09/242.22 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.22 544.09/242.22 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.22 544.09/242.22 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1194) 544.09/242.22 Obligation: 544.09/242.22 Q DP problem: 544.09/242.22 The TRS P consists of the following rules: 544.09/242.22 544.09/242.22 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.22 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.22 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.22 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.22 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.22 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.22 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.22 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.22 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.22 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.22 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.22 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.22 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.22 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.22 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.22 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.22 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.22 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.22 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.22 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.22 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.22 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.22 544.09/242.22 The TRS R consists of the following rules: 544.09/242.22 544.09/242.22 down(a) -> up(f(a)) 544.09/242.22 down(b) -> up(g(b)) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.22 down(f(a)) -> f_flat(down(a)) 544.09/242.22 down(f(b)) -> f_flat(down(b)) 544.09/242.22 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.22 down(f(c)) -> f_flat(down(c)) 544.09/242.22 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.22 down(g(a)) -> g_flat(down(a)) 544.09/242.22 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.22 down(g(b)) -> g_flat(down(b)) 544.09/242.22 down(g(c)) -> g_flat(down(c)) 544.09/242.22 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.22 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.22 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.22 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.22 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.22 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.22 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.22 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.22 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.22 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.22 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.22 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.22 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.22 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.22 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.22 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.22 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.22 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.22 544.09/242.22 The set Q consists of the following terms: 544.09/242.22 544.09/242.22 down(a) 544.09/242.22 down(b) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.22 down(f(a)) 544.09/242.22 down(f(b)) 544.09/242.22 down(f(g(x0))) 544.09/242.22 down(f(c)) 544.09/242.22 down(f(fresh_constant)) 544.09/242.22 down(g(a)) 544.09/242.22 down(g(f(x0))) 544.09/242.22 down(g(b)) 544.09/242.22 down(g(c)) 544.09/242.22 down(g(fresh_constant)) 544.09/242.22 down(f(f(a))) 544.09/242.22 down(f(f(b))) 544.09/242.22 down(f(f(g(x0)))) 544.09/242.22 down(f(f(c))) 544.09/242.22 down(f(f(fresh_constant))) 544.09/242.22 down(g(g(a))) 544.09/242.22 down(g(g(f(x0)))) 544.09/242.22 down(g(g(b))) 544.09/242.22 down(g(g(c))) 544.09/242.22 down(g(g(fresh_constant))) 544.09/242.22 down(f(f(f(a)))) 544.09/242.22 down(f(f(f(b)))) 544.09/242.22 down(f(f(f(g(x0))))) 544.09/242.22 down(f(f(f(c)))) 544.09/242.22 down(f(f(f(fresh_constant)))) 544.09/242.22 down(g(g(g(a)))) 544.09/242.22 down(g(g(g(f(x0))))) 544.09/242.22 down(g(g(g(b)))) 544.09/242.22 down(g(g(g(c)))) 544.09/242.22 down(g(g(g(fresh_constant)))) 544.09/242.22 down(f(f(f(f(a))))) 544.09/242.22 down(f(f(f(f(b))))) 544.09/242.22 down(f(f(f(f(g(x0)))))) 544.09/242.22 down(f(f(f(f(c))))) 544.09/242.22 down(f(f(f(f(fresh_constant))))) 544.09/242.22 down(g(g(g(g(a))))) 544.09/242.22 down(g(g(g(g(f(x0)))))) 544.09/242.22 down(g(g(g(g(b))))) 544.09/242.22 down(g(g(g(g(c))))) 544.09/242.22 down(g(g(g(g(fresh_constant))))) 544.09/242.22 down(f(f(f(f(f(a)))))) 544.09/242.22 down(f(f(f(f(f(b)))))) 544.09/242.22 down(f(f(f(f(f(g(x0))))))) 544.09/242.22 down(f(f(f(f(f(c)))))) 544.09/242.22 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.22 down(g(g(g(g(g(a)))))) 544.09/242.22 down(g(g(g(g(g(f(x0))))))) 544.09/242.22 down(g(g(g(g(g(b)))))) 544.09/242.22 down(g(g(g(g(g(c)))))) 544.09/242.22 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.22 down(f(f(f(f(f(f(a))))))) 544.09/242.22 down(f(f(f(f(f(f(b))))))) 544.09/242.22 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.22 down(f(f(f(f(f(f(c))))))) 544.09/242.22 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.22 down(g(g(g(g(g(g(a))))))) 544.09/242.22 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.22 down(g(g(g(g(g(g(b))))))) 544.09/242.22 down(g(g(g(g(g(g(c))))))) 544.09/242.22 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.22 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.22 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.22 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.22 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.22 f_flat(up(x0)) 544.09/242.22 g_flat(up(x0)) 544.09/242.22 544.09/242.22 We have to consider all minimal (P,Q,R)-chains. 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1195) TransformationProof (EQUIVALENT) 544.09/242.22 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(g_flat(up(g(g(g(g(g(f(a))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.09/242.22 544.09/242.22 (TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))),TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.22 544.09/242.22 544.09/242.22 ---------------------------------------- 544.09/242.22 544.09/242.22 (1196) 544.09/242.22 Obligation: 544.09/242.22 Q DP problem: 544.09/242.22 The TRS P consists of the following rules: 544.09/242.22 544.09/242.22 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.22 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.22 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.22 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.22 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.22 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.22 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.22 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.22 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.22 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.22 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.22 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.22 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.22 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.22 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.22 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.22 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.22 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.22 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.22 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.22 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.22 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.22 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.22 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.22 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.22 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.23 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.23 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.23 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.23 544.09/242.23 The TRS R consists of the following rules: 544.09/242.23 544.09/242.23 down(a) -> up(f(a)) 544.09/242.23 down(b) -> up(g(b)) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.23 down(f(a)) -> f_flat(down(a)) 544.09/242.23 down(f(b)) -> f_flat(down(b)) 544.09/242.23 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.23 down(f(c)) -> f_flat(down(c)) 544.09/242.23 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.23 down(g(a)) -> g_flat(down(a)) 544.09/242.23 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.23 down(g(b)) -> g_flat(down(b)) 544.09/242.23 down(g(c)) -> g_flat(down(c)) 544.09/242.23 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.23 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.23 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.23 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.23 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.23 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.23 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.23 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.23 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.23 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.23 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.23 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.23 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.23 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.23 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.23 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.23 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.23 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.23 544.09/242.23 The set Q consists of the following terms: 544.09/242.23 544.09/242.23 down(a) 544.09/242.23 down(b) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.23 down(f(a)) 544.09/242.23 down(f(b)) 544.09/242.23 down(f(g(x0))) 544.09/242.23 down(f(c)) 544.09/242.23 down(f(fresh_constant)) 544.09/242.23 down(g(a)) 544.09/242.23 down(g(f(x0))) 544.09/242.23 down(g(b)) 544.09/242.23 down(g(c)) 544.09/242.23 down(g(fresh_constant)) 544.09/242.23 down(f(f(a))) 544.09/242.23 down(f(f(b))) 544.09/242.23 down(f(f(g(x0)))) 544.09/242.23 down(f(f(c))) 544.09/242.23 down(f(f(fresh_constant))) 544.09/242.23 down(g(g(a))) 544.09/242.23 down(g(g(f(x0)))) 544.09/242.23 down(g(g(b))) 544.09/242.23 down(g(g(c))) 544.09/242.23 down(g(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) 544.09/242.23 down(f(f(f(g(x0))))) 544.09/242.23 down(f(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) 544.09/242.23 down(g(g(g(f(x0))))) 544.09/242.23 down(g(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(x0)))))) 544.09/242.23 down(f(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(x0)))))) 544.09/242.23 down(g(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(x0))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(x0))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 f_flat(up(x0)) 544.09/242.23 g_flat(up(x0)) 544.09/242.23 544.09/242.23 We have to consider all minimal (P,Q,R)-chains. 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1197) TransformationProof (EQUIVALENT) 544.09/242.23 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.23 544.09/242.23 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.23 544.09/242.23 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1198) 544.09/242.23 Obligation: 544.09/242.23 Q DP problem: 544.09/242.23 The TRS P consists of the following rules: 544.09/242.23 544.09/242.23 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.23 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.23 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.23 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.23 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.23 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.23 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.23 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.23 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.23 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.23 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.23 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.23 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.23 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.23 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.23 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.23 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.23 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.23 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.23 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.23 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.23 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.23 544.09/242.23 The TRS R consists of the following rules: 544.09/242.23 544.09/242.23 down(a) -> up(f(a)) 544.09/242.23 down(b) -> up(g(b)) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.23 down(f(a)) -> f_flat(down(a)) 544.09/242.23 down(f(b)) -> f_flat(down(b)) 544.09/242.23 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.23 down(f(c)) -> f_flat(down(c)) 544.09/242.23 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.23 down(g(a)) -> g_flat(down(a)) 544.09/242.23 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.23 down(g(b)) -> g_flat(down(b)) 544.09/242.23 down(g(c)) -> g_flat(down(c)) 544.09/242.23 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.23 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.23 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.23 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.23 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.23 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.23 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.23 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.23 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.23 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.23 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.23 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.23 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.23 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.23 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.23 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.23 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.23 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.23 544.09/242.23 The set Q consists of the following terms: 544.09/242.23 544.09/242.23 down(a) 544.09/242.23 down(b) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.23 down(f(a)) 544.09/242.23 down(f(b)) 544.09/242.23 down(f(g(x0))) 544.09/242.23 down(f(c)) 544.09/242.23 down(f(fresh_constant)) 544.09/242.23 down(g(a)) 544.09/242.23 down(g(f(x0))) 544.09/242.23 down(g(b)) 544.09/242.23 down(g(c)) 544.09/242.23 down(g(fresh_constant)) 544.09/242.23 down(f(f(a))) 544.09/242.23 down(f(f(b))) 544.09/242.23 down(f(f(g(x0)))) 544.09/242.23 down(f(f(c))) 544.09/242.23 down(f(f(fresh_constant))) 544.09/242.23 down(g(g(a))) 544.09/242.23 down(g(g(f(x0)))) 544.09/242.23 down(g(g(b))) 544.09/242.23 down(g(g(c))) 544.09/242.23 down(g(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) 544.09/242.23 down(f(f(f(g(x0))))) 544.09/242.23 down(f(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) 544.09/242.23 down(g(g(g(f(x0))))) 544.09/242.23 down(g(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(x0)))))) 544.09/242.23 down(f(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(x0)))))) 544.09/242.23 down(g(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(x0))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(x0))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 f_flat(up(x0)) 544.09/242.23 g_flat(up(x0)) 544.09/242.23 544.09/242.23 We have to consider all minimal (P,Q,R)-chains. 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1199) TransformationProof (EQUIVALENT) 544.09/242.23 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.23 544.09/242.23 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.23 544.09/242.23 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1200) 544.09/242.23 Obligation: 544.09/242.23 Q DP problem: 544.09/242.23 The TRS P consists of the following rules: 544.09/242.23 544.09/242.23 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.23 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.23 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.23 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.23 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.23 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.23 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.23 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.23 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.23 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.23 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.23 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.23 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.23 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.23 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.23 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.23 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.23 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.23 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.23 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.23 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.23 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.23 544.09/242.23 The TRS R consists of the following rules: 544.09/242.23 544.09/242.23 down(a) -> up(f(a)) 544.09/242.23 down(b) -> up(g(b)) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.23 down(f(a)) -> f_flat(down(a)) 544.09/242.23 down(f(b)) -> f_flat(down(b)) 544.09/242.23 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.23 down(f(c)) -> f_flat(down(c)) 544.09/242.23 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.23 down(g(a)) -> g_flat(down(a)) 544.09/242.23 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.23 down(g(b)) -> g_flat(down(b)) 544.09/242.23 down(g(c)) -> g_flat(down(c)) 544.09/242.23 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.23 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.23 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.23 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.23 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.23 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.23 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.23 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.23 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.23 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.23 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.23 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.23 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.23 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.23 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.23 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.23 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.23 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.23 544.09/242.23 The set Q consists of the following terms: 544.09/242.23 544.09/242.23 down(a) 544.09/242.23 down(b) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.23 down(f(a)) 544.09/242.23 down(f(b)) 544.09/242.23 down(f(g(x0))) 544.09/242.23 down(f(c)) 544.09/242.23 down(f(fresh_constant)) 544.09/242.23 down(g(a)) 544.09/242.23 down(g(f(x0))) 544.09/242.23 down(g(b)) 544.09/242.23 down(g(c)) 544.09/242.23 down(g(fresh_constant)) 544.09/242.23 down(f(f(a))) 544.09/242.23 down(f(f(b))) 544.09/242.23 down(f(f(g(x0)))) 544.09/242.23 down(f(f(c))) 544.09/242.23 down(f(f(fresh_constant))) 544.09/242.23 down(g(g(a))) 544.09/242.23 down(g(g(f(x0)))) 544.09/242.23 down(g(g(b))) 544.09/242.23 down(g(g(c))) 544.09/242.23 down(g(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) 544.09/242.23 down(f(f(f(g(x0))))) 544.09/242.23 down(f(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) 544.09/242.23 down(g(g(g(f(x0))))) 544.09/242.23 down(g(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(x0)))))) 544.09/242.23 down(f(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(x0)))))) 544.09/242.23 down(g(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(x0))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(x0))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 f_flat(up(x0)) 544.09/242.23 g_flat(up(x0)) 544.09/242.23 544.09/242.23 We have to consider all minimal (P,Q,R)-chains. 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1201) TransformationProof (EQUIVALENT) 544.09/242.23 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(f(a)))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.23 544.09/242.23 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a))))))))))))) 544.09/242.23 544.09/242.23 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1202) 544.09/242.23 Obligation: 544.09/242.23 Q DP problem: 544.09/242.23 The TRS P consists of the following rules: 544.09/242.23 544.09/242.23 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.23 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.23 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.23 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.23 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.23 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.23 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.23 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.23 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.23 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.23 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.23 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.23 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.23 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.23 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.23 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.23 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.23 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.23 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.23 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.23 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.23 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.23 544.09/242.23 The TRS R consists of the following rules: 544.09/242.23 544.09/242.23 down(a) -> up(f(a)) 544.09/242.23 down(b) -> up(g(b)) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.23 down(f(a)) -> f_flat(down(a)) 544.09/242.23 down(f(b)) -> f_flat(down(b)) 544.09/242.23 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.23 down(f(c)) -> f_flat(down(c)) 544.09/242.23 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.23 down(g(a)) -> g_flat(down(a)) 544.09/242.23 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.23 down(g(b)) -> g_flat(down(b)) 544.09/242.23 down(g(c)) -> g_flat(down(c)) 544.09/242.23 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.23 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.23 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.23 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.23 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.23 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.23 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.23 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.23 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.23 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.23 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.23 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.23 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.23 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.23 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.23 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.23 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.23 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.23 544.09/242.23 The set Q consists of the following terms: 544.09/242.23 544.09/242.23 down(a) 544.09/242.23 down(b) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.23 down(f(a)) 544.09/242.23 down(f(b)) 544.09/242.23 down(f(g(x0))) 544.09/242.23 down(f(c)) 544.09/242.23 down(f(fresh_constant)) 544.09/242.23 down(g(a)) 544.09/242.23 down(g(f(x0))) 544.09/242.23 down(g(b)) 544.09/242.23 down(g(c)) 544.09/242.23 down(g(fresh_constant)) 544.09/242.23 down(f(f(a))) 544.09/242.23 down(f(f(b))) 544.09/242.23 down(f(f(g(x0)))) 544.09/242.23 down(f(f(c))) 544.09/242.23 down(f(f(fresh_constant))) 544.09/242.23 down(g(g(a))) 544.09/242.23 down(g(g(f(x0)))) 544.09/242.23 down(g(g(b))) 544.09/242.23 down(g(g(c))) 544.09/242.23 down(g(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) 544.09/242.23 down(f(f(f(g(x0))))) 544.09/242.23 down(f(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) 544.09/242.23 down(g(g(g(f(x0))))) 544.09/242.23 down(g(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(x0)))))) 544.09/242.23 down(f(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(x0)))))) 544.09/242.23 down(g(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(x0))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(x0))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 f_flat(up(x0)) 544.09/242.23 g_flat(up(x0)) 544.09/242.23 544.09/242.23 We have to consider all minimal (P,Q,R)-chains. 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1203) TransformationProof (EQUIVALENT) 544.09/242.23 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.09/242.23 544.09/242.23 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.23 544.09/242.23 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1204) 544.09/242.23 Obligation: 544.09/242.23 Q DP problem: 544.09/242.23 The TRS P consists of the following rules: 544.09/242.23 544.09/242.23 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.23 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.23 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.23 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.23 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.23 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.23 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.23 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.23 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.23 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.23 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.23 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.23 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.23 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.23 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.23 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.23 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.23 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.23 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.23 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.23 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.23 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.23 544.09/242.23 The TRS R consists of the following rules: 544.09/242.23 544.09/242.23 down(a) -> up(f(a)) 544.09/242.23 down(b) -> up(g(b)) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.23 down(f(a)) -> f_flat(down(a)) 544.09/242.23 down(f(b)) -> f_flat(down(b)) 544.09/242.23 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.23 down(f(c)) -> f_flat(down(c)) 544.09/242.23 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.23 down(g(a)) -> g_flat(down(a)) 544.09/242.23 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.23 down(g(b)) -> g_flat(down(b)) 544.09/242.23 down(g(c)) -> g_flat(down(c)) 544.09/242.23 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.23 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.23 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.23 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.23 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.23 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.23 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.23 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.23 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.23 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.23 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.23 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.23 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.23 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.23 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.23 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.23 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.23 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.23 544.09/242.23 The set Q consists of the following terms: 544.09/242.23 544.09/242.23 down(a) 544.09/242.23 down(b) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.23 down(f(a)) 544.09/242.23 down(f(b)) 544.09/242.23 down(f(g(x0))) 544.09/242.23 down(f(c)) 544.09/242.23 down(f(fresh_constant)) 544.09/242.23 down(g(a)) 544.09/242.23 down(g(f(x0))) 544.09/242.23 down(g(b)) 544.09/242.23 down(g(c)) 544.09/242.23 down(g(fresh_constant)) 544.09/242.23 down(f(f(a))) 544.09/242.23 down(f(f(b))) 544.09/242.23 down(f(f(g(x0)))) 544.09/242.23 down(f(f(c))) 544.09/242.23 down(f(f(fresh_constant))) 544.09/242.23 down(g(g(a))) 544.09/242.23 down(g(g(f(x0)))) 544.09/242.23 down(g(g(b))) 544.09/242.23 down(g(g(c))) 544.09/242.23 down(g(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) 544.09/242.23 down(f(f(f(g(x0))))) 544.09/242.23 down(f(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) 544.09/242.23 down(g(g(g(f(x0))))) 544.09/242.23 down(g(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(x0)))))) 544.09/242.23 down(f(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(x0)))))) 544.09/242.23 down(g(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(x0))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(x0))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 f_flat(up(x0)) 544.09/242.23 g_flat(up(x0)) 544.09/242.23 544.09/242.23 We have to consider all minimal (P,Q,R)-chains. 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1205) TransformationProof (EQUIVALENT) 544.09/242.23 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.23 544.09/242.23 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.23 544.09/242.23 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1206) 544.09/242.23 Obligation: 544.09/242.23 Q DP problem: 544.09/242.23 The TRS P consists of the following rules: 544.09/242.23 544.09/242.23 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.23 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.23 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.23 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.23 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.23 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.23 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.23 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.23 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.23 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.23 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.23 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.23 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.23 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.23 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.23 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.23 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.23 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.23 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.23 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.23 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.23 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.23 544.09/242.23 The TRS R consists of the following rules: 544.09/242.23 544.09/242.23 down(a) -> up(f(a)) 544.09/242.23 down(b) -> up(g(b)) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.23 down(f(a)) -> f_flat(down(a)) 544.09/242.23 down(f(b)) -> f_flat(down(b)) 544.09/242.23 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.23 down(f(c)) -> f_flat(down(c)) 544.09/242.23 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.23 down(g(a)) -> g_flat(down(a)) 544.09/242.23 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.23 down(g(b)) -> g_flat(down(b)) 544.09/242.23 down(g(c)) -> g_flat(down(c)) 544.09/242.23 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.23 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.23 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.23 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.23 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.23 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.23 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.23 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.23 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.23 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.23 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.23 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.23 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.23 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.23 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.23 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.23 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.23 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.23 544.09/242.23 The set Q consists of the following terms: 544.09/242.23 544.09/242.23 down(a) 544.09/242.23 down(b) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.23 down(f(a)) 544.09/242.23 down(f(b)) 544.09/242.23 down(f(g(x0))) 544.09/242.23 down(f(c)) 544.09/242.23 down(f(fresh_constant)) 544.09/242.23 down(g(a)) 544.09/242.23 down(g(f(x0))) 544.09/242.23 down(g(b)) 544.09/242.23 down(g(c)) 544.09/242.23 down(g(fresh_constant)) 544.09/242.23 down(f(f(a))) 544.09/242.23 down(f(f(b))) 544.09/242.23 down(f(f(g(x0)))) 544.09/242.23 down(f(f(c))) 544.09/242.23 down(f(f(fresh_constant))) 544.09/242.23 down(g(g(a))) 544.09/242.23 down(g(g(f(x0)))) 544.09/242.23 down(g(g(b))) 544.09/242.23 down(g(g(c))) 544.09/242.23 down(g(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) 544.09/242.23 down(f(f(f(g(x0))))) 544.09/242.23 down(f(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) 544.09/242.23 down(g(g(g(f(x0))))) 544.09/242.23 down(g(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(x0)))))) 544.09/242.23 down(f(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(x0)))))) 544.09/242.23 down(g(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(x0))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(x0))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 f_flat(up(x0)) 544.09/242.23 g_flat(up(x0)) 544.09/242.23 544.09/242.23 We have to consider all minimal (P,Q,R)-chains. 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1207) TransformationProof (EQUIVALENT) 544.09/242.23 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(a)))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.23 544.09/242.23 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a))))))))))))) 544.09/242.23 544.09/242.23 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1208) 544.09/242.23 Obligation: 544.09/242.23 Q DP problem: 544.09/242.23 The TRS P consists of the following rules: 544.09/242.23 544.09/242.23 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.23 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.23 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.23 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.23 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.23 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.23 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.23 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.23 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.23 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.23 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.23 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.23 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.23 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.23 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.23 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.23 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.23 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.23 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.23 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.23 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.23 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.23 544.09/242.23 The TRS R consists of the following rules: 544.09/242.23 544.09/242.23 down(a) -> up(f(a)) 544.09/242.23 down(b) -> up(g(b)) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.23 down(f(a)) -> f_flat(down(a)) 544.09/242.23 down(f(b)) -> f_flat(down(b)) 544.09/242.23 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.23 down(f(c)) -> f_flat(down(c)) 544.09/242.23 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.23 down(g(a)) -> g_flat(down(a)) 544.09/242.23 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.23 down(g(b)) -> g_flat(down(b)) 544.09/242.23 down(g(c)) -> g_flat(down(c)) 544.09/242.23 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.23 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.23 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.23 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.23 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.23 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.23 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.23 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.23 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.23 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.23 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.23 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.23 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.23 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.23 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.23 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.23 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.23 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.23 544.09/242.23 The set Q consists of the following terms: 544.09/242.23 544.09/242.23 down(a) 544.09/242.23 down(b) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.23 down(f(a)) 544.09/242.23 down(f(b)) 544.09/242.23 down(f(g(x0))) 544.09/242.23 down(f(c)) 544.09/242.23 down(f(fresh_constant)) 544.09/242.23 down(g(a)) 544.09/242.23 down(g(f(x0))) 544.09/242.23 down(g(b)) 544.09/242.23 down(g(c)) 544.09/242.23 down(g(fresh_constant)) 544.09/242.23 down(f(f(a))) 544.09/242.23 down(f(f(b))) 544.09/242.23 down(f(f(g(x0)))) 544.09/242.23 down(f(f(c))) 544.09/242.23 down(f(f(fresh_constant))) 544.09/242.23 down(g(g(a))) 544.09/242.23 down(g(g(f(x0)))) 544.09/242.23 down(g(g(b))) 544.09/242.23 down(g(g(c))) 544.09/242.23 down(g(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) 544.09/242.23 down(f(f(f(g(x0))))) 544.09/242.23 down(f(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) 544.09/242.23 down(g(g(g(f(x0))))) 544.09/242.23 down(g(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(x0)))))) 544.09/242.23 down(f(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(x0)))))) 544.09/242.23 down(g(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(x0))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(x0))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 f_flat(up(x0)) 544.09/242.23 g_flat(up(x0)) 544.09/242.23 544.09/242.23 We have to consider all minimal (P,Q,R)-chains. 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1209) TransformationProof (EQUIVALENT) 544.09/242.23 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(g(b)))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.23 544.09/242.23 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b))))))))))))) 544.09/242.23 544.09/242.23 544.09/242.23 ---------------------------------------- 544.09/242.23 544.09/242.23 (1210) 544.09/242.23 Obligation: 544.09/242.23 Q DP problem: 544.09/242.23 The TRS P consists of the following rules: 544.09/242.23 544.09/242.23 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.23 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.23 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.23 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.23 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.23 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.23 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.23 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.23 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.23 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.23 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.23 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.23 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.23 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.23 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.23 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.23 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.23 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.23 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.23 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.23 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.23 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.23 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.23 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.23 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.23 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.23 544.09/242.23 The TRS R consists of the following rules: 544.09/242.23 544.09/242.23 down(a) -> up(f(a)) 544.09/242.23 down(b) -> up(g(b)) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.23 down(f(a)) -> f_flat(down(a)) 544.09/242.23 down(f(b)) -> f_flat(down(b)) 544.09/242.23 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.23 down(f(c)) -> f_flat(down(c)) 544.09/242.23 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.23 down(g(a)) -> g_flat(down(a)) 544.09/242.23 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.23 down(g(b)) -> g_flat(down(b)) 544.09/242.23 down(g(c)) -> g_flat(down(c)) 544.09/242.23 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.23 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.23 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.23 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.23 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.23 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.23 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.23 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.23 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.23 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.23 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.23 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.23 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.23 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.23 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.23 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.23 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.23 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.23 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.23 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.23 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.23 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.23 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.23 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.23 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.23 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.23 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.23 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.23 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.23 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.23 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.23 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.23 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.23 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.23 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.23 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.23 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.23 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.23 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.23 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.23 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.23 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.23 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.23 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.23 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.23 544.09/242.23 The set Q consists of the following terms: 544.09/242.23 544.09/242.23 down(a) 544.09/242.23 down(b) 544.09/242.23 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.23 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.23 down(f(a)) 544.09/242.23 down(f(b)) 544.09/242.23 down(f(g(x0))) 544.09/242.23 down(f(c)) 544.09/242.23 down(f(fresh_constant)) 544.09/242.23 down(g(a)) 544.09/242.23 down(g(f(x0))) 544.09/242.23 down(g(b)) 544.09/242.23 down(g(c)) 544.09/242.23 down(g(fresh_constant)) 544.09/242.23 down(f(f(a))) 544.09/242.23 down(f(f(b))) 544.09/242.23 down(f(f(g(x0)))) 544.09/242.23 down(f(f(c))) 544.09/242.23 down(f(f(fresh_constant))) 544.09/242.23 down(g(g(a))) 544.09/242.23 down(g(g(f(x0)))) 544.09/242.23 down(g(g(b))) 544.09/242.23 down(g(g(c))) 544.09/242.23 down(g(g(fresh_constant))) 544.09/242.23 down(f(f(f(a)))) 544.09/242.23 down(f(f(f(b)))) 544.09/242.23 down(f(f(f(g(x0))))) 544.09/242.23 down(f(f(f(c)))) 544.09/242.23 down(f(f(f(fresh_constant)))) 544.09/242.23 down(g(g(g(a)))) 544.09/242.23 down(g(g(g(f(x0))))) 544.09/242.23 down(g(g(g(b)))) 544.09/242.23 down(g(g(g(c)))) 544.09/242.23 down(g(g(g(fresh_constant)))) 544.09/242.23 down(f(f(f(f(a))))) 544.09/242.23 down(f(f(f(f(b))))) 544.09/242.23 down(f(f(f(f(g(x0)))))) 544.09/242.23 down(f(f(f(f(c))))) 544.09/242.23 down(f(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(x0)))))) 544.09/242.24 down(g(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(x0))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(x0))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 f_flat(up(x0)) 544.09/242.24 g_flat(up(x0)) 544.09/242.24 544.09/242.24 We have to consider all minimal (P,Q,R)-chains. 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1211) TransformationProof (EQUIVALENT) 544.09/242.24 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(b)))))))))))) at position [0,0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.24 544.09/242.24 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b))))))))))))) 544.09/242.24 544.09/242.24 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1212) 544.09/242.24 Obligation: 544.09/242.24 Q DP problem: 544.09/242.24 The TRS P consists of the following rules: 544.09/242.24 544.09/242.24 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.24 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.24 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.24 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.24 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.24 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.24 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.24 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.24 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.24 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.24 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.24 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.24 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.24 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.24 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.24 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.24 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.24 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.24 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.24 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.24 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.24 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.24 544.09/242.24 The TRS R consists of the following rules: 544.09/242.24 544.09/242.24 down(a) -> up(f(a)) 544.09/242.24 down(b) -> up(g(b)) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.24 down(f(a)) -> f_flat(down(a)) 544.09/242.24 down(f(b)) -> f_flat(down(b)) 544.09/242.24 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.24 down(f(c)) -> f_flat(down(c)) 544.09/242.24 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.24 down(g(a)) -> g_flat(down(a)) 544.09/242.24 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.24 down(g(b)) -> g_flat(down(b)) 544.09/242.24 down(g(c)) -> g_flat(down(c)) 544.09/242.24 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.24 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.24 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.24 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.24 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.24 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.24 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.24 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.24 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.24 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.24 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.24 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.24 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.24 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.24 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.24 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.24 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.24 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.24 544.09/242.24 The set Q consists of the following terms: 544.09/242.24 544.09/242.24 down(a) 544.09/242.24 down(b) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.24 down(f(a)) 544.09/242.24 down(f(b)) 544.09/242.24 down(f(g(x0))) 544.09/242.24 down(f(c)) 544.09/242.24 down(f(fresh_constant)) 544.09/242.24 down(g(a)) 544.09/242.24 down(g(f(x0))) 544.09/242.24 down(g(b)) 544.09/242.24 down(g(c)) 544.09/242.24 down(g(fresh_constant)) 544.09/242.24 down(f(f(a))) 544.09/242.24 down(f(f(b))) 544.09/242.24 down(f(f(g(x0)))) 544.09/242.24 down(f(f(c))) 544.09/242.24 down(f(f(fresh_constant))) 544.09/242.24 down(g(g(a))) 544.09/242.24 down(g(g(f(x0)))) 544.09/242.24 down(g(g(b))) 544.09/242.24 down(g(g(c))) 544.09/242.24 down(g(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) 544.09/242.24 down(f(f(f(g(x0))))) 544.09/242.24 down(f(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) 544.09/242.24 down(g(g(g(f(x0))))) 544.09/242.24 down(g(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(x0)))))) 544.09/242.24 down(f(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(x0)))))) 544.09/242.24 down(g(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(x0))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(x0))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 f_flat(up(x0)) 544.09/242.24 g_flat(up(x0)) 544.09/242.24 544.09/242.24 We have to consider all minimal (P,Q,R)-chains. 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1213) TransformationProof (EQUIVALENT) 544.09/242.24 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.24 544.09/242.24 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.24 544.09/242.24 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1214) 544.09/242.24 Obligation: 544.09/242.24 Q DP problem: 544.09/242.24 The TRS P consists of the following rules: 544.09/242.24 544.09/242.24 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.24 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.24 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.24 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.24 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.24 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.24 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.24 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.24 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.24 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.24 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.24 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.24 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.24 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.24 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.24 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.24 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.24 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.24 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.24 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.24 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.24 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.24 544.09/242.24 The TRS R consists of the following rules: 544.09/242.24 544.09/242.24 down(a) -> up(f(a)) 544.09/242.24 down(b) -> up(g(b)) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.24 down(f(a)) -> f_flat(down(a)) 544.09/242.24 down(f(b)) -> f_flat(down(b)) 544.09/242.24 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.24 down(f(c)) -> f_flat(down(c)) 544.09/242.24 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.24 down(g(a)) -> g_flat(down(a)) 544.09/242.24 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.24 down(g(b)) -> g_flat(down(b)) 544.09/242.24 down(g(c)) -> g_flat(down(c)) 544.09/242.24 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.24 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.24 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.24 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.24 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.24 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.24 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.24 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.24 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.24 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.24 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.24 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.24 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.24 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.24 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.24 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.24 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.24 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.24 544.09/242.24 The set Q consists of the following terms: 544.09/242.24 544.09/242.24 down(a) 544.09/242.24 down(b) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.24 down(f(a)) 544.09/242.24 down(f(b)) 544.09/242.24 down(f(g(x0))) 544.09/242.24 down(f(c)) 544.09/242.24 down(f(fresh_constant)) 544.09/242.24 down(g(a)) 544.09/242.24 down(g(f(x0))) 544.09/242.24 down(g(b)) 544.09/242.24 down(g(c)) 544.09/242.24 down(g(fresh_constant)) 544.09/242.24 down(f(f(a))) 544.09/242.24 down(f(f(b))) 544.09/242.24 down(f(f(g(x0)))) 544.09/242.24 down(f(f(c))) 544.09/242.24 down(f(f(fresh_constant))) 544.09/242.24 down(g(g(a))) 544.09/242.24 down(g(g(f(x0)))) 544.09/242.24 down(g(g(b))) 544.09/242.24 down(g(g(c))) 544.09/242.24 down(g(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) 544.09/242.24 down(f(f(f(g(x0))))) 544.09/242.24 down(f(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) 544.09/242.24 down(g(g(g(f(x0))))) 544.09/242.24 down(g(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(x0)))))) 544.09/242.24 down(f(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(x0)))))) 544.09/242.24 down(g(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(x0))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(x0))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 f_flat(up(x0)) 544.09/242.24 g_flat(up(x0)) 544.09/242.24 544.09/242.24 We have to consider all minimal (P,Q,R)-chains. 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1215) TransformationProof (EQUIVALENT) 544.09/242.24 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.24 544.09/242.24 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) 544.09/242.24 544.09/242.24 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1216) 544.09/242.24 Obligation: 544.09/242.24 Q DP problem: 544.09/242.24 The TRS P consists of the following rules: 544.09/242.24 544.09/242.24 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.24 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.24 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.24 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.24 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.24 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.24 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.24 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.24 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.24 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.24 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.24 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.24 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.24 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.24 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.24 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.24 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.24 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.24 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.24 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.24 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.24 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.24 544.09/242.24 The TRS R consists of the following rules: 544.09/242.24 544.09/242.24 down(a) -> up(f(a)) 544.09/242.24 down(b) -> up(g(b)) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.24 down(f(a)) -> f_flat(down(a)) 544.09/242.24 down(f(b)) -> f_flat(down(b)) 544.09/242.24 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.24 down(f(c)) -> f_flat(down(c)) 544.09/242.24 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.24 down(g(a)) -> g_flat(down(a)) 544.09/242.24 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.24 down(g(b)) -> g_flat(down(b)) 544.09/242.24 down(g(c)) -> g_flat(down(c)) 544.09/242.24 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.24 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.24 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.24 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.24 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.24 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.24 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.24 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.24 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.24 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.24 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.24 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.24 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.24 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.24 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.24 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.24 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.24 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.24 544.09/242.24 The set Q consists of the following terms: 544.09/242.24 544.09/242.24 down(a) 544.09/242.24 down(b) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.24 down(f(a)) 544.09/242.24 down(f(b)) 544.09/242.24 down(f(g(x0))) 544.09/242.24 down(f(c)) 544.09/242.24 down(f(fresh_constant)) 544.09/242.24 down(g(a)) 544.09/242.24 down(g(f(x0))) 544.09/242.24 down(g(b)) 544.09/242.24 down(g(c)) 544.09/242.24 down(g(fresh_constant)) 544.09/242.24 down(f(f(a))) 544.09/242.24 down(f(f(b))) 544.09/242.24 down(f(f(g(x0)))) 544.09/242.24 down(f(f(c))) 544.09/242.24 down(f(f(fresh_constant))) 544.09/242.24 down(g(g(a))) 544.09/242.24 down(g(g(f(x0)))) 544.09/242.24 down(g(g(b))) 544.09/242.24 down(g(g(c))) 544.09/242.24 down(g(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) 544.09/242.24 down(f(f(f(g(x0))))) 544.09/242.24 down(f(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) 544.09/242.24 down(g(g(g(f(x0))))) 544.09/242.24 down(g(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(x0)))))) 544.09/242.24 down(f(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(x0)))))) 544.09/242.24 down(g(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(x0))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(x0))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 f_flat(up(x0)) 544.09/242.24 g_flat(up(x0)) 544.09/242.24 544.09/242.24 We have to consider all minimal (P,Q,R)-chains. 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1217) TransformationProof (EQUIVALENT) 544.09/242.24 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.09/242.24 544.09/242.24 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a))))))))))) 544.09/242.24 544.09/242.24 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1218) 544.09/242.24 Obligation: 544.09/242.24 Q DP problem: 544.09/242.24 The TRS P consists of the following rules: 544.09/242.24 544.09/242.24 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.24 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.24 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.24 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.24 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.24 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.24 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.24 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.24 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.24 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.24 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.24 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.24 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.24 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.24 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.24 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.24 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.24 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.24 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.24 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.24 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.24 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.24 544.09/242.24 The TRS R consists of the following rules: 544.09/242.24 544.09/242.24 down(a) -> up(f(a)) 544.09/242.24 down(b) -> up(g(b)) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.24 down(f(a)) -> f_flat(down(a)) 544.09/242.24 down(f(b)) -> f_flat(down(b)) 544.09/242.24 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.24 down(f(c)) -> f_flat(down(c)) 544.09/242.24 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.24 down(g(a)) -> g_flat(down(a)) 544.09/242.24 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.24 down(g(b)) -> g_flat(down(b)) 544.09/242.24 down(g(c)) -> g_flat(down(c)) 544.09/242.24 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.24 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.24 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.24 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.24 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.24 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.24 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.24 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.24 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.24 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.24 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.24 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.24 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.24 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.24 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.24 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.24 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.24 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.24 544.09/242.24 The set Q consists of the following terms: 544.09/242.24 544.09/242.24 down(a) 544.09/242.24 down(b) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.24 down(f(a)) 544.09/242.24 down(f(b)) 544.09/242.24 down(f(g(x0))) 544.09/242.24 down(f(c)) 544.09/242.24 down(f(fresh_constant)) 544.09/242.24 down(g(a)) 544.09/242.24 down(g(f(x0))) 544.09/242.24 down(g(b)) 544.09/242.24 down(g(c)) 544.09/242.24 down(g(fresh_constant)) 544.09/242.24 down(f(f(a))) 544.09/242.24 down(f(f(b))) 544.09/242.24 down(f(f(g(x0)))) 544.09/242.24 down(f(f(c))) 544.09/242.24 down(f(f(fresh_constant))) 544.09/242.24 down(g(g(a))) 544.09/242.24 down(g(g(f(x0)))) 544.09/242.24 down(g(g(b))) 544.09/242.24 down(g(g(c))) 544.09/242.24 down(g(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) 544.09/242.24 down(f(f(f(g(x0))))) 544.09/242.24 down(f(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) 544.09/242.24 down(g(g(g(f(x0))))) 544.09/242.24 down(g(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(x0)))))) 544.09/242.24 down(f(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(x0)))))) 544.09/242.24 down(g(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(x0))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(x0))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 f_flat(up(x0)) 544.09/242.24 g_flat(up(x0)) 544.09/242.24 544.09/242.24 We have to consider all minimal (P,Q,R)-chains. 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1219) TransformationProof (EQUIVALENT) 544.09/242.24 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.24 544.09/242.24 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) 544.09/242.24 544.09/242.24 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1220) 544.09/242.24 Obligation: 544.09/242.24 Q DP problem: 544.09/242.24 The TRS P consists of the following rules: 544.09/242.24 544.09/242.24 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.24 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.24 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.24 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.24 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.24 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.24 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.24 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.24 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.24 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.24 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.24 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.24 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.24 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.24 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.24 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.24 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.24 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.24 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.24 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.24 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.24 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.24 544.09/242.24 The TRS R consists of the following rules: 544.09/242.24 544.09/242.24 down(a) -> up(f(a)) 544.09/242.24 down(b) -> up(g(b)) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.24 down(f(a)) -> f_flat(down(a)) 544.09/242.24 down(f(b)) -> f_flat(down(b)) 544.09/242.24 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.24 down(f(c)) -> f_flat(down(c)) 544.09/242.24 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.24 down(g(a)) -> g_flat(down(a)) 544.09/242.24 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.24 down(g(b)) -> g_flat(down(b)) 544.09/242.24 down(g(c)) -> g_flat(down(c)) 544.09/242.24 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.24 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.24 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.24 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.24 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.24 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.24 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.24 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.24 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.24 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.24 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.24 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.24 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.24 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.24 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.24 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.24 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.24 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.24 544.09/242.24 The set Q consists of the following terms: 544.09/242.24 544.09/242.24 down(a) 544.09/242.24 down(b) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.24 down(f(a)) 544.09/242.24 down(f(b)) 544.09/242.24 down(f(g(x0))) 544.09/242.24 down(f(c)) 544.09/242.24 down(f(fresh_constant)) 544.09/242.24 down(g(a)) 544.09/242.24 down(g(f(x0))) 544.09/242.24 down(g(b)) 544.09/242.24 down(g(c)) 544.09/242.24 down(g(fresh_constant)) 544.09/242.24 down(f(f(a))) 544.09/242.24 down(f(f(b))) 544.09/242.24 down(f(f(g(x0)))) 544.09/242.24 down(f(f(c))) 544.09/242.24 down(f(f(fresh_constant))) 544.09/242.24 down(g(g(a))) 544.09/242.24 down(g(g(f(x0)))) 544.09/242.24 down(g(g(b))) 544.09/242.24 down(g(g(c))) 544.09/242.24 down(g(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) 544.09/242.24 down(f(f(f(g(x0))))) 544.09/242.24 down(f(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) 544.09/242.24 down(g(g(g(f(x0))))) 544.09/242.24 down(g(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(x0)))))) 544.09/242.24 down(f(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(x0)))))) 544.09/242.24 down(g(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(x0))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(x0))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 f_flat(up(x0)) 544.09/242.24 g_flat(up(x0)) 544.09/242.24 544.09/242.24 We have to consider all minimal (P,Q,R)-chains. 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1221) TransformationProof (EQUIVALENT) 544.09/242.24 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(f(a)))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.24 544.09/242.24 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a))))))))))))) 544.09/242.24 544.09/242.24 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1222) 544.09/242.24 Obligation: 544.09/242.24 Q DP problem: 544.09/242.24 The TRS P consists of the following rules: 544.09/242.24 544.09/242.24 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.24 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.24 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.24 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.24 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.24 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.24 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.24 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.24 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.24 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.24 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.24 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.24 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.24 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.24 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.24 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.24 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.24 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.24 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.24 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.24 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.24 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.24 544.09/242.24 The TRS R consists of the following rules: 544.09/242.24 544.09/242.24 down(a) -> up(f(a)) 544.09/242.24 down(b) -> up(g(b)) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.24 down(f(a)) -> f_flat(down(a)) 544.09/242.24 down(f(b)) -> f_flat(down(b)) 544.09/242.24 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.24 down(f(c)) -> f_flat(down(c)) 544.09/242.24 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.24 down(g(a)) -> g_flat(down(a)) 544.09/242.24 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.24 down(g(b)) -> g_flat(down(b)) 544.09/242.24 down(g(c)) -> g_flat(down(c)) 544.09/242.24 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.24 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.24 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.24 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.24 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.24 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.24 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.24 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.24 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.24 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.24 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.24 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.24 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.24 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.24 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.24 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.24 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.24 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.24 544.09/242.24 The set Q consists of the following terms: 544.09/242.24 544.09/242.24 down(a) 544.09/242.24 down(b) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.24 down(f(a)) 544.09/242.24 down(f(b)) 544.09/242.24 down(f(g(x0))) 544.09/242.24 down(f(c)) 544.09/242.24 down(f(fresh_constant)) 544.09/242.24 down(g(a)) 544.09/242.24 down(g(f(x0))) 544.09/242.24 down(g(b)) 544.09/242.24 down(g(c)) 544.09/242.24 down(g(fresh_constant)) 544.09/242.24 down(f(f(a))) 544.09/242.24 down(f(f(b))) 544.09/242.24 down(f(f(g(x0)))) 544.09/242.24 down(f(f(c))) 544.09/242.24 down(f(f(fresh_constant))) 544.09/242.24 down(g(g(a))) 544.09/242.24 down(g(g(f(x0)))) 544.09/242.24 down(g(g(b))) 544.09/242.24 down(g(g(c))) 544.09/242.24 down(g(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) 544.09/242.24 down(f(f(f(g(x0))))) 544.09/242.24 down(f(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) 544.09/242.24 down(g(g(g(f(x0))))) 544.09/242.24 down(g(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(x0)))))) 544.09/242.24 down(f(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(x0)))))) 544.09/242.24 down(g(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(x0))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(x0))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 f_flat(up(x0)) 544.09/242.24 g_flat(up(x0)) 544.09/242.24 544.09/242.24 We have to consider all minimal (P,Q,R)-chains. 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1223) TransformationProof (EQUIVALENT) 544.09/242.24 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(g(b)))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.09/242.24 544.09/242.24 (TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))),TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.24 544.09/242.24 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1224) 544.09/242.24 Obligation: 544.09/242.24 Q DP problem: 544.09/242.24 The TRS P consists of the following rules: 544.09/242.24 544.09/242.24 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.24 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.24 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.24 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.24 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.24 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.24 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.24 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.24 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.24 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.24 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.24 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.24 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.24 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.24 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.24 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.24 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.24 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.24 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.24 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.24 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.24 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.24 544.09/242.24 The TRS R consists of the following rules: 544.09/242.24 544.09/242.24 down(a) -> up(f(a)) 544.09/242.24 down(b) -> up(g(b)) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.24 down(f(a)) -> f_flat(down(a)) 544.09/242.24 down(f(b)) -> f_flat(down(b)) 544.09/242.24 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.24 down(f(c)) -> f_flat(down(c)) 544.09/242.24 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.24 down(g(a)) -> g_flat(down(a)) 544.09/242.24 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.24 down(g(b)) -> g_flat(down(b)) 544.09/242.24 down(g(c)) -> g_flat(down(c)) 544.09/242.24 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.24 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.24 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.24 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.24 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.24 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.24 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.24 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.24 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.24 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.24 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.24 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.24 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.24 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.24 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.24 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.24 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.24 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.24 544.09/242.24 The set Q consists of the following terms: 544.09/242.24 544.09/242.24 down(a) 544.09/242.24 down(b) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.24 down(f(a)) 544.09/242.24 down(f(b)) 544.09/242.24 down(f(g(x0))) 544.09/242.24 down(f(c)) 544.09/242.24 down(f(fresh_constant)) 544.09/242.24 down(g(a)) 544.09/242.24 down(g(f(x0))) 544.09/242.24 down(g(b)) 544.09/242.24 down(g(c)) 544.09/242.24 down(g(fresh_constant)) 544.09/242.24 down(f(f(a))) 544.09/242.24 down(f(f(b))) 544.09/242.24 down(f(f(g(x0)))) 544.09/242.24 down(f(f(c))) 544.09/242.24 down(f(f(fresh_constant))) 544.09/242.24 down(g(g(a))) 544.09/242.24 down(g(g(f(x0)))) 544.09/242.24 down(g(g(b))) 544.09/242.24 down(g(g(c))) 544.09/242.24 down(g(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) 544.09/242.24 down(f(f(f(g(x0))))) 544.09/242.24 down(f(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) 544.09/242.24 down(g(g(g(f(x0))))) 544.09/242.24 down(g(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(x0)))))) 544.09/242.24 down(f(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(x0)))))) 544.09/242.24 down(g(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(x0))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(x0))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) 544.09/242.24 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.24 down(g(g(g(g(g(g(a))))))) 544.09/242.24 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.24 down(g(g(g(g(g(g(b))))))) 544.09/242.24 down(g(g(g(g(g(g(c))))))) 544.09/242.24 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.24 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.24 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.24 f_flat(up(x0)) 544.09/242.24 g_flat(up(x0)) 544.09/242.24 544.09/242.24 We have to consider all minimal (P,Q,R)-chains. 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1225) TransformationProof (EQUIVALENT) 544.09/242.24 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.24 544.09/242.24 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.24 544.09/242.24 544.09/242.24 ---------------------------------------- 544.09/242.24 544.09/242.24 (1226) 544.09/242.24 Obligation: 544.09/242.24 Q DP problem: 544.09/242.24 The TRS P consists of the following rules: 544.09/242.24 544.09/242.24 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.24 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.24 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.24 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.24 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.24 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.24 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.24 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.24 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.24 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.24 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.24 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.24 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.24 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.24 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.24 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.24 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.24 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.24 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.24 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.24 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.24 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.24 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.24 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.24 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.24 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.24 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.24 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.24 544.09/242.24 The TRS R consists of the following rules: 544.09/242.24 544.09/242.24 down(a) -> up(f(a)) 544.09/242.24 down(b) -> up(g(b)) 544.09/242.24 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.24 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.24 down(f(a)) -> f_flat(down(a)) 544.09/242.24 down(f(b)) -> f_flat(down(b)) 544.09/242.24 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.24 down(f(c)) -> f_flat(down(c)) 544.09/242.24 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.24 down(g(a)) -> g_flat(down(a)) 544.09/242.24 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.24 down(g(b)) -> g_flat(down(b)) 544.09/242.24 down(g(c)) -> g_flat(down(c)) 544.09/242.24 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.24 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.24 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.24 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.24 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.24 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.24 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.24 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.24 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.24 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.24 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.24 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.24 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.24 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.24 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.24 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.24 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.24 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.24 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.24 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.24 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.24 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.24 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.24 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.24 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.24 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.24 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.24 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.24 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.24 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.24 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.24 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.24 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.24 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.24 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.24 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.24 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.24 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.24 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.24 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.24 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.24 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.24 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.24 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.24 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.25 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.25 544.09/242.25 The set Q consists of the following terms: 544.09/242.25 544.09/242.25 down(a) 544.09/242.25 down(b) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.25 down(f(a)) 544.09/242.25 down(f(b)) 544.09/242.25 down(f(g(x0))) 544.09/242.25 down(f(c)) 544.09/242.25 down(f(fresh_constant)) 544.09/242.25 down(g(a)) 544.09/242.25 down(g(f(x0))) 544.09/242.25 down(g(b)) 544.09/242.25 down(g(c)) 544.09/242.25 down(g(fresh_constant)) 544.09/242.25 down(f(f(a))) 544.09/242.25 down(f(f(b))) 544.09/242.25 down(f(f(g(x0)))) 544.09/242.25 down(f(f(c))) 544.09/242.25 down(f(f(fresh_constant))) 544.09/242.25 down(g(g(a))) 544.09/242.25 down(g(g(f(x0)))) 544.09/242.25 down(g(g(b))) 544.09/242.25 down(g(g(c))) 544.09/242.25 down(g(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) 544.09/242.25 down(f(f(f(g(x0))))) 544.09/242.25 down(f(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) 544.09/242.25 down(g(g(g(f(x0))))) 544.09/242.25 down(g(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(x0)))))) 544.09/242.25 down(f(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(x0)))))) 544.09/242.25 down(g(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(x0))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(x0))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 f_flat(up(x0)) 544.09/242.25 g_flat(up(x0)) 544.09/242.25 544.09/242.25 We have to consider all minimal (P,Q,R)-chains. 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1227) TransformationProof (EQUIVALENT) 544.09/242.25 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(a)))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.25 544.09/242.25 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a))))))))))))) 544.09/242.25 544.09/242.25 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1228) 544.09/242.25 Obligation: 544.09/242.25 Q DP problem: 544.09/242.25 The TRS P consists of the following rules: 544.09/242.25 544.09/242.25 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.25 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.25 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.25 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.25 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.25 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.25 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.25 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.25 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.25 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.25 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.25 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.25 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.25 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.25 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.25 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.25 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.25 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.25 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.25 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.25 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.25 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.25 544.09/242.25 The TRS R consists of the following rules: 544.09/242.25 544.09/242.25 down(a) -> up(f(a)) 544.09/242.25 down(b) -> up(g(b)) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.25 down(f(a)) -> f_flat(down(a)) 544.09/242.25 down(f(b)) -> f_flat(down(b)) 544.09/242.25 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.25 down(f(c)) -> f_flat(down(c)) 544.09/242.25 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.25 down(g(a)) -> g_flat(down(a)) 544.09/242.25 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.25 down(g(b)) -> g_flat(down(b)) 544.09/242.25 down(g(c)) -> g_flat(down(c)) 544.09/242.25 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.25 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.25 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.25 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.25 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.25 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.25 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.25 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.25 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.25 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.25 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.25 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.25 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.25 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.25 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.25 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.25 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.25 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.25 544.09/242.25 The set Q consists of the following terms: 544.09/242.25 544.09/242.25 down(a) 544.09/242.25 down(b) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.25 down(f(a)) 544.09/242.25 down(f(b)) 544.09/242.25 down(f(g(x0))) 544.09/242.25 down(f(c)) 544.09/242.25 down(f(fresh_constant)) 544.09/242.25 down(g(a)) 544.09/242.25 down(g(f(x0))) 544.09/242.25 down(g(b)) 544.09/242.25 down(g(c)) 544.09/242.25 down(g(fresh_constant)) 544.09/242.25 down(f(f(a))) 544.09/242.25 down(f(f(b))) 544.09/242.25 down(f(f(g(x0)))) 544.09/242.25 down(f(f(c))) 544.09/242.25 down(f(f(fresh_constant))) 544.09/242.25 down(g(g(a))) 544.09/242.25 down(g(g(f(x0)))) 544.09/242.25 down(g(g(b))) 544.09/242.25 down(g(g(c))) 544.09/242.25 down(g(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) 544.09/242.25 down(f(f(f(g(x0))))) 544.09/242.25 down(f(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) 544.09/242.25 down(g(g(g(f(x0))))) 544.09/242.25 down(g(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(x0)))))) 544.09/242.25 down(f(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(x0)))))) 544.09/242.25 down(g(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(x0))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(x0))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 f_flat(up(x0)) 544.09/242.25 g_flat(up(x0)) 544.09/242.25 544.09/242.25 We have to consider all minimal (P,Q,R)-chains. 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1229) TransformationProof (EQUIVALENT) 544.09/242.25 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(g(b)))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.25 544.09/242.25 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b))))))))))))) 544.09/242.25 544.09/242.25 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1230) 544.09/242.25 Obligation: 544.09/242.25 Q DP problem: 544.09/242.25 The TRS P consists of the following rules: 544.09/242.25 544.09/242.25 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.25 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.25 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.25 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.25 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.25 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.25 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.25 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.25 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.25 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.25 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.25 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.25 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.25 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.25 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.25 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.25 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.25 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.25 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.25 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.25 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.25 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.25 544.09/242.25 The TRS R consists of the following rules: 544.09/242.25 544.09/242.25 down(a) -> up(f(a)) 544.09/242.25 down(b) -> up(g(b)) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.25 down(f(a)) -> f_flat(down(a)) 544.09/242.25 down(f(b)) -> f_flat(down(b)) 544.09/242.25 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.25 down(f(c)) -> f_flat(down(c)) 544.09/242.25 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.25 down(g(a)) -> g_flat(down(a)) 544.09/242.25 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.25 down(g(b)) -> g_flat(down(b)) 544.09/242.25 down(g(c)) -> g_flat(down(c)) 544.09/242.25 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.25 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.25 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.25 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.25 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.25 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.25 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.25 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.25 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.25 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.25 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.25 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.25 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.25 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.25 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.25 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.25 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.25 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.25 544.09/242.25 The set Q consists of the following terms: 544.09/242.25 544.09/242.25 down(a) 544.09/242.25 down(b) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.25 down(f(a)) 544.09/242.25 down(f(b)) 544.09/242.25 down(f(g(x0))) 544.09/242.25 down(f(c)) 544.09/242.25 down(f(fresh_constant)) 544.09/242.25 down(g(a)) 544.09/242.25 down(g(f(x0))) 544.09/242.25 down(g(b)) 544.09/242.25 down(g(c)) 544.09/242.25 down(g(fresh_constant)) 544.09/242.25 down(f(f(a))) 544.09/242.25 down(f(f(b))) 544.09/242.25 down(f(f(g(x0)))) 544.09/242.25 down(f(f(c))) 544.09/242.25 down(f(f(fresh_constant))) 544.09/242.25 down(g(g(a))) 544.09/242.25 down(g(g(f(x0)))) 544.09/242.25 down(g(g(b))) 544.09/242.25 down(g(g(c))) 544.09/242.25 down(g(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) 544.09/242.25 down(f(f(f(g(x0))))) 544.09/242.25 down(f(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) 544.09/242.25 down(g(g(g(f(x0))))) 544.09/242.25 down(g(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(x0)))))) 544.09/242.25 down(f(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(x0)))))) 544.09/242.25 down(g(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(x0))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(x0))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 f_flat(up(x0)) 544.09/242.25 g_flat(up(x0)) 544.09/242.25 544.09/242.25 We have to consider all minimal (P,Q,R)-chains. 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1231) TransformationProof (EQUIVALENT) 544.09/242.25 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(b)))))))))))) at position [0,0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.25 544.09/242.25 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b))))))))))))) 544.09/242.25 544.09/242.25 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1232) 544.09/242.25 Obligation: 544.09/242.25 Q DP problem: 544.09/242.25 The TRS P consists of the following rules: 544.09/242.25 544.09/242.25 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.25 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.25 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.25 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.25 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.25 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.25 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.25 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.25 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.25 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.25 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.25 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.25 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.25 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.25 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.25 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.25 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.25 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.25 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.25 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.25 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.25 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.25 544.09/242.25 The TRS R consists of the following rules: 544.09/242.25 544.09/242.25 down(a) -> up(f(a)) 544.09/242.25 down(b) -> up(g(b)) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.25 down(f(a)) -> f_flat(down(a)) 544.09/242.25 down(f(b)) -> f_flat(down(b)) 544.09/242.25 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.25 down(f(c)) -> f_flat(down(c)) 544.09/242.25 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.25 down(g(a)) -> g_flat(down(a)) 544.09/242.25 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.25 down(g(b)) -> g_flat(down(b)) 544.09/242.25 down(g(c)) -> g_flat(down(c)) 544.09/242.25 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.25 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.25 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.25 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.25 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.25 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.25 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.25 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.25 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.25 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.25 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.25 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.25 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.25 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.25 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.25 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.25 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.25 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.25 544.09/242.25 The set Q consists of the following terms: 544.09/242.25 544.09/242.25 down(a) 544.09/242.25 down(b) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.25 down(f(a)) 544.09/242.25 down(f(b)) 544.09/242.25 down(f(g(x0))) 544.09/242.25 down(f(c)) 544.09/242.25 down(f(fresh_constant)) 544.09/242.25 down(g(a)) 544.09/242.25 down(g(f(x0))) 544.09/242.25 down(g(b)) 544.09/242.25 down(g(c)) 544.09/242.25 down(g(fresh_constant)) 544.09/242.25 down(f(f(a))) 544.09/242.25 down(f(f(b))) 544.09/242.25 down(f(f(g(x0)))) 544.09/242.25 down(f(f(c))) 544.09/242.25 down(f(f(fresh_constant))) 544.09/242.25 down(g(g(a))) 544.09/242.25 down(g(g(f(x0)))) 544.09/242.25 down(g(g(b))) 544.09/242.25 down(g(g(c))) 544.09/242.25 down(g(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) 544.09/242.25 down(f(f(f(g(x0))))) 544.09/242.25 down(f(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) 544.09/242.25 down(g(g(g(f(x0))))) 544.09/242.25 down(g(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(x0)))))) 544.09/242.25 down(f(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(x0)))))) 544.09/242.25 down(g(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(x0))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(x0))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 f_flat(up(x0)) 544.09/242.25 g_flat(up(x0)) 544.09/242.25 544.09/242.25 We have to consider all minimal (P,Q,R)-chains. 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1233) TransformationProof (EQUIVALENT) 544.09/242.25 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.09/242.25 544.09/242.25 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.25 544.09/242.25 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1234) 544.09/242.25 Obligation: 544.09/242.25 Q DP problem: 544.09/242.25 The TRS P consists of the following rules: 544.09/242.25 544.09/242.25 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.25 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.25 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.25 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.25 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.25 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.25 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.25 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.25 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.25 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.25 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.25 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.25 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.25 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.25 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.25 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.25 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.25 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.25 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.25 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.25 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.25 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.25 544.09/242.25 The TRS R consists of the following rules: 544.09/242.25 544.09/242.25 down(a) -> up(f(a)) 544.09/242.25 down(b) -> up(g(b)) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.25 down(f(a)) -> f_flat(down(a)) 544.09/242.25 down(f(b)) -> f_flat(down(b)) 544.09/242.25 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.25 down(f(c)) -> f_flat(down(c)) 544.09/242.25 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.25 down(g(a)) -> g_flat(down(a)) 544.09/242.25 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.25 down(g(b)) -> g_flat(down(b)) 544.09/242.25 down(g(c)) -> g_flat(down(c)) 544.09/242.25 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.25 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.25 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.25 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.25 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.25 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.25 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.25 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.25 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.25 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.25 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.25 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.25 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.25 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.25 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.25 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.25 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.25 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.25 544.09/242.25 The set Q consists of the following terms: 544.09/242.25 544.09/242.25 down(a) 544.09/242.25 down(b) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.25 down(f(a)) 544.09/242.25 down(f(b)) 544.09/242.25 down(f(g(x0))) 544.09/242.25 down(f(c)) 544.09/242.25 down(f(fresh_constant)) 544.09/242.25 down(g(a)) 544.09/242.25 down(g(f(x0))) 544.09/242.25 down(g(b)) 544.09/242.25 down(g(c)) 544.09/242.25 down(g(fresh_constant)) 544.09/242.25 down(f(f(a))) 544.09/242.25 down(f(f(b))) 544.09/242.25 down(f(f(g(x0)))) 544.09/242.25 down(f(f(c))) 544.09/242.25 down(f(f(fresh_constant))) 544.09/242.25 down(g(g(a))) 544.09/242.25 down(g(g(f(x0)))) 544.09/242.25 down(g(g(b))) 544.09/242.25 down(g(g(c))) 544.09/242.25 down(g(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) 544.09/242.25 down(f(f(f(g(x0))))) 544.09/242.25 down(f(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) 544.09/242.25 down(g(g(g(f(x0))))) 544.09/242.25 down(g(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(x0)))))) 544.09/242.25 down(f(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(x0)))))) 544.09/242.25 down(g(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(x0))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(x0))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 f_flat(up(x0)) 544.09/242.25 g_flat(up(x0)) 544.09/242.25 544.09/242.25 We have to consider all minimal (P,Q,R)-chains. 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1235) TransformationProof (EQUIVALENT) 544.09/242.25 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.25 544.09/242.25 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b)))))))))))) 544.09/242.25 544.09/242.25 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1236) 544.09/242.25 Obligation: 544.09/242.25 Q DP problem: 544.09/242.25 The TRS P consists of the following rules: 544.09/242.25 544.09/242.25 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.25 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.25 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.25 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.25 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.25 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.25 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.25 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.25 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.25 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.25 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.25 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.25 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.25 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.25 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.25 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.25 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.25 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.25 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.25 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.25 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.25 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.09/242.25 544.09/242.25 The TRS R consists of the following rules: 544.09/242.25 544.09/242.25 down(a) -> up(f(a)) 544.09/242.25 down(b) -> up(g(b)) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.25 down(f(a)) -> f_flat(down(a)) 544.09/242.25 down(f(b)) -> f_flat(down(b)) 544.09/242.25 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.25 down(f(c)) -> f_flat(down(c)) 544.09/242.25 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.25 down(g(a)) -> g_flat(down(a)) 544.09/242.25 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.25 down(g(b)) -> g_flat(down(b)) 544.09/242.25 down(g(c)) -> g_flat(down(c)) 544.09/242.25 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.25 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.25 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.25 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.25 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.25 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.25 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.25 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.25 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.25 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.25 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.25 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.25 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.25 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.25 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.25 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.25 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.25 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.25 544.09/242.25 The set Q consists of the following terms: 544.09/242.25 544.09/242.25 down(a) 544.09/242.25 down(b) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.25 down(f(a)) 544.09/242.25 down(f(b)) 544.09/242.25 down(f(g(x0))) 544.09/242.25 down(f(c)) 544.09/242.25 down(f(fresh_constant)) 544.09/242.25 down(g(a)) 544.09/242.25 down(g(f(x0))) 544.09/242.25 down(g(b)) 544.09/242.25 down(g(c)) 544.09/242.25 down(g(fresh_constant)) 544.09/242.25 down(f(f(a))) 544.09/242.25 down(f(f(b))) 544.09/242.25 down(f(f(g(x0)))) 544.09/242.25 down(f(f(c))) 544.09/242.25 down(f(f(fresh_constant))) 544.09/242.25 down(g(g(a))) 544.09/242.25 down(g(g(f(x0)))) 544.09/242.25 down(g(g(b))) 544.09/242.25 down(g(g(c))) 544.09/242.25 down(g(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) 544.09/242.25 down(f(f(f(g(x0))))) 544.09/242.25 down(f(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) 544.09/242.25 down(g(g(g(f(x0))))) 544.09/242.25 down(g(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(x0)))))) 544.09/242.25 down(f(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(x0)))))) 544.09/242.25 down(g(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(x0))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(x0))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 f_flat(up(x0)) 544.09/242.25 g_flat(up(x0)) 544.09/242.25 544.09/242.25 We have to consider all minimal (P,Q,R)-chains. 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1237) TransformationProof (EQUIVALENT) 544.09/242.25 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(f(a)))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.09/242.25 544.09/242.25 (TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))),TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.25 544.09/242.25 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1238) 544.09/242.25 Obligation: 544.09/242.25 Q DP problem: 544.09/242.25 The TRS P consists of the following rules: 544.09/242.25 544.09/242.25 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.25 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.25 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.25 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.25 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.25 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.25 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.25 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.25 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.25 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.25 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.25 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.25 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.25 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.25 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.25 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.25 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.25 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.25 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.25 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.25 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.25 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.25 544.09/242.25 The TRS R consists of the following rules: 544.09/242.25 544.09/242.25 down(a) -> up(f(a)) 544.09/242.25 down(b) -> up(g(b)) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.25 down(f(a)) -> f_flat(down(a)) 544.09/242.25 down(f(b)) -> f_flat(down(b)) 544.09/242.25 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.25 down(f(c)) -> f_flat(down(c)) 544.09/242.25 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.25 down(g(a)) -> g_flat(down(a)) 544.09/242.25 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.25 down(g(b)) -> g_flat(down(b)) 544.09/242.25 down(g(c)) -> g_flat(down(c)) 544.09/242.25 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.25 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.25 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.25 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.25 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.25 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.25 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.25 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.25 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.25 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.25 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.25 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.25 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.25 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.25 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.25 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.25 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.25 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.25 544.09/242.25 The set Q consists of the following terms: 544.09/242.25 544.09/242.25 down(a) 544.09/242.25 down(b) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.25 down(f(a)) 544.09/242.25 down(f(b)) 544.09/242.25 down(f(g(x0))) 544.09/242.25 down(f(c)) 544.09/242.25 down(f(fresh_constant)) 544.09/242.25 down(g(a)) 544.09/242.25 down(g(f(x0))) 544.09/242.25 down(g(b)) 544.09/242.25 down(g(c)) 544.09/242.25 down(g(fresh_constant)) 544.09/242.25 down(f(f(a))) 544.09/242.25 down(f(f(b))) 544.09/242.25 down(f(f(g(x0)))) 544.09/242.25 down(f(f(c))) 544.09/242.25 down(f(f(fresh_constant))) 544.09/242.25 down(g(g(a))) 544.09/242.25 down(g(g(f(x0)))) 544.09/242.25 down(g(g(b))) 544.09/242.25 down(g(g(c))) 544.09/242.25 down(g(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) 544.09/242.25 down(f(f(f(g(x0))))) 544.09/242.25 down(f(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) 544.09/242.25 down(g(g(g(f(x0))))) 544.09/242.25 down(g(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(x0)))))) 544.09/242.25 down(f(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(x0)))))) 544.09/242.25 down(g(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(x0))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(x0))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 f_flat(up(x0)) 544.09/242.25 g_flat(up(x0)) 544.09/242.25 544.09/242.25 We have to consider all minimal (P,Q,R)-chains. 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1239) TransformationProof (EQUIVALENT) 544.09/242.25 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.25 544.09/242.25 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.25 544.09/242.25 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1240) 544.09/242.25 Obligation: 544.09/242.25 Q DP problem: 544.09/242.25 The TRS P consists of the following rules: 544.09/242.25 544.09/242.25 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.25 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.25 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.25 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.25 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.25 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.25 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.25 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.25 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.25 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.25 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.25 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.25 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.25 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.25 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.25 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.25 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.25 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.25 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.25 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.25 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.25 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))) 544.09/242.25 544.09/242.25 The TRS R consists of the following rules: 544.09/242.25 544.09/242.25 down(a) -> up(f(a)) 544.09/242.25 down(b) -> up(g(b)) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.25 down(f(a)) -> f_flat(down(a)) 544.09/242.25 down(f(b)) -> f_flat(down(b)) 544.09/242.25 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.25 down(f(c)) -> f_flat(down(c)) 544.09/242.25 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.25 down(g(a)) -> g_flat(down(a)) 544.09/242.25 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.25 down(g(b)) -> g_flat(down(b)) 544.09/242.25 down(g(c)) -> g_flat(down(c)) 544.09/242.25 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.25 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.25 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.25 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.25 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.25 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.25 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.25 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.25 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.25 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.25 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.25 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.25 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.25 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.25 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.25 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.25 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.25 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.25 544.09/242.25 The set Q consists of the following terms: 544.09/242.25 544.09/242.25 down(a) 544.09/242.25 down(b) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.25 down(f(a)) 544.09/242.25 down(f(b)) 544.09/242.25 down(f(g(x0))) 544.09/242.25 down(f(c)) 544.09/242.25 down(f(fresh_constant)) 544.09/242.25 down(g(a)) 544.09/242.25 down(g(f(x0))) 544.09/242.25 down(g(b)) 544.09/242.25 down(g(c)) 544.09/242.25 down(g(fresh_constant)) 544.09/242.25 down(f(f(a))) 544.09/242.25 down(f(f(b))) 544.09/242.25 down(f(f(g(x0)))) 544.09/242.25 down(f(f(c))) 544.09/242.25 down(f(f(fresh_constant))) 544.09/242.25 down(g(g(a))) 544.09/242.25 down(g(g(f(x0)))) 544.09/242.25 down(g(g(b))) 544.09/242.25 down(g(g(c))) 544.09/242.25 down(g(g(fresh_constant))) 544.09/242.25 down(f(f(f(a)))) 544.09/242.25 down(f(f(f(b)))) 544.09/242.25 down(f(f(f(g(x0))))) 544.09/242.25 down(f(f(f(c)))) 544.09/242.25 down(f(f(f(fresh_constant)))) 544.09/242.25 down(g(g(g(a)))) 544.09/242.25 down(g(g(g(f(x0))))) 544.09/242.25 down(g(g(g(b)))) 544.09/242.25 down(g(g(g(c)))) 544.09/242.25 down(g(g(g(fresh_constant)))) 544.09/242.25 down(f(f(f(f(a))))) 544.09/242.25 down(f(f(f(f(b))))) 544.09/242.25 down(f(f(f(f(g(x0)))))) 544.09/242.25 down(f(f(f(f(c))))) 544.09/242.25 down(f(f(f(f(fresh_constant))))) 544.09/242.25 down(g(g(g(g(a))))) 544.09/242.25 down(g(g(g(g(f(x0)))))) 544.09/242.25 down(g(g(g(g(b))))) 544.09/242.25 down(g(g(g(g(c))))) 544.09/242.25 down(g(g(g(g(fresh_constant))))) 544.09/242.25 down(f(f(f(f(f(a)))))) 544.09/242.25 down(f(f(f(f(f(b)))))) 544.09/242.25 down(f(f(f(f(f(g(x0))))))) 544.09/242.25 down(f(f(f(f(f(c)))))) 544.09/242.25 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.25 down(g(g(g(g(g(a)))))) 544.09/242.25 down(g(g(g(g(g(f(x0))))))) 544.09/242.25 down(g(g(g(g(g(b)))))) 544.09/242.25 down(g(g(g(g(g(c)))))) 544.09/242.25 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.25 down(f(f(f(f(f(f(a))))))) 544.09/242.25 down(f(f(f(f(f(f(b))))))) 544.09/242.25 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.25 down(f(f(f(f(f(f(c))))))) 544.09/242.25 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.25 down(g(g(g(g(g(g(a))))))) 544.09/242.25 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.25 down(g(g(g(g(g(g(b))))))) 544.09/242.25 down(g(g(g(g(g(g(c))))))) 544.09/242.25 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.25 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.25 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.25 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.25 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.25 f_flat(up(x0)) 544.09/242.25 g_flat(up(x0)) 544.09/242.25 544.09/242.25 We have to consider all minimal (P,Q,R)-chains. 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1241) TransformationProof (EQUIVALENT) 544.09/242.25 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(f(a)))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.25 544.09/242.25 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a))))))))))))) 544.09/242.25 544.09/242.25 544.09/242.25 ---------------------------------------- 544.09/242.25 544.09/242.25 (1242) 544.09/242.25 Obligation: 544.09/242.25 Q DP problem: 544.09/242.25 The TRS P consists of the following rules: 544.09/242.25 544.09/242.25 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.25 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.25 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.25 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.25 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.25 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.25 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.25 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.25 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.25 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.25 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.25 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.25 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.25 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.25 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.25 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.25 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.25 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.25 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.25 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.25 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.25 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.26 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.26 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.26 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.26 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.26 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.26 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) 544.09/242.26 544.09/242.26 The TRS R consists of the following rules: 544.09/242.26 544.09/242.26 down(a) -> up(f(a)) 544.09/242.26 down(b) -> up(g(b)) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.26 down(f(a)) -> f_flat(down(a)) 544.09/242.26 down(f(b)) -> f_flat(down(b)) 544.09/242.26 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.26 down(f(c)) -> f_flat(down(c)) 544.09/242.26 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.26 down(g(a)) -> g_flat(down(a)) 544.09/242.26 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.26 down(g(b)) -> g_flat(down(b)) 544.09/242.26 down(g(c)) -> g_flat(down(c)) 544.09/242.26 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.26 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.26 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.26 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.26 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.26 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.26 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.26 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.26 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.26 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.26 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.26 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.26 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.26 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.26 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.26 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.26 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.26 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.26 544.09/242.26 The set Q consists of the following terms: 544.09/242.26 544.09/242.26 down(a) 544.09/242.26 down(b) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.26 down(f(a)) 544.09/242.26 down(f(b)) 544.09/242.26 down(f(g(x0))) 544.09/242.26 down(f(c)) 544.09/242.26 down(f(fresh_constant)) 544.09/242.26 down(g(a)) 544.09/242.26 down(g(f(x0))) 544.09/242.26 down(g(b)) 544.09/242.26 down(g(c)) 544.09/242.26 down(g(fresh_constant)) 544.09/242.26 down(f(f(a))) 544.09/242.26 down(f(f(b))) 544.09/242.26 down(f(f(g(x0)))) 544.09/242.26 down(f(f(c))) 544.09/242.26 down(f(f(fresh_constant))) 544.09/242.26 down(g(g(a))) 544.09/242.26 down(g(g(f(x0)))) 544.09/242.26 down(g(g(b))) 544.09/242.26 down(g(g(c))) 544.09/242.26 down(g(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) 544.09/242.26 down(f(f(f(g(x0))))) 544.09/242.26 down(f(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) 544.09/242.26 down(g(g(g(f(x0))))) 544.09/242.26 down(g(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(x0)))))) 544.09/242.26 down(f(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(x0)))))) 544.09/242.26 down(g(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(x0))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(x0))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 f_flat(up(x0)) 544.09/242.26 g_flat(up(x0)) 544.09/242.26 544.09/242.26 We have to consider all minimal (P,Q,R)-chains. 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1243) TransformationProof (EQUIVALENT) 544.09/242.26 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.09/242.26 544.09/242.26 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.26 544.09/242.26 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1244) 544.09/242.26 Obligation: 544.09/242.26 Q DP problem: 544.09/242.26 The TRS P consists of the following rules: 544.09/242.26 544.09/242.26 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.26 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.26 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.26 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.26 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.26 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.26 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.26 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.26 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.26 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.26 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.26 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.26 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.26 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.26 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.26 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.26 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.26 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.26 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.26 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.26 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.26 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.26 544.09/242.26 The TRS R consists of the following rules: 544.09/242.26 544.09/242.26 down(a) -> up(f(a)) 544.09/242.26 down(b) -> up(g(b)) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.26 down(f(a)) -> f_flat(down(a)) 544.09/242.26 down(f(b)) -> f_flat(down(b)) 544.09/242.26 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.26 down(f(c)) -> f_flat(down(c)) 544.09/242.26 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.26 down(g(a)) -> g_flat(down(a)) 544.09/242.26 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.26 down(g(b)) -> g_flat(down(b)) 544.09/242.26 down(g(c)) -> g_flat(down(c)) 544.09/242.26 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.26 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.26 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.26 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.26 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.26 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.26 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.26 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.26 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.26 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.26 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.26 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.26 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.26 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.26 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.26 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.26 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.26 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.26 544.09/242.26 The set Q consists of the following terms: 544.09/242.26 544.09/242.26 down(a) 544.09/242.26 down(b) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.26 down(f(a)) 544.09/242.26 down(f(b)) 544.09/242.26 down(f(g(x0))) 544.09/242.26 down(f(c)) 544.09/242.26 down(f(fresh_constant)) 544.09/242.26 down(g(a)) 544.09/242.26 down(g(f(x0))) 544.09/242.26 down(g(b)) 544.09/242.26 down(g(c)) 544.09/242.26 down(g(fresh_constant)) 544.09/242.26 down(f(f(a))) 544.09/242.26 down(f(f(b))) 544.09/242.26 down(f(f(g(x0)))) 544.09/242.26 down(f(f(c))) 544.09/242.26 down(f(f(fresh_constant))) 544.09/242.26 down(g(g(a))) 544.09/242.26 down(g(g(f(x0)))) 544.09/242.26 down(g(g(b))) 544.09/242.26 down(g(g(c))) 544.09/242.26 down(g(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) 544.09/242.26 down(f(f(f(g(x0))))) 544.09/242.26 down(f(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) 544.09/242.26 down(g(g(g(f(x0))))) 544.09/242.26 down(g(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(x0)))))) 544.09/242.26 down(f(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(x0)))))) 544.09/242.26 down(g(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(x0))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(x0))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 f_flat(up(x0)) 544.09/242.26 g_flat(up(x0)) 544.09/242.26 544.09/242.26 We have to consider all minimal (P,Q,R)-chains. 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1245) TransformationProof (EQUIVALENT) 544.09/242.26 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(a)))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.26 544.09/242.26 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a))))))))))))) 544.09/242.26 544.09/242.26 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1246) 544.09/242.26 Obligation: 544.09/242.26 Q DP problem: 544.09/242.26 The TRS P consists of the following rules: 544.09/242.26 544.09/242.26 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.26 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.26 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.26 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.26 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.26 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.26 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.26 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.26 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.26 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.26 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.26 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.26 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.26 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.26 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.26 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.26 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.26 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.26 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.26 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.26 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.26 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.26 544.09/242.26 The TRS R consists of the following rules: 544.09/242.26 544.09/242.26 down(a) -> up(f(a)) 544.09/242.26 down(b) -> up(g(b)) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.26 down(f(a)) -> f_flat(down(a)) 544.09/242.26 down(f(b)) -> f_flat(down(b)) 544.09/242.26 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.26 down(f(c)) -> f_flat(down(c)) 544.09/242.26 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.26 down(g(a)) -> g_flat(down(a)) 544.09/242.26 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.26 down(g(b)) -> g_flat(down(b)) 544.09/242.26 down(g(c)) -> g_flat(down(c)) 544.09/242.26 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.26 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.26 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.26 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.26 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.26 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.26 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.26 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.26 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.26 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.26 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.26 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.26 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.26 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.26 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.26 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.26 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.26 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.26 544.09/242.26 The set Q consists of the following terms: 544.09/242.26 544.09/242.26 down(a) 544.09/242.26 down(b) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.26 down(f(a)) 544.09/242.26 down(f(b)) 544.09/242.26 down(f(g(x0))) 544.09/242.26 down(f(c)) 544.09/242.26 down(f(fresh_constant)) 544.09/242.26 down(g(a)) 544.09/242.26 down(g(f(x0))) 544.09/242.26 down(g(b)) 544.09/242.26 down(g(c)) 544.09/242.26 down(g(fresh_constant)) 544.09/242.26 down(f(f(a))) 544.09/242.26 down(f(f(b))) 544.09/242.26 down(f(f(g(x0)))) 544.09/242.26 down(f(f(c))) 544.09/242.26 down(f(f(fresh_constant))) 544.09/242.26 down(g(g(a))) 544.09/242.26 down(g(g(f(x0)))) 544.09/242.26 down(g(g(b))) 544.09/242.26 down(g(g(c))) 544.09/242.26 down(g(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) 544.09/242.26 down(f(f(f(g(x0))))) 544.09/242.26 down(f(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) 544.09/242.26 down(g(g(g(f(x0))))) 544.09/242.26 down(g(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(x0)))))) 544.09/242.26 down(f(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(x0)))))) 544.09/242.26 down(g(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(x0))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(x0))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 f_flat(up(x0)) 544.09/242.26 g_flat(up(x0)) 544.09/242.26 544.09/242.26 We have to consider all minimal (P,Q,R)-chains. 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1247) TransformationProof (EQUIVALENT) 544.09/242.26 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(up(f(f(f(f(f(g(b)))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.26 544.09/242.26 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b))))))))))))) 544.09/242.26 544.09/242.26 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1248) 544.09/242.26 Obligation: 544.09/242.26 Q DP problem: 544.09/242.26 The TRS P consists of the following rules: 544.09/242.26 544.09/242.26 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.26 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.26 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.26 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.26 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.26 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.26 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.26 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.26 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.26 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.26 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.26 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.26 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.26 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.26 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.26 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.26 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.26 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.26 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.26 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.26 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.26 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.26 544.09/242.26 The TRS R consists of the following rules: 544.09/242.26 544.09/242.26 down(a) -> up(f(a)) 544.09/242.26 down(b) -> up(g(b)) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.26 down(f(a)) -> f_flat(down(a)) 544.09/242.26 down(f(b)) -> f_flat(down(b)) 544.09/242.26 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.26 down(f(c)) -> f_flat(down(c)) 544.09/242.26 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.26 down(g(a)) -> g_flat(down(a)) 544.09/242.26 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.26 down(g(b)) -> g_flat(down(b)) 544.09/242.26 down(g(c)) -> g_flat(down(c)) 544.09/242.26 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.26 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.26 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.26 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.26 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.26 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.26 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.26 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.26 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.26 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.26 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.26 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.26 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.26 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.26 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.26 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.26 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.26 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.26 544.09/242.26 The set Q consists of the following terms: 544.09/242.26 544.09/242.26 down(a) 544.09/242.26 down(b) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.26 down(f(a)) 544.09/242.26 down(f(b)) 544.09/242.26 down(f(g(x0))) 544.09/242.26 down(f(c)) 544.09/242.26 down(f(fresh_constant)) 544.09/242.26 down(g(a)) 544.09/242.26 down(g(f(x0))) 544.09/242.26 down(g(b)) 544.09/242.26 down(g(c)) 544.09/242.26 down(g(fresh_constant)) 544.09/242.26 down(f(f(a))) 544.09/242.26 down(f(f(b))) 544.09/242.26 down(f(f(g(x0)))) 544.09/242.26 down(f(f(c))) 544.09/242.26 down(f(f(fresh_constant))) 544.09/242.26 down(g(g(a))) 544.09/242.26 down(g(g(f(x0)))) 544.09/242.26 down(g(g(b))) 544.09/242.26 down(g(g(c))) 544.09/242.26 down(g(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) 544.09/242.26 down(f(f(f(g(x0))))) 544.09/242.26 down(f(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) 544.09/242.26 down(g(g(g(f(x0))))) 544.09/242.26 down(g(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(x0)))))) 544.09/242.26 down(f(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(x0)))))) 544.09/242.26 down(g(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(x0))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(x0))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 f_flat(up(x0)) 544.09/242.26 g_flat(up(x0)) 544.09/242.26 544.09/242.26 We have to consider all minimal (P,Q,R)-chains. 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1249) TransformationProof (EQUIVALENT) 544.09/242.26 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(b)))))))))))) at position [0,0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.26 544.09/242.26 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b))))))))))))) 544.09/242.26 544.09/242.26 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1250) 544.09/242.26 Obligation: 544.09/242.26 Q DP problem: 544.09/242.26 The TRS P consists of the following rules: 544.09/242.26 544.09/242.26 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.26 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.26 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.26 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.26 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.26 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.26 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.26 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.26 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.26 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.26 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.26 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.26 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.26 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.26 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.26 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.26 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.26 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.26 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.26 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.26 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.26 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) 544.09/242.26 544.09/242.26 The TRS R consists of the following rules: 544.09/242.26 544.09/242.26 down(a) -> up(f(a)) 544.09/242.26 down(b) -> up(g(b)) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.26 down(f(a)) -> f_flat(down(a)) 544.09/242.26 down(f(b)) -> f_flat(down(b)) 544.09/242.26 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.26 down(f(c)) -> f_flat(down(c)) 544.09/242.26 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.26 down(g(a)) -> g_flat(down(a)) 544.09/242.26 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.26 down(g(b)) -> g_flat(down(b)) 544.09/242.26 down(g(c)) -> g_flat(down(c)) 544.09/242.26 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.26 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.26 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.26 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.26 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.26 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.26 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.26 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.26 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.26 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.26 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.26 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.26 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.26 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.26 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.26 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.26 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.26 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.26 544.09/242.26 The set Q consists of the following terms: 544.09/242.26 544.09/242.26 down(a) 544.09/242.26 down(b) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.26 down(f(a)) 544.09/242.26 down(f(b)) 544.09/242.26 down(f(g(x0))) 544.09/242.26 down(f(c)) 544.09/242.26 down(f(fresh_constant)) 544.09/242.26 down(g(a)) 544.09/242.26 down(g(f(x0))) 544.09/242.26 down(g(b)) 544.09/242.26 down(g(c)) 544.09/242.26 down(g(fresh_constant)) 544.09/242.26 down(f(f(a))) 544.09/242.26 down(f(f(b))) 544.09/242.26 down(f(f(g(x0)))) 544.09/242.26 down(f(f(c))) 544.09/242.26 down(f(f(fresh_constant))) 544.09/242.26 down(g(g(a))) 544.09/242.26 down(g(g(f(x0)))) 544.09/242.26 down(g(g(b))) 544.09/242.26 down(g(g(c))) 544.09/242.26 down(g(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) 544.09/242.26 down(f(f(f(g(x0))))) 544.09/242.26 down(f(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) 544.09/242.26 down(g(g(g(f(x0))))) 544.09/242.26 down(g(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(x0)))))) 544.09/242.26 down(f(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(x0)))))) 544.09/242.26 down(g(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(x0))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(x0))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 f_flat(up(x0)) 544.09/242.26 g_flat(up(x0)) 544.09/242.26 544.09/242.26 We have to consider all minimal (P,Q,R)-chains. 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1251) TransformationProof (EQUIVALENT) 544.09/242.26 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.09/242.26 544.09/242.26 (TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))),TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.26 544.09/242.26 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1252) 544.09/242.26 Obligation: 544.09/242.26 Q DP problem: 544.09/242.26 The TRS P consists of the following rules: 544.09/242.26 544.09/242.26 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.26 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.26 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.26 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.26 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.26 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.26 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.26 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.26 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.26 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.26 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.26 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.26 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.26 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.26 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.26 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.26 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.26 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.26 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.26 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.26 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.26 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.26 544.09/242.26 The TRS R consists of the following rules: 544.09/242.26 544.09/242.26 down(a) -> up(f(a)) 544.09/242.26 down(b) -> up(g(b)) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.26 down(f(a)) -> f_flat(down(a)) 544.09/242.26 down(f(b)) -> f_flat(down(b)) 544.09/242.26 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.26 down(f(c)) -> f_flat(down(c)) 544.09/242.26 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.26 down(g(a)) -> g_flat(down(a)) 544.09/242.26 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.26 down(g(b)) -> g_flat(down(b)) 544.09/242.26 down(g(c)) -> g_flat(down(c)) 544.09/242.26 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.26 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.26 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.26 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.26 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.26 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.26 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.26 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.26 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.26 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.26 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.26 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.26 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.26 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.26 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.26 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.26 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.26 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.26 544.09/242.26 The set Q consists of the following terms: 544.09/242.26 544.09/242.26 down(a) 544.09/242.26 down(b) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.26 down(f(a)) 544.09/242.26 down(f(b)) 544.09/242.26 down(f(g(x0))) 544.09/242.26 down(f(c)) 544.09/242.26 down(f(fresh_constant)) 544.09/242.26 down(g(a)) 544.09/242.26 down(g(f(x0))) 544.09/242.26 down(g(b)) 544.09/242.26 down(g(c)) 544.09/242.26 down(g(fresh_constant)) 544.09/242.26 down(f(f(a))) 544.09/242.26 down(f(f(b))) 544.09/242.26 down(f(f(g(x0)))) 544.09/242.26 down(f(f(c))) 544.09/242.26 down(f(f(fresh_constant))) 544.09/242.26 down(g(g(a))) 544.09/242.26 down(g(g(f(x0)))) 544.09/242.26 down(g(g(b))) 544.09/242.26 down(g(g(c))) 544.09/242.26 down(g(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) 544.09/242.26 down(f(f(f(g(x0))))) 544.09/242.26 down(f(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) 544.09/242.26 down(g(g(g(f(x0))))) 544.09/242.26 down(g(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(x0)))))) 544.09/242.26 down(f(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(x0)))))) 544.09/242.26 down(g(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(x0))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(x0))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 f_flat(up(x0)) 544.09/242.26 g_flat(up(x0)) 544.09/242.26 544.09/242.26 We have to consider all minimal (P,Q,R)-chains. 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1253) TransformationProof (EQUIVALENT) 544.09/242.26 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.09/242.26 544.09/242.26 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b)))))))))))) 544.09/242.26 544.09/242.26 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1254) 544.09/242.26 Obligation: 544.09/242.26 Q DP problem: 544.09/242.26 The TRS P consists of the following rules: 544.09/242.26 544.09/242.26 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.26 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.26 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.26 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.26 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.26 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.26 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.26 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.26 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.26 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.26 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.26 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.26 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.26 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.26 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.26 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.26 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.26 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.26 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.26 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.26 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.26 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.26 544.09/242.26 The TRS R consists of the following rules: 544.09/242.26 544.09/242.26 down(a) -> up(f(a)) 544.09/242.26 down(b) -> up(g(b)) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.26 down(f(a)) -> f_flat(down(a)) 544.09/242.26 down(f(b)) -> f_flat(down(b)) 544.09/242.26 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.26 down(f(c)) -> f_flat(down(c)) 544.09/242.26 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.26 down(g(a)) -> g_flat(down(a)) 544.09/242.26 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.26 down(g(b)) -> g_flat(down(b)) 544.09/242.26 down(g(c)) -> g_flat(down(c)) 544.09/242.26 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.26 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.26 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.26 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.26 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.26 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.26 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.26 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.26 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.26 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.26 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.26 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.26 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.26 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.26 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.26 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.26 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.26 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.26 544.09/242.26 The set Q consists of the following terms: 544.09/242.26 544.09/242.26 down(a) 544.09/242.26 down(b) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.26 down(f(a)) 544.09/242.26 down(f(b)) 544.09/242.26 down(f(g(x0))) 544.09/242.26 down(f(c)) 544.09/242.26 down(f(fresh_constant)) 544.09/242.26 down(g(a)) 544.09/242.26 down(g(f(x0))) 544.09/242.26 down(g(b)) 544.09/242.26 down(g(c)) 544.09/242.26 down(g(fresh_constant)) 544.09/242.26 down(f(f(a))) 544.09/242.26 down(f(f(b))) 544.09/242.26 down(f(f(g(x0)))) 544.09/242.26 down(f(f(c))) 544.09/242.26 down(f(f(fresh_constant))) 544.09/242.26 down(g(g(a))) 544.09/242.26 down(g(g(f(x0)))) 544.09/242.26 down(g(g(b))) 544.09/242.26 down(g(g(c))) 544.09/242.26 down(g(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) 544.09/242.26 down(f(f(f(g(x0))))) 544.09/242.26 down(f(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) 544.09/242.26 down(g(g(g(f(x0))))) 544.09/242.26 down(g(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(x0)))))) 544.09/242.26 down(f(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(x0)))))) 544.09/242.26 down(g(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(x0))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(x0))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 f_flat(up(x0)) 544.09/242.26 g_flat(up(x0)) 544.09/242.26 544.09/242.26 We have to consider all minimal (P,Q,R)-chains. 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1255) TransformationProof (EQUIVALENT) 544.09/242.26 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.09/242.26 544.09/242.26 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.26 544.09/242.26 544.09/242.26 ---------------------------------------- 544.09/242.26 544.09/242.26 (1256) 544.09/242.26 Obligation: 544.09/242.26 Q DP problem: 544.09/242.26 The TRS P consists of the following rules: 544.09/242.26 544.09/242.26 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.26 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.26 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.26 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.26 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.26 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.26 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.26 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.26 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.26 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.26 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.26 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.26 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.26 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.26 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.26 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.26 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.26 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.26 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.26 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.26 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.26 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.26 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.26 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) 544.09/242.26 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.26 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.26 544.09/242.26 The TRS R consists of the following rules: 544.09/242.26 544.09/242.26 down(a) -> up(f(a)) 544.09/242.26 down(b) -> up(g(b)) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.26 down(f(a)) -> f_flat(down(a)) 544.09/242.26 down(f(b)) -> f_flat(down(b)) 544.09/242.26 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.26 down(f(c)) -> f_flat(down(c)) 544.09/242.26 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.26 down(g(a)) -> g_flat(down(a)) 544.09/242.26 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.26 down(g(b)) -> g_flat(down(b)) 544.09/242.26 down(g(c)) -> g_flat(down(c)) 544.09/242.26 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.26 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.26 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.26 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.26 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.26 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.26 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.26 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.26 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.26 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.26 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.26 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.26 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.26 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.26 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.26 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.26 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.26 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.26 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.26 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.26 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.26 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.26 544.09/242.26 The set Q consists of the following terms: 544.09/242.26 544.09/242.26 down(a) 544.09/242.26 down(b) 544.09/242.26 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.26 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.26 down(f(a)) 544.09/242.26 down(f(b)) 544.09/242.26 down(f(g(x0))) 544.09/242.26 down(f(c)) 544.09/242.26 down(f(fresh_constant)) 544.09/242.26 down(g(a)) 544.09/242.26 down(g(f(x0))) 544.09/242.26 down(g(b)) 544.09/242.26 down(g(c)) 544.09/242.26 down(g(fresh_constant)) 544.09/242.26 down(f(f(a))) 544.09/242.26 down(f(f(b))) 544.09/242.26 down(f(f(g(x0)))) 544.09/242.26 down(f(f(c))) 544.09/242.26 down(f(f(fresh_constant))) 544.09/242.26 down(g(g(a))) 544.09/242.26 down(g(g(f(x0)))) 544.09/242.26 down(g(g(b))) 544.09/242.26 down(g(g(c))) 544.09/242.26 down(g(g(fresh_constant))) 544.09/242.26 down(f(f(f(a)))) 544.09/242.26 down(f(f(f(b)))) 544.09/242.26 down(f(f(f(g(x0))))) 544.09/242.26 down(f(f(f(c)))) 544.09/242.26 down(f(f(f(fresh_constant)))) 544.09/242.26 down(g(g(g(a)))) 544.09/242.26 down(g(g(g(f(x0))))) 544.09/242.26 down(g(g(g(b)))) 544.09/242.26 down(g(g(g(c)))) 544.09/242.26 down(g(g(g(fresh_constant)))) 544.09/242.26 down(f(f(f(f(a))))) 544.09/242.26 down(f(f(f(f(b))))) 544.09/242.26 down(f(f(f(f(g(x0)))))) 544.09/242.26 down(f(f(f(f(c))))) 544.09/242.26 down(f(f(f(f(fresh_constant))))) 544.09/242.26 down(g(g(g(g(a))))) 544.09/242.26 down(g(g(g(g(f(x0)))))) 544.09/242.26 down(g(g(g(g(b))))) 544.09/242.26 down(g(g(g(g(c))))) 544.09/242.26 down(g(g(g(g(fresh_constant))))) 544.09/242.26 down(f(f(f(f(f(a)))))) 544.09/242.26 down(f(f(f(f(f(b)))))) 544.09/242.26 down(f(f(f(f(f(g(x0))))))) 544.09/242.26 down(f(f(f(f(f(c)))))) 544.09/242.26 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.26 down(g(g(g(g(g(a)))))) 544.09/242.26 down(g(g(g(g(g(f(x0))))))) 544.09/242.26 down(g(g(g(g(g(b)))))) 544.09/242.26 down(g(g(g(g(g(c)))))) 544.09/242.26 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.26 down(f(f(f(f(f(f(a))))))) 544.09/242.26 down(f(f(f(f(f(f(b))))))) 544.09/242.26 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.26 down(f(f(f(f(f(f(c))))))) 544.09/242.26 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.26 down(g(g(g(g(g(g(a))))))) 544.09/242.26 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.26 down(g(g(g(g(g(g(b))))))) 544.09/242.26 down(g(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 f_flat(up(x0)) 544.09/242.27 g_flat(up(x0)) 544.09/242.27 544.09/242.27 We have to consider all minimal (P,Q,R)-chains. 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1257) TransformationProof (EQUIVALENT) 544.09/242.27 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(f(a)))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.27 544.09/242.27 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a))))))))))))) 544.09/242.27 544.09/242.27 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1258) 544.09/242.27 Obligation: 544.09/242.27 Q DP problem: 544.09/242.27 The TRS P consists of the following rules: 544.09/242.27 544.09/242.27 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.27 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.27 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.27 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.27 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.27 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.27 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.27 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.27 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.27 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.27 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.27 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.27 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.27 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.27 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.27 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.27 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.27 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.27 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.27 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.27 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.27 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.27 544.09/242.27 The TRS R consists of the following rules: 544.09/242.27 544.09/242.27 down(a) -> up(f(a)) 544.09/242.27 down(b) -> up(g(b)) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.27 down(f(a)) -> f_flat(down(a)) 544.09/242.27 down(f(b)) -> f_flat(down(b)) 544.09/242.27 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.27 down(f(c)) -> f_flat(down(c)) 544.09/242.27 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.27 down(g(a)) -> g_flat(down(a)) 544.09/242.27 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.27 down(g(b)) -> g_flat(down(b)) 544.09/242.27 down(g(c)) -> g_flat(down(c)) 544.09/242.27 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.27 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.27 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.27 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.27 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.27 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.27 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.27 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.27 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.27 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.27 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.27 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.27 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.27 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.27 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.27 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.27 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.27 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.27 544.09/242.27 The set Q consists of the following terms: 544.09/242.27 544.09/242.27 down(a) 544.09/242.27 down(b) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.27 down(f(a)) 544.09/242.27 down(f(b)) 544.09/242.27 down(f(g(x0))) 544.09/242.27 down(f(c)) 544.09/242.27 down(f(fresh_constant)) 544.09/242.27 down(g(a)) 544.09/242.27 down(g(f(x0))) 544.09/242.27 down(g(b)) 544.09/242.27 down(g(c)) 544.09/242.27 down(g(fresh_constant)) 544.09/242.27 down(f(f(a))) 544.09/242.27 down(f(f(b))) 544.09/242.27 down(f(f(g(x0)))) 544.09/242.27 down(f(f(c))) 544.09/242.27 down(f(f(fresh_constant))) 544.09/242.27 down(g(g(a))) 544.09/242.27 down(g(g(f(x0)))) 544.09/242.27 down(g(g(b))) 544.09/242.27 down(g(g(c))) 544.09/242.27 down(g(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) 544.09/242.27 down(f(f(f(g(x0))))) 544.09/242.27 down(f(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) 544.09/242.27 down(g(g(g(f(x0))))) 544.09/242.27 down(g(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(x0)))))) 544.09/242.27 down(f(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(x0)))))) 544.09/242.27 down(g(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(x0))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(x0))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 f_flat(up(x0)) 544.09/242.27 g_flat(up(x0)) 544.09/242.27 544.09/242.27 We have to consider all minimal (P,Q,R)-chains. 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1259) TransformationProof (EQUIVALENT) 544.09/242.27 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.09/242.27 544.09/242.27 (TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))),TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.27 544.09/242.27 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1260) 544.09/242.27 Obligation: 544.09/242.27 Q DP problem: 544.09/242.27 The TRS P consists of the following rules: 544.09/242.27 544.09/242.27 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.27 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.27 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.27 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.27 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.27 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.27 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.27 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.27 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.27 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.27 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.27 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.27 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.27 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.27 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.27 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.27 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.27 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.27 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.27 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.27 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.27 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.27 544.09/242.27 The TRS R consists of the following rules: 544.09/242.27 544.09/242.27 down(a) -> up(f(a)) 544.09/242.27 down(b) -> up(g(b)) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.27 down(f(a)) -> f_flat(down(a)) 544.09/242.27 down(f(b)) -> f_flat(down(b)) 544.09/242.27 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.27 down(f(c)) -> f_flat(down(c)) 544.09/242.27 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.27 down(g(a)) -> g_flat(down(a)) 544.09/242.27 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.27 down(g(b)) -> g_flat(down(b)) 544.09/242.27 down(g(c)) -> g_flat(down(c)) 544.09/242.27 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.27 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.27 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.27 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.27 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.27 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.27 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.27 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.27 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.27 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.27 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.27 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.27 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.27 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.27 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.27 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.27 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.27 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.27 544.09/242.27 The set Q consists of the following terms: 544.09/242.27 544.09/242.27 down(a) 544.09/242.27 down(b) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.27 down(f(a)) 544.09/242.27 down(f(b)) 544.09/242.27 down(f(g(x0))) 544.09/242.27 down(f(c)) 544.09/242.27 down(f(fresh_constant)) 544.09/242.27 down(g(a)) 544.09/242.27 down(g(f(x0))) 544.09/242.27 down(g(b)) 544.09/242.27 down(g(c)) 544.09/242.27 down(g(fresh_constant)) 544.09/242.27 down(f(f(a))) 544.09/242.27 down(f(f(b))) 544.09/242.27 down(f(f(g(x0)))) 544.09/242.27 down(f(f(c))) 544.09/242.27 down(f(f(fresh_constant))) 544.09/242.27 down(g(g(a))) 544.09/242.27 down(g(g(f(x0)))) 544.09/242.27 down(g(g(b))) 544.09/242.27 down(g(g(c))) 544.09/242.27 down(g(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) 544.09/242.27 down(f(f(f(g(x0))))) 544.09/242.27 down(f(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) 544.09/242.27 down(g(g(g(f(x0))))) 544.09/242.27 down(g(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(x0)))))) 544.09/242.27 down(f(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(x0)))))) 544.09/242.27 down(g(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(x0))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(x0))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 f_flat(up(x0)) 544.09/242.27 g_flat(up(x0)) 544.09/242.27 544.09/242.27 We have to consider all minimal (P,Q,R)-chains. 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1261) TransformationProof (EQUIVALENT) 544.09/242.27 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(f(a)))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.27 544.09/242.27 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(f(a))))))))))))) 544.09/242.27 544.09/242.27 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1262) 544.09/242.27 Obligation: 544.09/242.27 Q DP problem: 544.09/242.27 The TRS P consists of the following rules: 544.09/242.27 544.09/242.27 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.27 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.27 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.27 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.27 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.27 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.27 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.27 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.27 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.27 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.27 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.27 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.27 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.27 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.27 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.27 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.27 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.27 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.27 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.27 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.27 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.27 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.27 544.09/242.27 The TRS R consists of the following rules: 544.09/242.27 544.09/242.27 down(a) -> up(f(a)) 544.09/242.27 down(b) -> up(g(b)) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.27 down(f(a)) -> f_flat(down(a)) 544.09/242.27 down(f(b)) -> f_flat(down(b)) 544.09/242.27 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.27 down(f(c)) -> f_flat(down(c)) 544.09/242.27 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.27 down(g(a)) -> g_flat(down(a)) 544.09/242.27 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.27 down(g(b)) -> g_flat(down(b)) 544.09/242.27 down(g(c)) -> g_flat(down(c)) 544.09/242.27 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.27 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.27 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.27 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.27 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.27 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.27 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.27 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.27 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.27 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.27 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.27 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.27 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.27 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.27 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.27 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.27 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.27 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.27 544.09/242.27 The set Q consists of the following terms: 544.09/242.27 544.09/242.27 down(a) 544.09/242.27 down(b) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.27 down(f(a)) 544.09/242.27 down(f(b)) 544.09/242.27 down(f(g(x0))) 544.09/242.27 down(f(c)) 544.09/242.27 down(f(fresh_constant)) 544.09/242.27 down(g(a)) 544.09/242.27 down(g(f(x0))) 544.09/242.27 down(g(b)) 544.09/242.27 down(g(c)) 544.09/242.27 down(g(fresh_constant)) 544.09/242.27 down(f(f(a))) 544.09/242.27 down(f(f(b))) 544.09/242.27 down(f(f(g(x0)))) 544.09/242.27 down(f(f(c))) 544.09/242.27 down(f(f(fresh_constant))) 544.09/242.27 down(g(g(a))) 544.09/242.27 down(g(g(f(x0)))) 544.09/242.27 down(g(g(b))) 544.09/242.27 down(g(g(c))) 544.09/242.27 down(g(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) 544.09/242.27 down(f(f(f(g(x0))))) 544.09/242.27 down(f(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) 544.09/242.27 down(g(g(g(f(x0))))) 544.09/242.27 down(g(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(x0)))))) 544.09/242.27 down(f(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(x0)))))) 544.09/242.27 down(g(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(x0))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(x0))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 f_flat(up(x0)) 544.09/242.27 g_flat(up(x0)) 544.09/242.27 544.09/242.27 We have to consider all minimal (P,Q,R)-chains. 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1263) TransformationProof (EQUIVALENT) 544.09/242.27 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(f_flat(up(f(f(f(f(f(f(g(b)))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.27 544.09/242.27 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(g(b))))))))))))) 544.09/242.27 544.09/242.27 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1264) 544.09/242.27 Obligation: 544.09/242.27 Q DP problem: 544.09/242.27 The TRS P consists of the following rules: 544.09/242.27 544.09/242.27 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.27 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.27 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.27 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.27 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.27 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.27 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.27 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.27 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.27 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.27 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.27 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.27 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.27 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.27 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.27 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.27 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.27 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.27 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.27 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.27 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.27 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.27 544.09/242.27 The TRS R consists of the following rules: 544.09/242.27 544.09/242.27 down(a) -> up(f(a)) 544.09/242.27 down(b) -> up(g(b)) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.27 down(f(a)) -> f_flat(down(a)) 544.09/242.27 down(f(b)) -> f_flat(down(b)) 544.09/242.27 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.27 down(f(c)) -> f_flat(down(c)) 544.09/242.27 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.27 down(g(a)) -> g_flat(down(a)) 544.09/242.27 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.27 down(g(b)) -> g_flat(down(b)) 544.09/242.27 down(g(c)) -> g_flat(down(c)) 544.09/242.27 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.27 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.27 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.27 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.27 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.27 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.27 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.27 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.27 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.27 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.27 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.27 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.27 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.27 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.27 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.27 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.27 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.27 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.27 544.09/242.27 The set Q consists of the following terms: 544.09/242.27 544.09/242.27 down(a) 544.09/242.27 down(b) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.27 down(f(a)) 544.09/242.27 down(f(b)) 544.09/242.27 down(f(g(x0))) 544.09/242.27 down(f(c)) 544.09/242.27 down(f(fresh_constant)) 544.09/242.27 down(g(a)) 544.09/242.27 down(g(f(x0))) 544.09/242.27 down(g(b)) 544.09/242.27 down(g(c)) 544.09/242.27 down(g(fresh_constant)) 544.09/242.27 down(f(f(a))) 544.09/242.27 down(f(f(b))) 544.09/242.27 down(f(f(g(x0)))) 544.09/242.27 down(f(f(c))) 544.09/242.27 down(f(f(fresh_constant))) 544.09/242.27 down(g(g(a))) 544.09/242.27 down(g(g(f(x0)))) 544.09/242.27 down(g(g(b))) 544.09/242.27 down(g(g(c))) 544.09/242.27 down(g(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) 544.09/242.27 down(f(f(f(g(x0))))) 544.09/242.27 down(f(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) 544.09/242.27 down(g(g(g(f(x0))))) 544.09/242.27 down(g(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(x0)))))) 544.09/242.27 down(f(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(x0)))))) 544.09/242.27 down(g(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(x0))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(x0))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 f_flat(up(x0)) 544.09/242.27 g_flat(up(x0)) 544.09/242.27 544.09/242.27 We have to consider all minimal (P,Q,R)-chains. 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1265) TransformationProof (EQUIVALENT) 544.09/242.27 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(b)))))))))))) at position [0,0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.27 544.09/242.27 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(g(b))))))))))))) 544.09/242.27 544.09/242.27 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1266) 544.09/242.27 Obligation: 544.09/242.27 Q DP problem: 544.09/242.27 The TRS P consists of the following rules: 544.09/242.27 544.09/242.27 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.27 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.27 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.27 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.27 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.27 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.27 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.27 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.27 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.27 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.27 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.27 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.27 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.27 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.27 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.27 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.27 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.27 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.27 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.27 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.27 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.27 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(g(b)))))))))))) 544.09/242.27 544.09/242.27 The TRS R consists of the following rules: 544.09/242.27 544.09/242.27 down(a) -> up(f(a)) 544.09/242.27 down(b) -> up(g(b)) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.27 down(f(a)) -> f_flat(down(a)) 544.09/242.27 down(f(b)) -> f_flat(down(b)) 544.09/242.27 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.27 down(f(c)) -> f_flat(down(c)) 544.09/242.27 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.27 down(g(a)) -> g_flat(down(a)) 544.09/242.27 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.27 down(g(b)) -> g_flat(down(b)) 544.09/242.27 down(g(c)) -> g_flat(down(c)) 544.09/242.27 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.27 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.27 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.27 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.27 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.27 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.27 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.27 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.27 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.27 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.27 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.27 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.27 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.27 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.27 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.27 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.27 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.27 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.27 544.09/242.27 The set Q consists of the following terms: 544.09/242.27 544.09/242.27 down(a) 544.09/242.27 down(b) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.27 down(f(a)) 544.09/242.27 down(f(b)) 544.09/242.27 down(f(g(x0))) 544.09/242.27 down(f(c)) 544.09/242.27 down(f(fresh_constant)) 544.09/242.27 down(g(a)) 544.09/242.27 down(g(f(x0))) 544.09/242.27 down(g(b)) 544.09/242.27 down(g(c)) 544.09/242.27 down(g(fresh_constant)) 544.09/242.27 down(f(f(a))) 544.09/242.27 down(f(f(b))) 544.09/242.27 down(f(f(g(x0)))) 544.09/242.27 down(f(f(c))) 544.09/242.27 down(f(f(fresh_constant))) 544.09/242.27 down(g(g(a))) 544.09/242.27 down(g(g(f(x0)))) 544.09/242.27 down(g(g(b))) 544.09/242.27 down(g(g(c))) 544.09/242.27 down(g(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) 544.09/242.27 down(f(f(f(g(x0))))) 544.09/242.27 down(f(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) 544.09/242.27 down(g(g(g(f(x0))))) 544.09/242.27 down(g(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(x0)))))) 544.09/242.27 down(f(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(x0)))))) 544.09/242.27 down(g(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(x0))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(x0))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 f_flat(up(x0)) 544.09/242.27 g_flat(up(x0)) 544.09/242.27 544.09/242.27 We have to consider all minimal (P,Q,R)-chains. 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1267) TransformationProof (EQUIVALENT) 544.09/242.27 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.09/242.27 544.09/242.27 (TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))),TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b)))))))))))) 544.09/242.27 544.09/242.27 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1268) 544.09/242.27 Obligation: 544.09/242.27 Q DP problem: 544.09/242.27 The TRS P consists of the following rules: 544.09/242.27 544.09/242.27 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.27 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.27 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.27 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.27 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.27 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.27 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.27 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.27 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.27 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.27 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.27 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.27 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.27 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.27 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.27 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.27 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.27 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.27 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.27 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.27 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.27 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.27 544.09/242.27 The TRS R consists of the following rules: 544.09/242.27 544.09/242.27 down(a) -> up(f(a)) 544.09/242.27 down(b) -> up(g(b)) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.27 down(f(a)) -> f_flat(down(a)) 544.09/242.27 down(f(b)) -> f_flat(down(b)) 544.09/242.27 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.27 down(f(c)) -> f_flat(down(c)) 544.09/242.27 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.27 down(g(a)) -> g_flat(down(a)) 544.09/242.27 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.27 down(g(b)) -> g_flat(down(b)) 544.09/242.27 down(g(c)) -> g_flat(down(c)) 544.09/242.27 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.27 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.27 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.27 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.27 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.27 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.27 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.27 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.27 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.27 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.27 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.27 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.27 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.27 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.27 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.27 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.27 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.27 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.27 544.09/242.27 The set Q consists of the following terms: 544.09/242.27 544.09/242.27 down(a) 544.09/242.27 down(b) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.27 down(f(a)) 544.09/242.27 down(f(b)) 544.09/242.27 down(f(g(x0))) 544.09/242.27 down(f(c)) 544.09/242.27 down(f(fresh_constant)) 544.09/242.27 down(g(a)) 544.09/242.27 down(g(f(x0))) 544.09/242.27 down(g(b)) 544.09/242.27 down(g(c)) 544.09/242.27 down(g(fresh_constant)) 544.09/242.27 down(f(f(a))) 544.09/242.27 down(f(f(b))) 544.09/242.27 down(f(f(g(x0)))) 544.09/242.27 down(f(f(c))) 544.09/242.27 down(f(f(fresh_constant))) 544.09/242.27 down(g(g(a))) 544.09/242.27 down(g(g(f(x0)))) 544.09/242.27 down(g(g(b))) 544.09/242.27 down(g(g(c))) 544.09/242.27 down(g(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) 544.09/242.27 down(f(f(f(g(x0))))) 544.09/242.27 down(f(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) 544.09/242.27 down(g(g(g(f(x0))))) 544.09/242.27 down(g(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(x0)))))) 544.09/242.27 down(f(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(x0)))))) 544.09/242.27 down(g(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(x0))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(x0))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 f_flat(up(x0)) 544.09/242.27 g_flat(up(x0)) 544.09/242.27 544.09/242.27 We have to consider all minimal (P,Q,R)-chains. 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1269) TransformationProof (EQUIVALENT) 544.09/242.27 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.09/242.27 544.09/242.27 (TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))),TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.27 544.09/242.27 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1270) 544.09/242.27 Obligation: 544.09/242.27 Q DP problem: 544.09/242.27 The TRS P consists of the following rules: 544.09/242.27 544.09/242.27 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.27 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.27 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.27 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.27 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.27 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.27 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.27 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.27 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.27 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.27 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.27 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.27 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.27 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.27 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.27 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.27 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.27 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.27 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.27 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.27 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.27 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.27 544.09/242.27 The TRS R consists of the following rules: 544.09/242.27 544.09/242.27 down(a) -> up(f(a)) 544.09/242.27 down(b) -> up(g(b)) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.27 down(f(a)) -> f_flat(down(a)) 544.09/242.27 down(f(b)) -> f_flat(down(b)) 544.09/242.27 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.27 down(f(c)) -> f_flat(down(c)) 544.09/242.27 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.27 down(g(a)) -> g_flat(down(a)) 544.09/242.27 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.27 down(g(b)) -> g_flat(down(b)) 544.09/242.27 down(g(c)) -> g_flat(down(c)) 544.09/242.27 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.27 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.27 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.27 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.27 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.27 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.27 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.27 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.27 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.27 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.27 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.27 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.27 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.27 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.27 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.27 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.27 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.27 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.27 544.09/242.27 The set Q consists of the following terms: 544.09/242.27 544.09/242.27 down(a) 544.09/242.27 down(b) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.27 down(f(a)) 544.09/242.27 down(f(b)) 544.09/242.27 down(f(g(x0))) 544.09/242.27 down(f(c)) 544.09/242.27 down(f(fresh_constant)) 544.09/242.27 down(g(a)) 544.09/242.27 down(g(f(x0))) 544.09/242.27 down(g(b)) 544.09/242.27 down(g(c)) 544.09/242.27 down(g(fresh_constant)) 544.09/242.27 down(f(f(a))) 544.09/242.27 down(f(f(b))) 544.09/242.27 down(f(f(g(x0)))) 544.09/242.27 down(f(f(c))) 544.09/242.27 down(f(f(fresh_constant))) 544.09/242.27 down(g(g(a))) 544.09/242.27 down(g(g(f(x0)))) 544.09/242.27 down(g(g(b))) 544.09/242.27 down(g(g(c))) 544.09/242.27 down(g(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) 544.09/242.27 down(f(f(f(g(x0))))) 544.09/242.27 down(f(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) 544.09/242.27 down(g(g(g(f(x0))))) 544.09/242.27 down(g(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) 544.09/242.27 down(f(f(f(f(g(x0)))))) 544.09/242.27 down(f(f(f(f(c))))) 544.09/242.27 down(f(f(f(f(fresh_constant))))) 544.09/242.27 down(g(g(g(g(a))))) 544.09/242.27 down(g(g(g(g(f(x0)))))) 544.09/242.27 down(g(g(g(g(b))))) 544.09/242.27 down(g(g(g(g(c))))) 544.09/242.27 down(g(g(g(g(fresh_constant))))) 544.09/242.27 down(f(f(f(f(f(a)))))) 544.09/242.27 down(f(f(f(f(f(b)))))) 544.09/242.27 down(f(f(f(f(f(g(x0))))))) 544.09/242.27 down(f(f(f(f(f(c)))))) 544.09/242.27 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.27 down(g(g(g(g(g(a)))))) 544.09/242.27 down(g(g(g(g(g(f(x0))))))) 544.09/242.27 down(g(g(g(g(g(b)))))) 544.09/242.27 down(g(g(g(g(g(c)))))) 544.09/242.27 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.27 down(f(f(f(f(f(f(a))))))) 544.09/242.27 down(f(f(f(f(f(f(b))))))) 544.09/242.27 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.27 down(f(f(f(f(f(f(c))))))) 544.09/242.27 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.27 down(g(g(g(g(g(g(a))))))) 544.09/242.27 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.27 down(g(g(g(g(g(g(b))))))) 544.09/242.27 down(g(g(g(g(g(g(c))))))) 544.09/242.27 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.27 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.27 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.27 f_flat(up(x0)) 544.09/242.27 g_flat(up(x0)) 544.09/242.27 544.09/242.27 We have to consider all minimal (P,Q,R)-chains. 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1271) TransformationProof (EQUIVALENT) 544.09/242.27 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(f(a)))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.09/242.27 544.09/242.27 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(f(a))))))))))))) 544.09/242.27 544.09/242.27 544.09/242.27 ---------------------------------------- 544.09/242.27 544.09/242.27 (1272) 544.09/242.27 Obligation: 544.09/242.27 Q DP problem: 544.09/242.27 The TRS P consists of the following rules: 544.09/242.27 544.09/242.27 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.27 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.27 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.27 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.27 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.27 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.27 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.27 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.27 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.27 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.27 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.27 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.27 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.27 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.27 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.27 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.27 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.27 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.27 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.27 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.27 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.27 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.27 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.27 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.27 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.27 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.27 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(g(b)))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.27 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.27 544.09/242.27 The TRS R consists of the following rules: 544.09/242.27 544.09/242.27 down(a) -> up(f(a)) 544.09/242.27 down(b) -> up(g(b)) 544.09/242.27 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.27 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.27 down(f(a)) -> f_flat(down(a)) 544.09/242.27 down(f(b)) -> f_flat(down(b)) 544.09/242.27 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.27 down(f(c)) -> f_flat(down(c)) 544.09/242.27 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.27 down(g(a)) -> g_flat(down(a)) 544.09/242.27 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.27 down(g(b)) -> g_flat(down(b)) 544.09/242.27 down(g(c)) -> g_flat(down(c)) 544.09/242.27 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.27 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.27 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.27 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.27 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.27 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.27 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.27 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.27 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.27 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.27 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.27 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.27 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.27 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.27 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.27 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.27 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.27 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.27 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.27 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.27 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.27 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.27 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.28 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.28 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.28 544.09/242.28 The set Q consists of the following terms: 544.09/242.28 544.09/242.28 down(a) 544.09/242.28 down(b) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.28 down(f(a)) 544.09/242.28 down(f(b)) 544.09/242.28 down(f(g(x0))) 544.09/242.28 down(f(c)) 544.09/242.28 down(f(fresh_constant)) 544.09/242.28 down(g(a)) 544.09/242.28 down(g(f(x0))) 544.09/242.28 down(g(b)) 544.09/242.28 down(g(c)) 544.09/242.28 down(g(fresh_constant)) 544.09/242.28 down(f(f(a))) 544.09/242.28 down(f(f(b))) 544.09/242.28 down(f(f(g(x0)))) 544.09/242.28 down(f(f(c))) 544.09/242.28 down(f(f(fresh_constant))) 544.09/242.28 down(g(g(a))) 544.09/242.28 down(g(g(f(x0)))) 544.09/242.28 down(g(g(b))) 544.09/242.28 down(g(g(c))) 544.09/242.28 down(g(g(fresh_constant))) 544.09/242.28 down(f(f(f(a)))) 544.09/242.28 down(f(f(f(b)))) 544.09/242.28 down(f(f(f(g(x0))))) 544.09/242.28 down(f(f(f(c)))) 544.09/242.28 down(f(f(f(fresh_constant)))) 544.09/242.28 down(g(g(g(a)))) 544.09/242.28 down(g(g(g(f(x0))))) 544.09/242.28 down(g(g(g(b)))) 544.09/242.28 down(g(g(g(c)))) 544.09/242.28 down(g(g(g(fresh_constant)))) 544.09/242.28 down(f(f(f(f(a))))) 544.09/242.28 down(f(f(f(f(b))))) 544.09/242.28 down(f(f(f(f(g(x0)))))) 544.09/242.28 down(f(f(f(f(c))))) 544.09/242.28 down(f(f(f(f(fresh_constant))))) 544.09/242.28 down(g(g(g(g(a))))) 544.09/242.28 down(g(g(g(g(f(x0)))))) 544.09/242.28 down(g(g(g(g(b))))) 544.09/242.28 down(g(g(g(g(c))))) 544.09/242.28 down(g(g(g(g(fresh_constant))))) 544.09/242.28 down(f(f(f(f(f(a)))))) 544.09/242.28 down(f(f(f(f(f(b)))))) 544.09/242.28 down(f(f(f(f(f(g(x0))))))) 544.09/242.28 down(f(f(f(f(f(c)))))) 544.09/242.28 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.28 down(g(g(g(g(g(a)))))) 544.09/242.28 down(g(g(g(g(g(f(x0))))))) 544.09/242.28 down(g(g(g(g(g(b)))))) 544.09/242.28 down(g(g(g(g(g(c)))))) 544.09/242.28 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.28 down(f(f(f(f(f(f(a))))))) 544.09/242.28 down(f(f(f(f(f(f(b))))))) 544.09/242.28 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.28 down(f(f(f(f(f(f(c))))))) 544.09/242.28 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.28 down(g(g(g(g(g(g(a))))))) 544.09/242.28 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.28 down(g(g(g(g(g(g(b))))))) 544.09/242.28 down(g(g(g(g(g(g(c))))))) 544.09/242.28 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.28 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.28 f_flat(up(x0)) 544.09/242.28 g_flat(up(x0)) 544.09/242.28 544.09/242.28 We have to consider all minimal (P,Q,R)-chains. 544.09/242.28 ---------------------------------------- 544.09/242.28 544.09/242.28 (1273) TransformationProof (EQUIVALENT) 544.09/242.28 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(f(a)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.09/242.28 544.09/242.28 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(f(a))))))))))))) 544.09/242.28 544.09/242.28 544.09/242.28 ---------------------------------------- 544.09/242.28 544.09/242.28 (1274) 544.09/242.28 Obligation: 544.09/242.28 Q DP problem: 544.09/242.28 The TRS P consists of the following rules: 544.09/242.28 544.09/242.28 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.28 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.28 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.28 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.28 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.28 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.28 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.28 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.28 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.28 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.28 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.28 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.28 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.28 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.28 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.28 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.28 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.28 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.28 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.28 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.09/242.28 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.09/242.28 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.09/242.28 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.09/242.28 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.09/242.28 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.09/242.28 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.09/242.28 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.09/242.28 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.09/242.28 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(g(b)))))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(g(b)))))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(f(a)))))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(f(a)))))))))))) 544.09/242.28 544.09/242.28 The TRS R consists of the following rules: 544.09/242.28 544.09/242.28 down(a) -> up(f(a)) 544.09/242.28 down(b) -> up(g(b)) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.09/242.28 down(f(a)) -> f_flat(down(a)) 544.09/242.28 down(f(b)) -> f_flat(down(b)) 544.09/242.28 down(f(g(y4))) -> f_flat(down(g(y4))) 544.09/242.28 down(f(c)) -> f_flat(down(c)) 544.09/242.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.09/242.28 down(g(a)) -> g_flat(down(a)) 544.09/242.28 down(g(f(y6))) -> g_flat(down(f(y6))) 544.09/242.28 down(g(b)) -> g_flat(down(b)) 544.09/242.28 down(g(c)) -> g_flat(down(c)) 544.09/242.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.09/242.28 down(f(f(a))) -> f_flat(down(f(a))) 544.09/242.28 down(f(f(b))) -> f_flat(down(f(b))) 544.09/242.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.09/242.28 down(f(f(c))) -> f_flat(down(f(c))) 544.09/242.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.09/242.28 down(g(g(a))) -> g_flat(down(g(a))) 544.09/242.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.09/242.28 down(g(g(b))) -> g_flat(down(g(b))) 544.09/242.28 down(g(g(c))) -> g_flat(down(g(c))) 544.09/242.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.09/242.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.09/242.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.09/242.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.09/242.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.09/242.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.09/242.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.09/242.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.09/242.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.09/242.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.09/242.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.09/242.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.09/242.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.09/242.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.09/242.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.09/242.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.09/242.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.09/242.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.09/242.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.09/242.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.09/242.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.09/242.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.09/242.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.09/242.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.09/242.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.09/242.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.09/242.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.09/242.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.09/242.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.09/242.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.09/242.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.09/242.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.09/242.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.09/242.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.09/242.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.09/242.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.09/242.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.09/242.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.09/242.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.09/242.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.09/242.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.09/242.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.28 g_flat(up(x_1)) -> up(g(x_1)) 544.09/242.28 f_flat(up(x_1)) -> up(f(x_1)) 544.09/242.28 544.09/242.28 The set Q consists of the following terms: 544.09/242.28 544.09/242.28 down(a) 544.09/242.28 down(b) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.09/242.28 down(f(a)) 544.09/242.28 down(f(b)) 544.09/242.28 down(f(g(x0))) 544.09/242.28 down(f(c)) 544.09/242.28 down(f(fresh_constant)) 544.09/242.28 down(g(a)) 544.09/242.28 down(g(f(x0))) 544.09/242.28 down(g(b)) 544.09/242.28 down(g(c)) 544.09/242.28 down(g(fresh_constant)) 544.09/242.28 down(f(f(a))) 544.09/242.28 down(f(f(b))) 544.09/242.28 down(f(f(g(x0)))) 544.09/242.28 down(f(f(c))) 544.09/242.28 down(f(f(fresh_constant))) 544.09/242.28 down(g(g(a))) 544.09/242.28 down(g(g(f(x0)))) 544.09/242.28 down(g(g(b))) 544.09/242.28 down(g(g(c))) 544.09/242.28 down(g(g(fresh_constant))) 544.09/242.28 down(f(f(f(a)))) 544.09/242.28 down(f(f(f(b)))) 544.09/242.28 down(f(f(f(g(x0))))) 544.09/242.28 down(f(f(f(c)))) 544.09/242.28 down(f(f(f(fresh_constant)))) 544.09/242.28 down(g(g(g(a)))) 544.09/242.28 down(g(g(g(f(x0))))) 544.09/242.28 down(g(g(g(b)))) 544.09/242.28 down(g(g(g(c)))) 544.09/242.28 down(g(g(g(fresh_constant)))) 544.09/242.28 down(f(f(f(f(a))))) 544.09/242.28 down(f(f(f(f(b))))) 544.09/242.28 down(f(f(f(f(g(x0)))))) 544.09/242.28 down(f(f(f(f(c))))) 544.09/242.28 down(f(f(f(f(fresh_constant))))) 544.09/242.28 down(g(g(g(g(a))))) 544.09/242.28 down(g(g(g(g(f(x0)))))) 544.09/242.28 down(g(g(g(g(b))))) 544.09/242.28 down(g(g(g(g(c))))) 544.09/242.28 down(g(g(g(g(fresh_constant))))) 544.09/242.28 down(f(f(f(f(f(a)))))) 544.09/242.28 down(f(f(f(f(f(b)))))) 544.09/242.28 down(f(f(f(f(f(g(x0))))))) 544.09/242.28 down(f(f(f(f(f(c)))))) 544.09/242.28 down(f(f(f(f(f(fresh_constant)))))) 544.09/242.28 down(g(g(g(g(g(a)))))) 544.09/242.28 down(g(g(g(g(g(f(x0))))))) 544.09/242.28 down(g(g(g(g(g(b)))))) 544.09/242.28 down(g(g(g(g(g(c)))))) 544.09/242.28 down(g(g(g(g(g(fresh_constant)))))) 544.09/242.28 down(f(f(f(f(f(f(a))))))) 544.09/242.28 down(f(f(f(f(f(f(b))))))) 544.09/242.28 down(f(f(f(f(f(f(g(x0)))))))) 544.09/242.28 down(f(f(f(f(f(f(c))))))) 544.09/242.28 down(f(f(f(f(f(f(fresh_constant))))))) 544.09/242.28 down(g(g(g(g(g(g(a))))))) 544.09/242.28 down(g(g(g(g(g(g(f(x0)))))))) 544.09/242.28 down(g(g(g(g(g(g(b))))))) 544.09/242.28 down(g(g(g(g(g(g(c))))))) 544.09/242.28 down(g(g(g(g(g(g(fresh_constant))))))) 544.09/242.28 down(f(f(f(f(f(f(f(a)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(b)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(g(x0))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(c)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(a)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(f(x0))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(b)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(c)))))))) 544.09/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(a))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(b))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(c))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(a))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(b))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(c))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.09/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.09/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.09/242.28 f_flat(up(x0)) 544.09/242.28 g_flat(up(x0)) 544.09/242.28 544.09/242.28 We have to consider all minimal (P,Q,R)-chains. 544.09/242.28 ---------------------------------------- 544.09/242.28 544.09/242.28 (1275) TransformationProof (EQUIVALENT) 544.09/242.28 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(f_flat(up(f(f(f(f(f(f(f(g(b)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.09/242.28 544.09/242.28 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(g(b))))))))))))) 544.09/242.28 544.09/242.28 544.09/242.28 ---------------------------------------- 544.09/242.28 544.09/242.28 (1276) 544.09/242.28 Obligation: 544.09/242.28 Q DP problem: 544.09/242.28 The TRS P consists of the following rules: 544.09/242.28 544.09/242.28 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.09/242.28 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.09/242.28 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.09/242.28 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.09/242.28 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.09/242.28 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.09/242.28 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.09/242.28 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.09/242.28 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.09/242.28 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.09/242.28 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.09/242.28 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.09/242.28 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.09/242.28 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.09/242.28 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.09/242.28 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.09/242.28 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.09/242.28 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.09/242.28 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.09/242.28 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.09/242.28 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.09/242.28 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.28 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.28 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.28 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.28 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.28 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.28 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(g(b)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(f(a)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.28 544.15/242.28 The TRS R consists of the following rules: 544.15/242.28 544.15/242.28 down(a) -> up(f(a)) 544.15/242.28 down(b) -> up(g(b)) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.28 down(f(a)) -> f_flat(down(a)) 544.15/242.28 down(f(b)) -> f_flat(down(b)) 544.15/242.28 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.28 down(f(c)) -> f_flat(down(c)) 544.15/242.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.28 down(g(a)) -> g_flat(down(a)) 544.15/242.28 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.28 down(g(b)) -> g_flat(down(b)) 544.15/242.28 down(g(c)) -> g_flat(down(c)) 544.15/242.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.28 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.28 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.28 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.28 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.28 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.28 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.28 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.28 544.15/242.28 The set Q consists of the following terms: 544.15/242.28 544.15/242.28 down(a) 544.15/242.28 down(b) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.28 down(f(a)) 544.15/242.28 down(f(b)) 544.15/242.28 down(f(g(x0))) 544.15/242.28 down(f(c)) 544.15/242.28 down(f(fresh_constant)) 544.15/242.28 down(g(a)) 544.15/242.28 down(g(f(x0))) 544.15/242.28 down(g(b)) 544.15/242.28 down(g(c)) 544.15/242.28 down(g(fresh_constant)) 544.15/242.28 down(f(f(a))) 544.15/242.28 down(f(f(b))) 544.15/242.28 down(f(f(g(x0)))) 544.15/242.28 down(f(f(c))) 544.15/242.28 down(f(f(fresh_constant))) 544.15/242.28 down(g(g(a))) 544.15/242.28 down(g(g(f(x0)))) 544.15/242.28 down(g(g(b))) 544.15/242.28 down(g(g(c))) 544.15/242.28 down(g(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) 544.15/242.28 down(f(f(f(g(x0))))) 544.15/242.28 down(f(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) 544.15/242.28 down(g(g(g(f(x0))))) 544.15/242.28 down(g(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(x0)))))) 544.15/242.28 down(f(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(x0)))))) 544.15/242.28 down(g(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(x0))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(x0))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 f_flat(up(x0)) 544.15/242.28 g_flat(up(x0)) 544.15/242.28 544.15/242.28 We have to consider all minimal (P,Q,R)-chains. 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1277) TransformationProof (EQUIVALENT) 544.15/242.28 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(g_flat(up(g(g(g(g(g(g(g(b)))))))))))) at position [0,0,0] we obtained the following new rules [LPAR04]: 544.15/242.28 544.15/242.28 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(g(b))))))))))))) 544.15/242.28 544.15/242.28 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1278) 544.15/242.28 Obligation: 544.15/242.28 Q DP problem: 544.15/242.28 The TRS P consists of the following rules: 544.15/242.28 544.15/242.28 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.28 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.28 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.28 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.28 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.15/242.28 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.15/242.28 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.15/242.28 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.15/242.28 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.28 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.28 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.15/242.28 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.15/242.28 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.15/242.28 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.28 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.28 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.28 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.28 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.28 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.28 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.28 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.28 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.28 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(f(a)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(g(b)))))))))))) 544.15/242.28 544.15/242.28 The TRS R consists of the following rules: 544.15/242.28 544.15/242.28 down(a) -> up(f(a)) 544.15/242.28 down(b) -> up(g(b)) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.28 down(f(a)) -> f_flat(down(a)) 544.15/242.28 down(f(b)) -> f_flat(down(b)) 544.15/242.28 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.28 down(f(c)) -> f_flat(down(c)) 544.15/242.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.28 down(g(a)) -> g_flat(down(a)) 544.15/242.28 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.28 down(g(b)) -> g_flat(down(b)) 544.15/242.28 down(g(c)) -> g_flat(down(c)) 544.15/242.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.28 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.28 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.28 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.28 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.28 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.28 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.28 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.28 544.15/242.28 The set Q consists of the following terms: 544.15/242.28 544.15/242.28 down(a) 544.15/242.28 down(b) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.28 down(f(a)) 544.15/242.28 down(f(b)) 544.15/242.28 down(f(g(x0))) 544.15/242.28 down(f(c)) 544.15/242.28 down(f(fresh_constant)) 544.15/242.28 down(g(a)) 544.15/242.28 down(g(f(x0))) 544.15/242.28 down(g(b)) 544.15/242.28 down(g(c)) 544.15/242.28 down(g(fresh_constant)) 544.15/242.28 down(f(f(a))) 544.15/242.28 down(f(f(b))) 544.15/242.28 down(f(f(g(x0)))) 544.15/242.28 down(f(f(c))) 544.15/242.28 down(f(f(fresh_constant))) 544.15/242.28 down(g(g(a))) 544.15/242.28 down(g(g(f(x0)))) 544.15/242.28 down(g(g(b))) 544.15/242.28 down(g(g(c))) 544.15/242.28 down(g(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) 544.15/242.28 down(f(f(f(g(x0))))) 544.15/242.28 down(f(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) 544.15/242.28 down(g(g(g(f(x0))))) 544.15/242.28 down(g(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(x0)))))) 544.15/242.28 down(f(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(x0)))))) 544.15/242.28 down(g(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(x0))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(x0))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 f_flat(up(x0)) 544.15/242.28 g_flat(up(x0)) 544.15/242.28 544.15/242.28 We have to consider all minimal (P,Q,R)-chains. 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1279) TransformationProof (EQUIVALENT) 544.15/242.28 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(f(a)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.15/242.28 544.15/242.28 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(f(a))))))))))))) 544.15/242.28 544.15/242.28 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1280) 544.15/242.28 Obligation: 544.15/242.28 Q DP problem: 544.15/242.28 The TRS P consists of the following rules: 544.15/242.28 544.15/242.28 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.28 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.28 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.28 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.28 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.15/242.28 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.15/242.28 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.15/242.28 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.15/242.28 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.28 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.28 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.15/242.28 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.15/242.28 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.15/242.28 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.28 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.28 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.28 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.28 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.28 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.28 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.28 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.28 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.28 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(f(a)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(g(b)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.28 544.15/242.28 The TRS R consists of the following rules: 544.15/242.28 544.15/242.28 down(a) -> up(f(a)) 544.15/242.28 down(b) -> up(g(b)) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.28 down(f(a)) -> f_flat(down(a)) 544.15/242.28 down(f(b)) -> f_flat(down(b)) 544.15/242.28 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.28 down(f(c)) -> f_flat(down(c)) 544.15/242.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.28 down(g(a)) -> g_flat(down(a)) 544.15/242.28 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.28 down(g(b)) -> g_flat(down(b)) 544.15/242.28 down(g(c)) -> g_flat(down(c)) 544.15/242.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.28 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.28 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.28 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.28 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.28 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.28 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.28 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.28 544.15/242.28 The set Q consists of the following terms: 544.15/242.28 544.15/242.28 down(a) 544.15/242.28 down(b) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.28 down(f(a)) 544.15/242.28 down(f(b)) 544.15/242.28 down(f(g(x0))) 544.15/242.28 down(f(c)) 544.15/242.28 down(f(fresh_constant)) 544.15/242.28 down(g(a)) 544.15/242.28 down(g(f(x0))) 544.15/242.28 down(g(b)) 544.15/242.28 down(g(c)) 544.15/242.28 down(g(fresh_constant)) 544.15/242.28 down(f(f(a))) 544.15/242.28 down(f(f(b))) 544.15/242.28 down(f(f(g(x0)))) 544.15/242.28 down(f(f(c))) 544.15/242.28 down(f(f(fresh_constant))) 544.15/242.28 down(g(g(a))) 544.15/242.28 down(g(g(f(x0)))) 544.15/242.28 down(g(g(b))) 544.15/242.28 down(g(g(c))) 544.15/242.28 down(g(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) 544.15/242.28 down(f(f(f(g(x0))))) 544.15/242.28 down(f(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) 544.15/242.28 down(g(g(g(f(x0))))) 544.15/242.28 down(g(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(x0)))))) 544.15/242.28 down(f(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(x0)))))) 544.15/242.28 down(g(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(x0))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(x0))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 f_flat(up(x0)) 544.15/242.28 g_flat(up(x0)) 544.15/242.28 544.15/242.28 We have to consider all minimal (P,Q,R)-chains. 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1281) TransformationProof (EQUIVALENT) 544.15/242.28 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(f(a)))))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.15/242.28 544.15/242.28 (TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(f(a)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(f(a))))))))))))) 544.15/242.28 544.15/242.28 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1282) 544.15/242.28 Obligation: 544.15/242.28 Q DP problem: 544.15/242.28 The TRS P consists of the following rules: 544.15/242.28 544.15/242.28 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.28 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.28 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.28 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.28 TOP(up(f(a))) -> TOP(up(f(f(a)))) 544.15/242.28 TOP(up(f(f(a)))) -> TOP(up(f(f(f(a))))) 544.15/242.28 TOP(up(f(f(f(a))))) -> TOP(up(f(f(f(f(a)))))) 544.15/242.28 TOP(up(f(f(f(f(a)))))) -> TOP(up(f(f(f(f(f(a))))))) 544.15/242.28 TOP(up(f(f(f(f(f(a))))))) -> TOP(up(f(f(f(f(f(f(a)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(a)))))))) -> TOP(up(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(a))))))))) -> TOP(up(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.28 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.28 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.15/242.28 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.15/242.28 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.15/242.28 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.28 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.28 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.28 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.28 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.28 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.28 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.28 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.28 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.28 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(a)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(g(b)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(a))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(f(a)))))))))))) 544.15/242.28 544.15/242.28 The TRS R consists of the following rules: 544.15/242.28 544.15/242.28 down(a) -> up(f(a)) 544.15/242.28 down(b) -> up(g(b)) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.28 down(f(a)) -> f_flat(down(a)) 544.15/242.28 down(f(b)) -> f_flat(down(b)) 544.15/242.28 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.28 down(f(c)) -> f_flat(down(c)) 544.15/242.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.28 down(g(a)) -> g_flat(down(a)) 544.15/242.28 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.28 down(g(b)) -> g_flat(down(b)) 544.15/242.28 down(g(c)) -> g_flat(down(c)) 544.15/242.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.28 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.28 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.28 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.28 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.28 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.28 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.28 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.28 544.15/242.28 The set Q consists of the following terms: 544.15/242.28 544.15/242.28 down(a) 544.15/242.28 down(b) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.28 down(f(a)) 544.15/242.28 down(f(b)) 544.15/242.28 down(f(g(x0))) 544.15/242.28 down(f(c)) 544.15/242.28 down(f(fresh_constant)) 544.15/242.28 down(g(a)) 544.15/242.28 down(g(f(x0))) 544.15/242.28 down(g(b)) 544.15/242.28 down(g(c)) 544.15/242.28 down(g(fresh_constant)) 544.15/242.28 down(f(f(a))) 544.15/242.28 down(f(f(b))) 544.15/242.28 down(f(f(g(x0)))) 544.15/242.28 down(f(f(c))) 544.15/242.28 down(f(f(fresh_constant))) 544.15/242.28 down(g(g(a))) 544.15/242.28 down(g(g(f(x0)))) 544.15/242.28 down(g(g(b))) 544.15/242.28 down(g(g(c))) 544.15/242.28 down(g(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) 544.15/242.28 down(f(f(f(g(x0))))) 544.15/242.28 down(f(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) 544.15/242.28 down(g(g(g(f(x0))))) 544.15/242.28 down(g(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(x0)))))) 544.15/242.28 down(f(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(x0)))))) 544.15/242.28 down(g(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(x0))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(x0))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 f_flat(up(x0)) 544.15/242.28 g_flat(up(x0)) 544.15/242.28 544.15/242.28 We have to consider all minimal (P,Q,R)-chains. 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1283) DependencyGraphProof (EQUIVALENT) 544.15/242.28 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 9 less nodes. 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1284) 544.15/242.28 Obligation: 544.15/242.28 Q DP problem: 544.15/242.28 The TRS P consists of the following rules: 544.15/242.28 544.15/242.28 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.28 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.28 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.28 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.28 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.28 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.15/242.28 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.15/242.28 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.15/242.28 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(g(b)))))))))))) 544.15/242.28 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.28 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.28 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.28 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.28 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.28 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.28 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.28 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.28 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.28 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.28 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.28 544.15/242.28 The TRS R consists of the following rules: 544.15/242.28 544.15/242.28 down(a) -> up(f(a)) 544.15/242.28 down(b) -> up(g(b)) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.28 down(f(a)) -> f_flat(down(a)) 544.15/242.28 down(f(b)) -> f_flat(down(b)) 544.15/242.28 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.28 down(f(c)) -> f_flat(down(c)) 544.15/242.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.28 down(g(a)) -> g_flat(down(a)) 544.15/242.28 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.28 down(g(b)) -> g_flat(down(b)) 544.15/242.28 down(g(c)) -> g_flat(down(c)) 544.15/242.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.28 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.28 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.28 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.28 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.28 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.28 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.28 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.28 544.15/242.28 The set Q consists of the following terms: 544.15/242.28 544.15/242.28 down(a) 544.15/242.28 down(b) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.28 down(f(a)) 544.15/242.28 down(f(b)) 544.15/242.28 down(f(g(x0))) 544.15/242.28 down(f(c)) 544.15/242.28 down(f(fresh_constant)) 544.15/242.28 down(g(a)) 544.15/242.28 down(g(f(x0))) 544.15/242.28 down(g(b)) 544.15/242.28 down(g(c)) 544.15/242.28 down(g(fresh_constant)) 544.15/242.28 down(f(f(a))) 544.15/242.28 down(f(f(b))) 544.15/242.28 down(f(f(g(x0)))) 544.15/242.28 down(f(f(c))) 544.15/242.28 down(f(f(fresh_constant))) 544.15/242.28 down(g(g(a))) 544.15/242.28 down(g(g(f(x0)))) 544.15/242.28 down(g(g(b))) 544.15/242.28 down(g(g(c))) 544.15/242.28 down(g(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) 544.15/242.28 down(f(f(f(g(x0))))) 544.15/242.28 down(f(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) 544.15/242.28 down(g(g(g(f(x0))))) 544.15/242.28 down(g(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(x0)))))) 544.15/242.28 down(f(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(x0)))))) 544.15/242.28 down(g(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(x0))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(x0))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 f_flat(up(x0)) 544.15/242.28 g_flat(up(x0)) 544.15/242.28 544.15/242.28 We have to consider all minimal (P,Q,R)-chains. 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1285) TransformationProof (EQUIVALENT) 544.15/242.28 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(g_flat(up(g(g(g(g(g(g(g(g(b)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 544.15/242.28 544.15/242.28 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(g(b))))))))))))) 544.15/242.28 544.15/242.28 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1286) 544.15/242.28 Obligation: 544.15/242.28 Q DP problem: 544.15/242.28 The TRS P consists of the following rules: 544.15/242.28 544.15/242.28 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.28 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.28 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.28 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.28 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.28 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.15/242.28 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.15/242.28 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.15/242.28 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.15/242.28 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.28 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.28 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.28 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.28 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.28 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.28 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.28 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.28 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.28 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.28 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.28 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(g(b)))))))))))) 544.15/242.28 544.15/242.28 The TRS R consists of the following rules: 544.15/242.28 544.15/242.28 down(a) -> up(f(a)) 544.15/242.28 down(b) -> up(g(b)) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.28 down(f(a)) -> f_flat(down(a)) 544.15/242.28 down(f(b)) -> f_flat(down(b)) 544.15/242.28 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.28 down(f(c)) -> f_flat(down(c)) 544.15/242.28 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.28 down(g(a)) -> g_flat(down(a)) 544.15/242.28 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.28 down(g(b)) -> g_flat(down(b)) 544.15/242.28 down(g(c)) -> g_flat(down(c)) 544.15/242.28 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.28 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.28 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.28 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.28 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.28 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.28 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.28 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.28 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.28 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.28 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.28 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.28 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.28 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.28 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.28 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.28 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.28 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.28 544.15/242.28 The set Q consists of the following terms: 544.15/242.28 544.15/242.28 down(a) 544.15/242.28 down(b) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.28 down(f(a)) 544.15/242.28 down(f(b)) 544.15/242.28 down(f(g(x0))) 544.15/242.28 down(f(c)) 544.15/242.28 down(f(fresh_constant)) 544.15/242.28 down(g(a)) 544.15/242.28 down(g(f(x0))) 544.15/242.28 down(g(b)) 544.15/242.28 down(g(c)) 544.15/242.28 down(g(fresh_constant)) 544.15/242.28 down(f(f(a))) 544.15/242.28 down(f(f(b))) 544.15/242.28 down(f(f(g(x0)))) 544.15/242.28 down(f(f(c))) 544.15/242.28 down(f(f(fresh_constant))) 544.15/242.28 down(g(g(a))) 544.15/242.28 down(g(g(f(x0)))) 544.15/242.28 down(g(g(b))) 544.15/242.28 down(g(g(c))) 544.15/242.28 down(g(g(fresh_constant))) 544.15/242.28 down(f(f(f(a)))) 544.15/242.28 down(f(f(f(b)))) 544.15/242.28 down(f(f(f(g(x0))))) 544.15/242.28 down(f(f(f(c)))) 544.15/242.28 down(f(f(f(fresh_constant)))) 544.15/242.28 down(g(g(g(a)))) 544.15/242.28 down(g(g(g(f(x0))))) 544.15/242.28 down(g(g(g(b)))) 544.15/242.28 down(g(g(g(c)))) 544.15/242.28 down(g(g(g(fresh_constant)))) 544.15/242.28 down(f(f(f(f(a))))) 544.15/242.28 down(f(f(f(f(b))))) 544.15/242.28 down(f(f(f(f(g(x0)))))) 544.15/242.28 down(f(f(f(f(c))))) 544.15/242.28 down(f(f(f(f(fresh_constant))))) 544.15/242.28 down(g(g(g(g(a))))) 544.15/242.28 down(g(g(g(g(f(x0)))))) 544.15/242.28 down(g(g(g(g(b))))) 544.15/242.28 down(g(g(g(g(c))))) 544.15/242.28 down(g(g(g(g(fresh_constant))))) 544.15/242.28 down(f(f(f(f(f(a)))))) 544.15/242.28 down(f(f(f(f(f(b)))))) 544.15/242.28 down(f(f(f(f(f(g(x0))))))) 544.15/242.28 down(f(f(f(f(f(c)))))) 544.15/242.28 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.28 down(g(g(g(g(g(a)))))) 544.15/242.28 down(g(g(g(g(g(f(x0))))))) 544.15/242.28 down(g(g(g(g(g(b)))))) 544.15/242.28 down(g(g(g(g(g(c)))))) 544.15/242.28 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.28 down(f(f(f(f(f(f(a))))))) 544.15/242.28 down(f(f(f(f(f(f(b))))))) 544.15/242.28 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.28 down(f(f(f(f(f(f(c))))))) 544.15/242.28 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.28 down(g(g(g(g(g(g(a))))))) 544.15/242.28 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.28 down(g(g(g(g(g(g(b))))))) 544.15/242.28 down(g(g(g(g(g(g(c))))))) 544.15/242.28 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.28 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.28 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.28 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.28 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.28 f_flat(up(x0)) 544.15/242.28 g_flat(up(x0)) 544.15/242.28 544.15/242.28 We have to consider all minimal (P,Q,R)-chains. 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1287) TransformationProof (EQUIVALENT) 544.15/242.28 By rewriting [LPAR04] the rule TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(f_flat(up(f(f(f(f(f(f(f(f(g(b)))))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.15/242.28 544.15/242.28 (TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(g(b)))))))))))),TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(g(b))))))))))))) 544.15/242.28 544.15/242.28 544.15/242.28 ---------------------------------------- 544.15/242.28 544.15/242.28 (1288) 544.15/242.28 Obligation: 544.15/242.28 Q DP problem: 544.15/242.28 The TRS P consists of the following rules: 544.15/242.28 544.15/242.28 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.28 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.28 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.28 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.28 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.28 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.15/242.28 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.15/242.28 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.15/242.28 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.15/242.28 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.28 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.15/242.28 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.28 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.28 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.28 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.28 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.28 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.28 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.28 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.28 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.29 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.29 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.29 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.29 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(g(b)))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.29 544.15/242.29 The TRS R consists of the following rules: 544.15/242.29 544.15/242.29 down(a) -> up(f(a)) 544.15/242.29 down(b) -> up(g(b)) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.29 down(f(a)) -> f_flat(down(a)) 544.15/242.29 down(f(b)) -> f_flat(down(b)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(c)) -> f_flat(down(c)) 544.15/242.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.29 down(g(a)) -> g_flat(down(a)) 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(b)) -> g_flat(down(b)) 544.15/242.29 down(g(c)) -> g_flat(down(c)) 544.15/242.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.29 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.29 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.29 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.29 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 544.15/242.29 The set Q consists of the following terms: 544.15/242.29 544.15/242.29 down(a) 544.15/242.29 down(b) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.29 down(f(a)) 544.15/242.29 down(f(b)) 544.15/242.29 down(f(g(x0))) 544.15/242.29 down(f(c)) 544.15/242.29 down(f(fresh_constant)) 544.15/242.29 down(g(a)) 544.15/242.29 down(g(f(x0))) 544.15/242.29 down(g(b)) 544.15/242.29 down(g(c)) 544.15/242.29 down(g(fresh_constant)) 544.15/242.29 down(f(f(a))) 544.15/242.29 down(f(f(b))) 544.15/242.29 down(f(f(g(x0)))) 544.15/242.29 down(f(f(c))) 544.15/242.29 down(f(f(fresh_constant))) 544.15/242.29 down(g(g(a))) 544.15/242.29 down(g(g(f(x0)))) 544.15/242.29 down(g(g(b))) 544.15/242.29 down(g(g(c))) 544.15/242.29 down(g(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) 544.15/242.29 down(f(f(f(g(x0))))) 544.15/242.29 down(f(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) 544.15/242.29 down(g(g(g(f(x0))))) 544.15/242.29 down(g(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(x0)))))) 544.15/242.29 down(f(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(x0)))))) 544.15/242.29 down(g(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(x0))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(x0))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 f_flat(up(x0)) 544.15/242.29 g_flat(up(x0)) 544.15/242.29 544.15/242.29 We have to consider all minimal (P,Q,R)-chains. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1289) TransformationProof (EQUIVALENT) 544.15/242.29 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(f(a)))))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.15/242.29 544.15/242.29 (TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(f(a)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(f(a))))))))))))) 544.15/242.29 544.15/242.29 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1290) 544.15/242.29 Obligation: 544.15/242.29 Q DP problem: 544.15/242.29 The TRS P consists of the following rules: 544.15/242.29 544.15/242.29 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.29 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.29 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.29 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.29 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.29 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.15/242.29 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.15/242.29 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.15/242.29 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.15/242.29 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.15/242.29 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.29 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.29 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.29 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.29 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.29 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.29 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.29 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.29 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.29 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.29 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.29 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(g(b)))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.29 544.15/242.29 The TRS R consists of the following rules: 544.15/242.29 544.15/242.29 down(a) -> up(f(a)) 544.15/242.29 down(b) -> up(g(b)) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.29 down(f(a)) -> f_flat(down(a)) 544.15/242.29 down(f(b)) -> f_flat(down(b)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(c)) -> f_flat(down(c)) 544.15/242.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.29 down(g(a)) -> g_flat(down(a)) 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(b)) -> g_flat(down(b)) 544.15/242.29 down(g(c)) -> g_flat(down(c)) 544.15/242.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.29 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.29 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.29 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.29 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 544.15/242.29 The set Q consists of the following terms: 544.15/242.29 544.15/242.29 down(a) 544.15/242.29 down(b) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.29 down(f(a)) 544.15/242.29 down(f(b)) 544.15/242.29 down(f(g(x0))) 544.15/242.29 down(f(c)) 544.15/242.29 down(f(fresh_constant)) 544.15/242.29 down(g(a)) 544.15/242.29 down(g(f(x0))) 544.15/242.29 down(g(b)) 544.15/242.29 down(g(c)) 544.15/242.29 down(g(fresh_constant)) 544.15/242.29 down(f(f(a))) 544.15/242.29 down(f(f(b))) 544.15/242.29 down(f(f(g(x0)))) 544.15/242.29 down(f(f(c))) 544.15/242.29 down(f(f(fresh_constant))) 544.15/242.29 down(g(g(a))) 544.15/242.29 down(g(g(f(x0)))) 544.15/242.29 down(g(g(b))) 544.15/242.29 down(g(g(c))) 544.15/242.29 down(g(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) 544.15/242.29 down(f(f(f(g(x0))))) 544.15/242.29 down(f(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) 544.15/242.29 down(g(g(g(f(x0))))) 544.15/242.29 down(g(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(x0)))))) 544.15/242.29 down(f(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(x0)))))) 544.15/242.29 down(g(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(x0))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(x0))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 f_flat(up(x0)) 544.15/242.29 g_flat(up(x0)) 544.15/242.29 544.15/242.29 We have to consider all minimal (P,Q,R)-chains. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1291) TransformationProof (EQUIVALENT) 544.15/242.29 By rewriting [LPAR04] the rule TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(g_flat(up(g(g(g(g(g(g(g(g(g(b)))))))))))) at position [0] we obtained the following new rules [LPAR04]: 544.15/242.29 544.15/242.29 (TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(g(b)))))))))))),TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(g(b))))))))))))) 544.15/242.29 544.15/242.29 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1292) 544.15/242.29 Obligation: 544.15/242.29 Q DP problem: 544.15/242.29 The TRS P consists of the following rules: 544.15/242.29 544.15/242.29 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.29 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.29 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.29 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.29 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.29 TOP(up(g(b))) -> TOP(up(g(g(b)))) 544.15/242.29 TOP(up(g(g(b)))) -> TOP(up(g(g(g(b))))) 544.15/242.29 TOP(up(g(g(g(b))))) -> TOP(up(g(g(g(g(b)))))) 544.15/242.29 TOP(up(g(g(g(g(b)))))) -> TOP(up(g(g(g(g(g(b))))))) 544.15/242.29 TOP(up(g(g(g(g(g(b))))))) -> TOP(up(g(g(g(g(g(g(b)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(b)))))))) -> TOP(up(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(b))))))))) -> TOP(up(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(b)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) 544.15/242.29 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.29 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.29 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.29 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.29 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.29 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.29 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.29 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.29 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.29 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.29 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.29 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(b))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(g(b)))))))))))) 544.15/242.29 544.15/242.29 The TRS R consists of the following rules: 544.15/242.29 544.15/242.29 down(a) -> up(f(a)) 544.15/242.29 down(b) -> up(g(b)) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.29 down(f(a)) -> f_flat(down(a)) 544.15/242.29 down(f(b)) -> f_flat(down(b)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(c)) -> f_flat(down(c)) 544.15/242.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.29 down(g(a)) -> g_flat(down(a)) 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(b)) -> g_flat(down(b)) 544.15/242.29 down(g(c)) -> g_flat(down(c)) 544.15/242.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.29 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.29 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.29 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.29 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 544.15/242.29 The set Q consists of the following terms: 544.15/242.29 544.15/242.29 down(a) 544.15/242.29 down(b) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.29 down(f(a)) 544.15/242.29 down(f(b)) 544.15/242.29 down(f(g(x0))) 544.15/242.29 down(f(c)) 544.15/242.29 down(f(fresh_constant)) 544.15/242.29 down(g(a)) 544.15/242.29 down(g(f(x0))) 544.15/242.29 down(g(b)) 544.15/242.29 down(g(c)) 544.15/242.29 down(g(fresh_constant)) 544.15/242.29 down(f(f(a))) 544.15/242.29 down(f(f(b))) 544.15/242.29 down(f(f(g(x0)))) 544.15/242.29 down(f(f(c))) 544.15/242.29 down(f(f(fresh_constant))) 544.15/242.29 down(g(g(a))) 544.15/242.29 down(g(g(f(x0)))) 544.15/242.29 down(g(g(b))) 544.15/242.29 down(g(g(c))) 544.15/242.29 down(g(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) 544.15/242.29 down(f(f(f(g(x0))))) 544.15/242.29 down(f(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) 544.15/242.29 down(g(g(g(f(x0))))) 544.15/242.29 down(g(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(x0)))))) 544.15/242.29 down(f(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(x0)))))) 544.15/242.29 down(g(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(x0))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(x0))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 f_flat(up(x0)) 544.15/242.29 g_flat(up(x0)) 544.15/242.29 544.15/242.29 We have to consider all minimal (P,Q,R)-chains. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1293) DependencyGraphProof (EQUIVALENT) 544.15/242.29 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 9 less nodes. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1294) 544.15/242.29 Obligation: 544.15/242.29 Q DP problem: 544.15/242.29 The TRS P consists of the following rules: 544.15/242.29 544.15/242.29 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.29 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.29 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.29 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.29 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.29 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.29 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.29 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.29 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.29 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.29 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.29 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.29 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.29 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.29 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.29 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.29 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.29 544.15/242.29 The TRS R consists of the following rules: 544.15/242.29 544.15/242.29 down(a) -> up(f(a)) 544.15/242.29 down(b) -> up(g(b)) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.29 down(f(a)) -> f_flat(down(a)) 544.15/242.29 down(f(b)) -> f_flat(down(b)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(c)) -> f_flat(down(c)) 544.15/242.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.29 down(g(a)) -> g_flat(down(a)) 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(b)) -> g_flat(down(b)) 544.15/242.29 down(g(c)) -> g_flat(down(c)) 544.15/242.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.29 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.29 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.29 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.29 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 544.15/242.29 The set Q consists of the following terms: 544.15/242.29 544.15/242.29 down(a) 544.15/242.29 down(b) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.29 down(f(a)) 544.15/242.29 down(f(b)) 544.15/242.29 down(f(g(x0))) 544.15/242.29 down(f(c)) 544.15/242.29 down(f(fresh_constant)) 544.15/242.29 down(g(a)) 544.15/242.29 down(g(f(x0))) 544.15/242.29 down(g(b)) 544.15/242.29 down(g(c)) 544.15/242.29 down(g(fresh_constant)) 544.15/242.29 down(f(f(a))) 544.15/242.29 down(f(f(b))) 544.15/242.29 down(f(f(g(x0)))) 544.15/242.29 down(f(f(c))) 544.15/242.29 down(f(f(fresh_constant))) 544.15/242.29 down(g(g(a))) 544.15/242.29 down(g(g(f(x0)))) 544.15/242.29 down(g(g(b))) 544.15/242.29 down(g(g(c))) 544.15/242.29 down(g(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) 544.15/242.29 down(f(f(f(g(x0))))) 544.15/242.29 down(f(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) 544.15/242.29 down(g(g(g(f(x0))))) 544.15/242.29 down(g(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(x0)))))) 544.15/242.29 down(f(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(x0)))))) 544.15/242.29 down(g(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(x0))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(x0))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 f_flat(up(x0)) 544.15/242.29 g_flat(up(x0)) 544.15/242.29 544.15/242.29 We have to consider all minimal (P,Q,R)-chains. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1295) QDPOrderProof (EQUIVALENT) 544.15/242.29 We use the reduction pair processor [LPAR04,JAR06]. 544.15/242.29 544.15/242.29 544.15/242.29 The following pairs can be oriented strictly and are deleted. 544.15/242.29 544.15/242.29 TOP(up(f(b))) -> TOP(up(f(g(b)))) 544.15/242.29 TOP(up(f(f(b)))) -> TOP(up(f(f(g(b))))) 544.15/242.29 TOP(up(f(f(f(b))))) -> TOP(up(f(f(f(g(b)))))) 544.15/242.29 TOP(up(f(f(f(f(b)))))) -> TOP(up(f(f(f(f(g(b))))))) 544.15/242.29 TOP(up(f(f(f(f(f(b))))))) -> TOP(up(f(f(f(f(f(g(b)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(b)))))))) -> TOP(up(f(f(f(f(f(f(g(b))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(b))))))))) -> TOP(up(f(f(f(f(f(f(f(g(b)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(b)))))))))) -> TOP(up(f(f(f(f(f(f(f(f(g(b))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(b))))))))))) -> TOP(up(f(f(f(f(f(f(f(f(f(g(b)))))))))))) 544.15/242.29 The remaining pairs can at least be oriented weakly. 544.15/242.29 Used ordering: Polynomial interpretation [POLO]: 544.15/242.29 544.15/242.29 POL(TOP(x_1)) = x_1 544.15/242.29 POL(a) = 0 544.15/242.29 POL(b) = 1 544.15/242.29 POL(c) = 0 544.15/242.29 POL(down(x_1)) = 0 544.15/242.29 POL(f(x_1)) = x_1 544.15/242.29 POL(f_flat(x_1)) = x_1 544.15/242.29 POL(fresh_constant) = 0 544.15/242.29 POL(g(x_1)) = 0 544.15/242.29 POL(g_flat(x_1)) = 0 544.15/242.29 POL(up(x_1)) = x_1 544.15/242.29 544.15/242.29 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 544.15/242.29 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.29 down(g(a)) -> g_flat(down(a)) 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(b)) -> g_flat(down(b)) 544.15/242.29 down(g(c)) -> g_flat(down(c)) 544.15/242.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.29 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.29 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 544.15/242.29 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1296) 544.15/242.29 Obligation: 544.15/242.29 Q DP problem: 544.15/242.29 The TRS P consists of the following rules: 544.15/242.29 544.15/242.29 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.29 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.29 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.29 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.29 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.29 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.29 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.29 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.29 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.29 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.29 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.29 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.29 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.29 544.15/242.29 The TRS R consists of the following rules: 544.15/242.29 544.15/242.29 down(a) -> up(f(a)) 544.15/242.29 down(b) -> up(g(b)) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.29 down(f(a)) -> f_flat(down(a)) 544.15/242.29 down(f(b)) -> f_flat(down(b)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(c)) -> f_flat(down(c)) 544.15/242.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.29 down(g(a)) -> g_flat(down(a)) 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(b)) -> g_flat(down(b)) 544.15/242.29 down(g(c)) -> g_flat(down(c)) 544.15/242.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.29 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.29 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.29 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.29 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 544.15/242.29 The set Q consists of the following terms: 544.15/242.29 544.15/242.29 down(a) 544.15/242.29 down(b) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.29 down(f(a)) 544.15/242.29 down(f(b)) 544.15/242.29 down(f(g(x0))) 544.15/242.29 down(f(c)) 544.15/242.29 down(f(fresh_constant)) 544.15/242.29 down(g(a)) 544.15/242.29 down(g(f(x0))) 544.15/242.29 down(g(b)) 544.15/242.29 down(g(c)) 544.15/242.29 down(g(fresh_constant)) 544.15/242.29 down(f(f(a))) 544.15/242.29 down(f(f(b))) 544.15/242.29 down(f(f(g(x0)))) 544.15/242.29 down(f(f(c))) 544.15/242.29 down(f(f(fresh_constant))) 544.15/242.29 down(g(g(a))) 544.15/242.29 down(g(g(f(x0)))) 544.15/242.29 down(g(g(b))) 544.15/242.29 down(g(g(c))) 544.15/242.29 down(g(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) 544.15/242.29 down(f(f(f(g(x0))))) 544.15/242.29 down(f(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) 544.15/242.29 down(g(g(g(f(x0))))) 544.15/242.29 down(g(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(x0)))))) 544.15/242.29 down(f(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(x0)))))) 544.15/242.29 down(g(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(x0))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(x0))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 f_flat(up(x0)) 544.15/242.29 g_flat(up(x0)) 544.15/242.29 544.15/242.29 We have to consider all minimal (P,Q,R)-chains. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1297) QDPOrderProof (EQUIVALENT) 544.15/242.29 We use the reduction pair processor [LPAR04,JAR06]. 544.15/242.29 544.15/242.29 544.15/242.29 The following pairs can be oriented strictly and are deleted. 544.15/242.29 544.15/242.29 TOP(up(g(a))) -> TOP(up(g(f(a)))) 544.15/242.29 TOP(up(g(g(a)))) -> TOP(up(g(g(f(a))))) 544.15/242.29 TOP(up(g(g(g(a))))) -> TOP(up(g(g(g(f(a)))))) 544.15/242.29 TOP(up(g(g(g(g(a)))))) -> TOP(up(g(g(g(g(f(a))))))) 544.15/242.29 TOP(up(g(g(g(g(g(a))))))) -> TOP(up(g(g(g(g(g(f(a)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(a)))))))) -> TOP(up(g(g(g(g(g(g(f(a))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(a))))))))) -> TOP(up(g(g(g(g(g(g(g(f(a)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(a)))))))))) -> TOP(up(g(g(g(g(g(g(g(g(f(a))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(a))))))))))) -> TOP(up(g(g(g(g(g(g(g(g(g(f(a)))))))))))) 544.15/242.29 The remaining pairs can at least be oriented weakly. 544.15/242.29 Used ordering: Polynomial interpretation [POLO]: 544.15/242.29 544.15/242.29 POL(TOP(x_1)) = x_1 544.15/242.29 POL(a) = 1 544.15/242.29 POL(b) = 0 544.15/242.29 POL(c) = 0 544.15/242.29 POL(down(x_1)) = 0 544.15/242.29 POL(f(x_1)) = 0 544.15/242.29 POL(f_flat(x_1)) = 0 544.15/242.29 POL(fresh_constant) = 0 544.15/242.29 POL(g(x_1)) = x_1 544.15/242.29 POL(g_flat(x_1)) = x_1 544.15/242.29 POL(up(x_1)) = x_1 544.15/242.29 544.15/242.29 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 544.15/242.29 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.29 down(f(a)) -> f_flat(down(a)) 544.15/242.29 down(f(b)) -> f_flat(down(b)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(c)) -> f_flat(down(c)) 544.15/242.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.29 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.29 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 544.15/242.29 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1298) 544.15/242.29 Obligation: 544.15/242.29 Q DP problem: 544.15/242.29 The TRS P consists of the following rules: 544.15/242.29 544.15/242.29 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.29 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.29 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.29 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.29 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.29 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.29 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.29 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.29 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.29 544.15/242.29 The TRS R consists of the following rules: 544.15/242.29 544.15/242.29 down(a) -> up(f(a)) 544.15/242.29 down(b) -> up(g(b)) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.29 down(f(a)) -> f_flat(down(a)) 544.15/242.29 down(f(b)) -> f_flat(down(b)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(c)) -> f_flat(down(c)) 544.15/242.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.29 down(g(a)) -> g_flat(down(a)) 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(b)) -> g_flat(down(b)) 544.15/242.29 down(g(c)) -> g_flat(down(c)) 544.15/242.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.29 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.29 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.29 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.29 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 544.15/242.29 The set Q consists of the following terms: 544.15/242.29 544.15/242.29 down(a) 544.15/242.29 down(b) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.29 down(f(a)) 544.15/242.29 down(f(b)) 544.15/242.29 down(f(g(x0))) 544.15/242.29 down(f(c)) 544.15/242.29 down(f(fresh_constant)) 544.15/242.29 down(g(a)) 544.15/242.29 down(g(f(x0))) 544.15/242.29 down(g(b)) 544.15/242.29 down(g(c)) 544.15/242.29 down(g(fresh_constant)) 544.15/242.29 down(f(f(a))) 544.15/242.29 down(f(f(b))) 544.15/242.29 down(f(f(g(x0)))) 544.15/242.29 down(f(f(c))) 544.15/242.29 down(f(f(fresh_constant))) 544.15/242.29 down(g(g(a))) 544.15/242.29 down(g(g(f(x0)))) 544.15/242.29 down(g(g(b))) 544.15/242.29 down(g(g(c))) 544.15/242.29 down(g(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) 544.15/242.29 down(f(f(f(g(x0))))) 544.15/242.29 down(f(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) 544.15/242.29 down(g(g(g(f(x0))))) 544.15/242.29 down(g(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(x0)))))) 544.15/242.29 down(f(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(x0)))))) 544.15/242.29 down(g(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(x0))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(x0))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 f_flat(up(x0)) 544.15/242.29 g_flat(up(x0)) 544.15/242.29 544.15/242.29 We have to consider all minimal (P,Q,R)-chains. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1299) MNOCProof (EQUIVALENT) 544.15/242.29 We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1300) 544.15/242.29 Obligation: 544.15/242.29 Q DP problem: 544.15/242.29 The TRS P consists of the following rules: 544.15/242.29 544.15/242.29 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.29 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.29 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.29 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.29 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.29 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.29 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.29 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.29 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.29 544.15/242.29 The TRS R consists of the following rules: 544.15/242.29 544.15/242.29 down(a) -> up(f(a)) 544.15/242.29 down(b) -> up(g(b)) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.29 down(f(a)) -> f_flat(down(a)) 544.15/242.29 down(f(b)) -> f_flat(down(b)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(c)) -> f_flat(down(c)) 544.15/242.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.29 down(g(a)) -> g_flat(down(a)) 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(b)) -> g_flat(down(b)) 544.15/242.29 down(g(c)) -> g_flat(down(c)) 544.15/242.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.29 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.29 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.29 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.29 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 544.15/242.29 Q is empty. 544.15/242.29 We have to consider all (P,Q,R)-chains. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1301) SplitQDPProof (EQUIVALENT) 544.15/242.29 We show in the first subproof that some pairs and rules can be removed, afterwards, we continue with the remaining DP-Problem 544.15/242.29 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1302) 544.15/242.29 Complex Obligation (AND) 544.15/242.29 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1303) 544.15/242.29 Obligation: 544.15/242.29 Q DP problem: 544.15/242.29 The TRS P consists of the following rules: 544.15/242.29 544.15/242.29 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.29 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.29 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.29 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.29 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.29 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.29 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.29 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.29 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.29 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.29 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.29 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.29 544.15/242.29 The TRS R consists of the following rules: 544.15/242.29 544.15/242.29 down(a) -> up(f(a)) 544.15/242.29 down(b) -> up(g(b)) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.29 down(f(a)) -> f_flat(down(a)) 544.15/242.29 down(f(b)) -> f_flat(down(b)) 544.15/242.29 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.29 down(f(c)) -> f_flat(down(c)) 544.15/242.29 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 544.15/242.29 down(g(a)) -> g_flat(down(a)) 544.15/242.29 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.29 down(g(b)) -> g_flat(down(b)) 544.15/242.29 down(g(c)) -> g_flat(down(c)) 544.15/242.29 down(g(fresh_constant)) -> g_flat(down(fresh_constant)) 544.15/242.29 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.29 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.29 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.29 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.29 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.29 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.29 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.29 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.29 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.29 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.29 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.29 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.29 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.29 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.29 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.29 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.29 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.29 544.15/242.29 The set Q consists of the following terms: 544.15/242.29 544.15/242.29 down(a) 544.15/242.29 down(b) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.29 down(f(a)) 544.15/242.29 down(f(b)) 544.15/242.29 down(f(g(x0))) 544.15/242.29 down(f(c)) 544.15/242.29 down(f(fresh_constant)) 544.15/242.29 down(g(a)) 544.15/242.29 down(g(f(x0))) 544.15/242.29 down(g(b)) 544.15/242.29 down(g(c)) 544.15/242.29 down(g(fresh_constant)) 544.15/242.29 down(f(f(a))) 544.15/242.29 down(f(f(b))) 544.15/242.29 down(f(f(g(x0)))) 544.15/242.29 down(f(f(c))) 544.15/242.29 down(f(f(fresh_constant))) 544.15/242.29 down(g(g(a))) 544.15/242.29 down(g(g(f(x0)))) 544.15/242.29 down(g(g(b))) 544.15/242.29 down(g(g(c))) 544.15/242.29 down(g(g(fresh_constant))) 544.15/242.29 down(f(f(f(a)))) 544.15/242.29 down(f(f(f(b)))) 544.15/242.29 down(f(f(f(g(x0))))) 544.15/242.29 down(f(f(f(c)))) 544.15/242.29 down(f(f(f(fresh_constant)))) 544.15/242.29 down(g(g(g(a)))) 544.15/242.29 down(g(g(g(f(x0))))) 544.15/242.29 down(g(g(g(b)))) 544.15/242.29 down(g(g(g(c)))) 544.15/242.29 down(g(g(g(fresh_constant)))) 544.15/242.29 down(f(f(f(f(a))))) 544.15/242.29 down(f(f(f(f(b))))) 544.15/242.29 down(f(f(f(f(g(x0)))))) 544.15/242.29 down(f(f(f(f(c))))) 544.15/242.29 down(f(f(f(f(fresh_constant))))) 544.15/242.29 down(g(g(g(g(a))))) 544.15/242.29 down(g(g(g(g(f(x0)))))) 544.15/242.29 down(g(g(g(g(b))))) 544.15/242.29 down(g(g(g(g(c))))) 544.15/242.29 down(g(g(g(g(fresh_constant))))) 544.15/242.29 down(f(f(f(f(f(a)))))) 544.15/242.29 down(f(f(f(f(f(b)))))) 544.15/242.29 down(f(f(f(f(f(g(x0))))))) 544.15/242.29 down(f(f(f(f(f(c)))))) 544.15/242.29 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.29 down(g(g(g(g(g(a)))))) 544.15/242.29 down(g(g(g(g(g(f(x0))))))) 544.15/242.29 down(g(g(g(g(g(b)))))) 544.15/242.29 down(g(g(g(g(g(c)))))) 544.15/242.29 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.29 down(f(f(f(f(f(f(a))))))) 544.15/242.29 down(f(f(f(f(f(f(b))))))) 544.15/242.29 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.29 down(f(f(f(f(f(f(c))))))) 544.15/242.29 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.29 down(g(g(g(g(g(g(a))))))) 544.15/242.29 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.29 down(g(g(g(g(g(g(b))))))) 544.15/242.29 down(g(g(g(g(g(g(c))))))) 544.15/242.29 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.29 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.29 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.29 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.29 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.29 f_flat(up(x0)) 544.15/242.29 g_flat(up(x0)) 544.15/242.29 544.15/242.29 We have to consider all minimal (P,Q,R)-chains. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1304) SemLabProof (SOUND) 544.15/242.29 We found the following model for the rules of the TRSs R and P. 544.15/242.29 Interpretation over the domain with elements from 0 to 1. 544.15/242.29 a: 0 544.15/242.29 b: 0 544.15/242.29 c: 0 544.15/242.29 down: 0 544.15/242.29 f: 0 544.15/242.29 fresh_constant: 1 544.15/242.29 up: 0 544.15/242.29 f_flat: 0 544.15/242.29 TOP: 0 544.15/242.29 g_flat: 0 544.15/242.29 g: 0 544.15/242.29 By semantic labelling [SEMLAB] we obtain the following labelled QDP problem. 544.15/242.29 ---------------------------------------- 544.15/242.29 544.15/242.29 (1305) 544.15/242.29 Obligation: 544.15/242.29 Q DP problem: 544.15/242.29 The TRS P consists of the following rules: 544.15/242.29 544.15/242.29 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.29 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.29 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.29 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.29 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.29 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.29 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.30 544.15/242.30 The TRS R consists of the following rules: 544.15/242.30 544.15/242.30 down.0(a.) -> up.0(f.0(a.)) 544.15/242.30 down.0(b.) -> up.0(g.0(b.)) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.30 down.0(f.0(b.)) -> f_flat.0(down.0(b.)) 544.15/242.30 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.30 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.30 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.30 down.0(f.1(fresh_constant.)) -> f_flat.0(down.1(fresh_constant.)) 544.15/242.30 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.30 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.30 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.30 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.30 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.30 down.0(g.1(fresh_constant.)) -> g_flat.0(down.1(fresh_constant.)) 544.15/242.30 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.30 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.30 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.1(fresh_constant.))) -> f_flat.0(down.0(f.1(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.30 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.30 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.1(fresh_constant.))) -> g_flat.0(down.0(g.1(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.1(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.1(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.30 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.1(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.1(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.1(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) 544.15/242.30 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.30 g_flat.0(up.1(x_1)) -> up.0(g.1(x_1)) 544.15/242.30 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.30 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.30 544.15/242.30 The set Q consists of the following terms: 544.15/242.30 544.15/242.30 down.0(a.) 544.15/242.30 down.0(b.) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(a.)) 544.15/242.30 down.0(f.0(b.)) 544.15/242.30 down.0(f.0(g.0(x0))) 544.15/242.30 down.0(f.0(g.1(x0))) 544.15/242.30 down.0(f.0(c.)) 544.15/242.30 down.0(f.1(fresh_constant.)) 544.15/242.30 down.0(g.0(a.)) 544.15/242.30 down.0(g.0(f.0(x0))) 544.15/242.30 down.0(g.0(f.1(x0))) 544.15/242.30 down.0(g.0(b.)) 544.15/242.30 down.0(g.0(c.)) 544.15/242.30 down.0(g.1(fresh_constant.)) 544.15/242.30 down.0(f.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.0(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(x0)))) 544.15/242.30 down.0(f.0(f.0(g.1(x0)))) 544.15/242.30 down.0(f.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.1(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(x0)))) 544.15/242.30 down.0(g.0(g.0(f.1(x0)))) 544.15/242.30 down.0(g.0(g.0(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.1(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.0(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.1(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.30 down.0(g.0(g.0(g.0(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.1(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) 544.15/242.30 f_flat.0(up.0(x0)) 544.15/242.30 f_flat.0(up.1(x0)) 544.15/242.30 g_flat.0(up.0(x0)) 544.15/242.30 g_flat.0(up.1(x0)) 544.15/242.30 544.15/242.30 We have to consider all minimal (P,Q,R)-chains. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1306) UsableRulesReductionPairsProof (EQUIVALENT) 544.15/242.30 By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well. 544.15/242.30 544.15/242.30 No dependency pairs are removed. 544.15/242.30 544.15/242.30 The following rules are removed from R: 544.15/242.30 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x))))))))))) -> up.0(c.) 544.15/242.30 g_flat.0(up.1(x_1)) -> up.0(g.1(x_1)) 544.15/242.30 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.30 Used ordering: POLO with Polynomial interpretation [POLO]: 544.15/242.30 544.15/242.30 POL(TOP.0(x_1)) = x_1 544.15/242.30 POL(a.) = 0 544.15/242.30 POL(b.) = 0 544.15/242.30 POL(c.) = 0 544.15/242.30 POL(down.0(x_1)) = x_1 544.15/242.30 POL(down.1(x_1)) = 1 + x_1 544.15/242.30 POL(f.0(x_1)) = x_1 544.15/242.30 POL(f.1(x_1)) = 1 + x_1 544.15/242.30 POL(f_flat.0(x_1)) = x_1 544.15/242.30 POL(fresh_constant.) = 0 544.15/242.30 POL(g.0(x_1)) = x_1 544.15/242.30 POL(g.1(x_1)) = 1 + x_1 544.15/242.30 POL(g_flat.0(x_1)) = x_1 544.15/242.30 POL(up.0(x_1)) = x_1 544.15/242.30 POL(up.1(x_1)) = 1 + x_1 544.15/242.30 544.15/242.30 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1307) 544.15/242.30 Obligation: 544.15/242.30 Q DP problem: 544.15/242.30 The TRS P consists of the following rules: 544.15/242.30 544.15/242.30 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.30 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.30 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.30 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.30 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.30 544.15/242.30 The TRS R consists of the following rules: 544.15/242.30 544.15/242.30 down.0(f.1(fresh_constant.)) -> f_flat.0(down.1(fresh_constant.)) 544.15/242.30 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.30 down.0(f.0(b.)) -> f_flat.0(down.0(b.)) 544.15/242.30 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.30 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.30 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.30 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.30 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.30 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.1(fresh_constant.))) -> f_flat.0(down.0(f.1(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.1(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.1(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.30 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.30 down.0(g.1(fresh_constant.)) -> g_flat.0(down.1(fresh_constant.)) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.30 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.30 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.30 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.30 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.30 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.30 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.30 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.1(fresh_constant.))) -> g_flat.0(down.0(g.1(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.30 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.1(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.1(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.1(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) 544.15/242.30 down.0(b.) -> up.0(g.0(b.)) 544.15/242.30 down.0(a.) -> up.0(f.0(a.)) 544.15/242.30 544.15/242.30 The set Q consists of the following terms: 544.15/242.30 544.15/242.30 down.0(a.) 544.15/242.30 down.0(b.) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(a.)) 544.15/242.30 down.0(f.0(b.)) 544.15/242.30 down.0(f.0(g.0(x0))) 544.15/242.30 down.0(f.0(g.1(x0))) 544.15/242.30 down.0(f.0(c.)) 544.15/242.30 down.0(f.1(fresh_constant.)) 544.15/242.30 down.0(g.0(a.)) 544.15/242.30 down.0(g.0(f.0(x0))) 544.15/242.30 down.0(g.0(f.1(x0))) 544.15/242.30 down.0(g.0(b.)) 544.15/242.30 down.0(g.0(c.)) 544.15/242.30 down.0(g.1(fresh_constant.)) 544.15/242.30 down.0(f.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.0(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(x0)))) 544.15/242.30 down.0(f.0(f.0(g.1(x0)))) 544.15/242.30 down.0(f.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.1(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(x0)))) 544.15/242.30 down.0(g.0(g.0(f.1(x0)))) 544.15/242.30 down.0(g.0(g.0(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.1(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.0(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.1(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.30 down.0(g.0(g.0(g.0(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.1(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) 544.15/242.30 f_flat.0(up.0(x0)) 544.15/242.30 f_flat.0(up.1(x0)) 544.15/242.30 g_flat.0(up.0(x0)) 544.15/242.30 g_flat.0(up.1(x0)) 544.15/242.30 544.15/242.30 We have to consider all minimal (P,Q,R)-chains. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1308) MRRProof (EQUIVALENT) 544.15/242.30 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 544.15/242.30 544.15/242.30 544.15/242.30 Strictly oriented rules of the TRS R: 544.15/242.30 544.15/242.30 down.0(f.1(fresh_constant.)) -> f_flat.0(down.1(fresh_constant.)) 544.15/242.30 down.0(g.1(fresh_constant.)) -> g_flat.0(down.1(fresh_constant.)) 544.15/242.30 544.15/242.30 Used ordering: Polynomial interpretation [POLO]: 544.15/242.30 544.15/242.30 POL(TOP.0(x_1)) = x_1 544.15/242.30 POL(a.) = 0 544.15/242.30 POL(b.) = 0 544.15/242.30 POL(c.) = 0 544.15/242.30 POL(down.0(x_1)) = 1 + x_1 544.15/242.30 POL(down.1(x_1)) = x_1 544.15/242.30 POL(f.0(x_1)) = x_1 544.15/242.30 POL(f.1(x_1)) = 1 + x_1 544.15/242.30 POL(f_flat.0(x_1)) = x_1 544.15/242.30 POL(fresh_constant.) = 0 544.15/242.30 POL(g.0(x_1)) = x_1 544.15/242.30 POL(g.1(x_1)) = x_1 544.15/242.30 POL(g_flat.0(x_1)) = x_1 544.15/242.30 POL(up.0(x_1)) = 1 + x_1 544.15/242.30 544.15/242.30 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1309) 544.15/242.30 Obligation: 544.15/242.30 Q DP problem: 544.15/242.30 The TRS P consists of the following rules: 544.15/242.30 544.15/242.30 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.30 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.30 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.30 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.30 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.30 544.15/242.30 The TRS R consists of the following rules: 544.15/242.30 544.15/242.30 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.30 down.0(f.0(b.)) -> f_flat.0(down.0(b.)) 544.15/242.30 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.30 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.30 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.30 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.30 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.30 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.1(fresh_constant.))) -> f_flat.0(down.0(f.1(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.1(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.1(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.30 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.30 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.30 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.30 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.30 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.30 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.30 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.30 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.1(fresh_constant.))) -> g_flat.0(down.0(g.1(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.30 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.1(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.1(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.1(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) 544.15/242.30 down.0(b.) -> up.0(g.0(b.)) 544.15/242.30 down.0(a.) -> up.0(f.0(a.)) 544.15/242.30 544.15/242.30 The set Q consists of the following terms: 544.15/242.30 544.15/242.30 down.0(a.) 544.15/242.30 down.0(b.) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(a.)) 544.15/242.30 down.0(f.0(b.)) 544.15/242.30 down.0(f.0(g.0(x0))) 544.15/242.30 down.0(f.0(g.1(x0))) 544.15/242.30 down.0(f.0(c.)) 544.15/242.30 down.0(f.1(fresh_constant.)) 544.15/242.30 down.0(g.0(a.)) 544.15/242.30 down.0(g.0(f.0(x0))) 544.15/242.30 down.0(g.0(f.1(x0))) 544.15/242.30 down.0(g.0(b.)) 544.15/242.30 down.0(g.0(c.)) 544.15/242.30 down.0(g.1(fresh_constant.)) 544.15/242.30 down.0(f.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.0(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(x0)))) 544.15/242.30 down.0(f.0(f.0(g.1(x0)))) 544.15/242.30 down.0(f.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.1(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(x0)))) 544.15/242.30 down.0(g.0(g.0(f.1(x0)))) 544.15/242.30 down.0(g.0(g.0(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.1(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.0(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.1(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.30 down.0(g.0(g.0(g.0(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.1(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) 544.15/242.30 f_flat.0(up.0(x0)) 544.15/242.30 f_flat.0(up.1(x0)) 544.15/242.30 g_flat.0(up.0(x0)) 544.15/242.30 g_flat.0(up.1(x0)) 544.15/242.30 544.15/242.30 We have to consider all minimal (P,Q,R)-chains. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1310) DependencyGraphProof (EQUIVALENT) 544.15/242.30 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 18 less nodes. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1311) 544.15/242.30 Obligation: 544.15/242.30 Q DP problem: 544.15/242.30 The TRS P consists of the following rules: 544.15/242.30 544.15/242.30 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.30 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.30 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.30 544.15/242.30 The TRS R consists of the following rules: 544.15/242.30 544.15/242.30 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.30 down.0(f.0(b.)) -> f_flat.0(down.0(b.)) 544.15/242.30 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.30 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.30 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.30 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.30 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.30 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.1(fresh_constant.))) -> f_flat.0(down.0(f.1(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.1(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.1(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.30 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.30 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.30 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.30 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.30 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.30 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.30 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.30 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.1(fresh_constant.))) -> g_flat.0(down.0(g.1(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.30 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.1(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.1(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.1(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) 544.15/242.30 down.0(b.) -> up.0(g.0(b.)) 544.15/242.30 down.0(a.) -> up.0(f.0(a.)) 544.15/242.30 544.15/242.30 The set Q consists of the following terms: 544.15/242.30 544.15/242.30 down.0(a.) 544.15/242.30 down.0(b.) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(a.)) 544.15/242.30 down.0(f.0(b.)) 544.15/242.30 down.0(f.0(g.0(x0))) 544.15/242.30 down.0(f.0(g.1(x0))) 544.15/242.30 down.0(f.0(c.)) 544.15/242.30 down.0(f.1(fresh_constant.)) 544.15/242.30 down.0(g.0(a.)) 544.15/242.30 down.0(g.0(f.0(x0))) 544.15/242.30 down.0(g.0(f.1(x0))) 544.15/242.30 down.0(g.0(b.)) 544.15/242.30 down.0(g.0(c.)) 544.15/242.30 down.0(g.1(fresh_constant.)) 544.15/242.30 down.0(f.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.0(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(x0)))) 544.15/242.30 down.0(f.0(f.0(g.1(x0)))) 544.15/242.30 down.0(f.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.1(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(x0)))) 544.15/242.30 down.0(g.0(g.0(f.1(x0)))) 544.15/242.30 down.0(g.0(g.0(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.1(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.0(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.1(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.30 down.0(g.0(g.0(g.0(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.1(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(fresh_constant.)))))))))) 544.15/242.30 f_flat.0(up.0(x0)) 544.15/242.30 f_flat.0(up.1(x0)) 544.15/242.30 g_flat.0(up.0(x0)) 544.15/242.30 g_flat.0(up.1(x0)) 544.15/242.30 544.15/242.30 We have to consider all minimal (P,Q,R)-chains. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1312) PisEmptyProof (SOUND) 544.15/242.30 The TRS P is empty. Hence, there is no (P,Q,R) chain. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1313) 544.15/242.30 TRUE 544.15/242.30 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1314) 544.15/242.30 Obligation: 544.15/242.30 Q DP problem: 544.15/242.30 The TRS P consists of the following rules: 544.15/242.30 544.15/242.30 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.30 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.30 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.30 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.30 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.30 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.30 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.30 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.30 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.30 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.30 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.30 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.30 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.30 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.30 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.30 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.30 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.30 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.30 544.15/242.30 The TRS R consists of the following rules: 544.15/242.30 544.15/242.30 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.30 down(f(a)) -> f_flat(down(a)) 544.15/242.30 down(f(b)) -> f_flat(down(b)) 544.15/242.30 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.30 down(f(c)) -> f_flat(down(c)) 544.15/242.30 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.30 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.30 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.30 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.30 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.30 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.30 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.30 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.30 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.30 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.30 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.30 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.30 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.30 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.30 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.30 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.30 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.30 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.30 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.30 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.30 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.30 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.30 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.30 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.30 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.30 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.30 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.30 down(g(a)) -> g_flat(down(a)) 544.15/242.30 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.30 down(g(b)) -> g_flat(down(b)) 544.15/242.30 down(g(c)) -> g_flat(down(c)) 544.15/242.30 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.30 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.30 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.30 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.30 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.30 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.30 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.30 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.30 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.30 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.30 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.30 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.30 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.30 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.30 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.30 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.30 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.30 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.30 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.30 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.30 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.30 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.30 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.30 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.30 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.30 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.30 down(b) -> up(g(b)) 544.15/242.30 down(a) -> up(f(a)) 544.15/242.30 544.15/242.30 The set Q consists of the following terms: 544.15/242.30 544.15/242.30 down(a) 544.15/242.30 down(b) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.30 down(f(a)) 544.15/242.30 down(f(b)) 544.15/242.30 down(f(g(x0))) 544.15/242.30 down(f(c)) 544.15/242.30 down(f(fresh_constant)) 544.15/242.30 down(g(a)) 544.15/242.30 down(g(f(x0))) 544.15/242.30 down(g(b)) 544.15/242.30 down(g(c)) 544.15/242.30 down(g(fresh_constant)) 544.15/242.30 down(f(f(a))) 544.15/242.30 down(f(f(b))) 544.15/242.30 down(f(f(g(x0)))) 544.15/242.30 down(f(f(c))) 544.15/242.30 down(f(f(fresh_constant))) 544.15/242.30 down(g(g(a))) 544.15/242.30 down(g(g(f(x0)))) 544.15/242.30 down(g(g(b))) 544.15/242.30 down(g(g(c))) 544.15/242.30 down(g(g(fresh_constant))) 544.15/242.30 down(f(f(f(a)))) 544.15/242.30 down(f(f(f(b)))) 544.15/242.30 down(f(f(f(g(x0))))) 544.15/242.30 down(f(f(f(c)))) 544.15/242.30 down(f(f(f(fresh_constant)))) 544.15/242.30 down(g(g(g(a)))) 544.15/242.30 down(g(g(g(f(x0))))) 544.15/242.30 down(g(g(g(b)))) 544.15/242.30 down(g(g(g(c)))) 544.15/242.30 down(g(g(g(fresh_constant)))) 544.15/242.30 down(f(f(f(f(a))))) 544.15/242.30 down(f(f(f(f(b))))) 544.15/242.30 down(f(f(f(f(g(x0)))))) 544.15/242.30 down(f(f(f(f(c))))) 544.15/242.30 down(f(f(f(f(fresh_constant))))) 544.15/242.30 down(g(g(g(g(a))))) 544.15/242.30 down(g(g(g(g(f(x0)))))) 544.15/242.30 down(g(g(g(g(b))))) 544.15/242.30 down(g(g(g(g(c))))) 544.15/242.30 down(g(g(g(g(fresh_constant))))) 544.15/242.30 down(f(f(f(f(f(a)))))) 544.15/242.30 down(f(f(f(f(f(b)))))) 544.15/242.30 down(f(f(f(f(f(g(x0))))))) 544.15/242.30 down(f(f(f(f(f(c)))))) 544.15/242.30 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.30 down(g(g(g(g(g(a)))))) 544.15/242.30 down(g(g(g(g(g(f(x0))))))) 544.15/242.30 down(g(g(g(g(g(b)))))) 544.15/242.30 down(g(g(g(g(g(c)))))) 544.15/242.30 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.30 down(f(f(f(f(f(f(a))))))) 544.15/242.30 down(f(f(f(f(f(f(b))))))) 544.15/242.30 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.30 down(f(f(f(f(f(f(c))))))) 544.15/242.30 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.30 down(g(g(g(g(g(g(a))))))) 544.15/242.30 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.30 down(g(g(g(g(g(g(b))))))) 544.15/242.30 down(g(g(g(g(g(g(c))))))) 544.15/242.30 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.30 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.30 f_flat(up(x0)) 544.15/242.30 g_flat(up(x0)) 544.15/242.30 544.15/242.30 We have to consider all minimal (P,Q,R)-chains. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1315) SplitQDPProof (EQUIVALENT) 544.15/242.30 We show in the first subproof that some pairs and rules can be removed, afterwards, we continue with the remaining DP-Problem 544.15/242.30 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1316) 544.15/242.30 Complex Obligation (AND) 544.15/242.30 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1317) 544.15/242.30 Obligation: 544.15/242.30 Q DP problem: 544.15/242.30 The TRS P consists of the following rules: 544.15/242.30 544.15/242.30 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.30 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.30 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.30 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.30 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.30 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.30 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.30 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.30 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.30 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.30 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.30 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.30 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.30 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.30 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.30 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.30 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.30 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.30 544.15/242.30 The TRS R consists of the following rules: 544.15/242.30 544.15/242.30 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.30 down(f(a)) -> f_flat(down(a)) 544.15/242.30 down(f(b)) -> f_flat(down(b)) 544.15/242.30 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.30 down(f(c)) -> f_flat(down(c)) 544.15/242.30 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.30 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.30 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.30 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.30 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.30 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.30 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.30 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.30 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.30 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.30 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.30 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.30 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.30 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.30 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.30 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.30 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.30 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.30 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.30 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.30 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.30 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.30 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.30 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.30 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.30 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.30 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.30 down(g(a)) -> g_flat(down(a)) 544.15/242.30 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.30 down(g(b)) -> g_flat(down(b)) 544.15/242.30 down(g(c)) -> g_flat(down(c)) 544.15/242.30 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.30 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.30 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.30 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.30 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.30 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.30 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.30 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.30 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.30 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.30 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.30 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.30 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.30 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.30 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.30 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.30 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.30 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.30 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.30 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.30 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.30 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.30 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.30 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.30 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.30 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.30 down(b) -> up(g(b)) 544.15/242.30 down(a) -> up(f(a)) 544.15/242.30 544.15/242.30 The set Q consists of the following terms: 544.15/242.30 544.15/242.30 down(a) 544.15/242.30 down(b) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.30 down(f(a)) 544.15/242.30 down(f(b)) 544.15/242.30 down(f(g(x0))) 544.15/242.30 down(f(c)) 544.15/242.30 down(f(fresh_constant)) 544.15/242.30 down(g(a)) 544.15/242.30 down(g(f(x0))) 544.15/242.30 down(g(b)) 544.15/242.30 down(g(c)) 544.15/242.30 down(g(fresh_constant)) 544.15/242.30 down(f(f(a))) 544.15/242.30 down(f(f(b))) 544.15/242.30 down(f(f(g(x0)))) 544.15/242.30 down(f(f(c))) 544.15/242.30 down(f(f(fresh_constant))) 544.15/242.30 down(g(g(a))) 544.15/242.30 down(g(g(f(x0)))) 544.15/242.30 down(g(g(b))) 544.15/242.30 down(g(g(c))) 544.15/242.30 down(g(g(fresh_constant))) 544.15/242.30 down(f(f(f(a)))) 544.15/242.30 down(f(f(f(b)))) 544.15/242.30 down(f(f(f(g(x0))))) 544.15/242.30 down(f(f(f(c)))) 544.15/242.30 down(f(f(f(fresh_constant)))) 544.15/242.30 down(g(g(g(a)))) 544.15/242.30 down(g(g(g(f(x0))))) 544.15/242.30 down(g(g(g(b)))) 544.15/242.30 down(g(g(g(c)))) 544.15/242.30 down(g(g(g(fresh_constant)))) 544.15/242.30 down(f(f(f(f(a))))) 544.15/242.30 down(f(f(f(f(b))))) 544.15/242.30 down(f(f(f(f(g(x0)))))) 544.15/242.30 down(f(f(f(f(c))))) 544.15/242.30 down(f(f(f(f(fresh_constant))))) 544.15/242.30 down(g(g(g(g(a))))) 544.15/242.30 down(g(g(g(g(f(x0)))))) 544.15/242.30 down(g(g(g(g(b))))) 544.15/242.30 down(g(g(g(g(c))))) 544.15/242.30 down(g(g(g(g(fresh_constant))))) 544.15/242.30 down(f(f(f(f(f(a)))))) 544.15/242.30 down(f(f(f(f(f(b)))))) 544.15/242.30 down(f(f(f(f(f(g(x0))))))) 544.15/242.30 down(f(f(f(f(f(c)))))) 544.15/242.30 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.30 down(g(g(g(g(g(a)))))) 544.15/242.30 down(g(g(g(g(g(f(x0))))))) 544.15/242.30 down(g(g(g(g(g(b)))))) 544.15/242.30 down(g(g(g(g(g(c)))))) 544.15/242.30 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.30 down(f(f(f(f(f(f(a))))))) 544.15/242.30 down(f(f(f(f(f(f(b))))))) 544.15/242.30 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.30 down(f(f(f(f(f(f(c))))))) 544.15/242.30 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.30 down(g(g(g(g(g(g(a))))))) 544.15/242.30 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.30 down(g(g(g(g(g(g(b))))))) 544.15/242.30 down(g(g(g(g(g(g(c))))))) 544.15/242.30 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.30 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.30 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.30 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.30 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.30 f_flat(up(x0)) 544.15/242.30 g_flat(up(x0)) 544.15/242.30 544.15/242.30 We have to consider all minimal (P,Q,R)-chains. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1318) SemLabProof (SOUND) 544.15/242.30 We found the following model for the rules of the TRSs R and P. 544.15/242.30 Interpretation over the domain with elements from 0 to 1. 544.15/242.30 a: 0 544.15/242.30 b: 1 544.15/242.30 c: 0 544.15/242.30 down: 0 544.15/242.30 f: 0 544.15/242.30 fresh_constant: 0 544.15/242.30 up: 0 544.15/242.30 f_flat: 0 544.15/242.30 TOP: 0 544.15/242.30 g_flat: 0 544.15/242.30 g: 0 544.15/242.30 By semantic labelling [SEMLAB] we obtain the following labelled QDP problem. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1319) 544.15/242.30 Obligation: 544.15/242.30 Q DP problem: 544.15/242.30 The TRS P consists of the following rules: 544.15/242.30 544.15/242.30 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.30 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.30 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.30 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.30 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.30 544.15/242.30 The TRS R consists of the following rules: 544.15/242.30 544.15/242.30 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.30 g_flat.0(up.1(x_1)) -> up.0(g.1(x_1)) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.30 down.0(f.1(b.)) -> f_flat.0(down.1(b.)) 544.15/242.30 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.30 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.30 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.30 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.1(b.))) -> f_flat.0(down.0(f.1(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.30 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.30 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.1(b.)))) -> f_flat.0(down.0(f.0(f.1(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(b.))))) -> f_flat.0(down.0(f.0(f.0(f.1(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.30 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.30 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.30 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.30 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.30 down.0(g.1(b.)) -> g_flat.0(down.1(b.)) 544.15/242.30 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.30 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.30 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.30 down.0(g.0(g.1(b.))) -> g_flat.0(down.0(g.1(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.30 down.0(g.0(g.0(g.1(b.)))) -> g_flat.0(down.0(g.0(g.1(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(b.))))) -> g_flat.0(down.0(g.0(g.0(g.1(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.30 down.1(b.) -> up.0(g.1(b.)) 544.15/242.30 down.0(a.) -> up.0(f.0(a.)) 544.15/242.30 544.15/242.30 The set Q consists of the following terms: 544.15/242.30 544.15/242.30 down.0(a.) 544.15/242.30 down.1(b.) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(a.)) 544.15/242.30 down.0(f.1(b.)) 544.15/242.30 down.0(f.0(g.0(x0))) 544.15/242.30 down.0(f.0(g.1(x0))) 544.15/242.30 down.0(f.0(c.)) 544.15/242.30 down.0(f.0(fresh_constant.)) 544.15/242.30 down.0(g.0(a.)) 544.15/242.30 down.0(g.0(f.0(x0))) 544.15/242.30 down.0(g.0(f.1(x0))) 544.15/242.30 down.0(g.1(b.)) 544.15/242.30 down.0(g.0(c.)) 544.15/242.30 down.0(g.0(fresh_constant.)) 544.15/242.30 down.0(f.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.1(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(x0)))) 544.15/242.30 down.0(f.0(f.0(g.1(x0)))) 544.15/242.30 down.0(f.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.0(fresh_constant.))) 544.15/242.30 down.0(g.0(g.0(a.))) 544.15/242.30 down.0(g.0(g.0(f.0(x0)))) 544.15/242.30 down.0(g.0(g.0(f.1(x0)))) 544.15/242.30 down.0(g.0(g.1(b.))) 544.15/242.30 down.0(g.0(g.0(c.))) 544.15/242.30 down.0(g.0(g.0(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.1(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.30 down.0(g.0(g.0(g.0(a.)))) 544.15/242.30 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.30 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.30 down.0(g.0(g.0(g.1(b.)))) 544.15/242.30 down.0(g.0(g.0(g.0(c.)))) 544.15/242.30 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.1(b.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.30 f_flat.0(up.0(x0)) 544.15/242.30 f_flat.0(up.1(x0)) 544.15/242.30 g_flat.0(up.0(x0)) 544.15/242.30 g_flat.0(up.1(x0)) 544.15/242.30 544.15/242.30 We have to consider all minimal (P,Q,R)-chains. 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1320) UsableRulesReductionPairsProof (EQUIVALENT) 544.15/242.30 By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well. 544.15/242.30 544.15/242.30 No dependency pairs are removed. 544.15/242.30 544.15/242.30 The following rules are removed from R: 544.15/242.30 544.15/242.30 g_flat.0(up.1(x_1)) -> up.0(g.1(x_1)) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.0(c.) 544.15/242.30 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.30 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x))))))))))) -> up.0(c.) 544.15/242.30 Used ordering: POLO with Polynomial interpretation [POLO]: 544.15/242.30 544.15/242.30 POL(TOP.0(x_1)) = x_1 544.15/242.30 POL(a.) = 0 544.15/242.30 POL(b.) = 0 544.15/242.30 POL(c.) = 0 544.15/242.30 POL(down.0(x_1)) = x_1 544.15/242.30 POL(down.1(x_1)) = 1 + x_1 544.15/242.30 POL(f.0(x_1)) = x_1 544.15/242.30 POL(f.1(x_1)) = 1 + x_1 544.15/242.30 POL(f_flat.0(x_1)) = x_1 544.15/242.30 POL(fresh_constant.) = 0 544.15/242.30 POL(g.0(x_1)) = x_1 544.15/242.30 POL(g.1(x_1)) = 1 + x_1 544.15/242.30 POL(g_flat.0(x_1)) = x_1 544.15/242.30 POL(up.0(x_1)) = x_1 544.15/242.30 POL(up.1(x_1)) = 1 + x_1 544.15/242.30 544.15/242.30 544.15/242.30 ---------------------------------------- 544.15/242.30 544.15/242.30 (1321) 544.15/242.30 Obligation: 544.15/242.30 Q DP problem: 544.15/242.30 The TRS P consists of the following rules: 544.15/242.30 544.15/242.30 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.30 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.30 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.30 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.30 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.30 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.30 544.15/242.30 The TRS R consists of the following rules: 544.15/242.30 544.15/242.30 down.0(f.1(b.)) -> f_flat.0(down.1(b.)) 544.15/242.30 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.30 down.1(b.) -> up.0(g.1(b.)) 544.15/242.30 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.30 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.30 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.30 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.30 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.30 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.30 down.0(f.0(f.1(b.))) -> f_flat.0(down.0(f.1(b.))) 544.15/242.30 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.30 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.30 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.30 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.30 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.30 down.0(f.0(f.0(f.1(b.)))) -> f_flat.0(down.0(f.0(f.1(b.)))) 544.15/242.30 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.30 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.30 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.1(b.))))) -> f_flat.0(down.0(f.0(f.0(f.1(b.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.30 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.1(b.)) -> g_flat.0(down.1(b.)) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.31 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.31 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.31 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.31 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.31 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.31 down.0(g.0(g.1(b.))) -> g_flat.0(down.0(g.1(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.31 down.0(g.0(g.0(g.1(b.)))) -> g_flat.0(down.0(g.0(g.1(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(b.))))) -> g_flat.0(down.0(g.0(g.0(g.1(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 down.0(a.) -> up.0(f.0(a.)) 544.15/242.31 544.15/242.31 The set Q consists of the following terms: 544.15/242.31 544.15/242.31 down.0(a.) 544.15/242.31 down.1(b.) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.0(a.)) 544.15/242.31 down.0(f.1(b.)) 544.15/242.31 down.0(f.0(g.0(x0))) 544.15/242.31 down.0(f.0(g.1(x0))) 544.15/242.31 down.0(f.0(c.)) 544.15/242.31 down.0(f.0(fresh_constant.)) 544.15/242.31 down.0(g.0(a.)) 544.15/242.31 down.0(g.0(f.0(x0))) 544.15/242.31 down.0(g.0(f.1(x0))) 544.15/242.31 down.0(g.1(b.)) 544.15/242.31 down.0(g.0(c.)) 544.15/242.31 down.0(g.0(fresh_constant.)) 544.15/242.31 down.0(f.0(f.0(a.))) 544.15/242.31 down.0(f.0(f.1(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(x0)))) 544.15/242.31 down.0(f.0(f.0(g.1(x0)))) 544.15/242.31 down.0(f.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(x0)))) 544.15/242.31 down.0(g.0(g.0(f.1(x0)))) 544.15/242.31 down.0(g.0(g.1(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.0(a.)))) 544.15/242.31 down.0(f.0(f.0(f.1(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.31 down.0(g.0(g.0(g.1(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(b.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 f_flat.0(up.0(x0)) 544.15/242.31 f_flat.0(up.1(x0)) 544.15/242.31 g_flat.0(up.0(x0)) 544.15/242.31 g_flat.0(up.1(x0)) 544.15/242.31 544.15/242.31 We have to consider all minimal (P,Q,R)-chains. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1322) MRRProof (EQUIVALENT) 544.15/242.31 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 544.15/242.31 544.15/242.31 544.15/242.31 Strictly oriented rules of the TRS R: 544.15/242.31 544.15/242.31 down.0(f.1(b.)) -> f_flat.0(down.1(b.)) 544.15/242.31 544.15/242.31 Used ordering: Polynomial interpretation [POLO]: 544.15/242.31 544.15/242.31 POL(TOP.0(x_1)) = x_1 544.15/242.31 POL(a.) = 0 544.15/242.31 POL(b.) = 0 544.15/242.31 POL(c.) = 0 544.15/242.31 POL(down.0(x_1)) = x_1 544.15/242.31 POL(down.1(x_1)) = x_1 544.15/242.31 POL(f.0(x_1)) = x_1 544.15/242.31 POL(f.1(x_1)) = 1 + x_1 544.15/242.31 POL(f_flat.0(x_1)) = x_1 544.15/242.31 POL(fresh_constant.) = 0 544.15/242.31 POL(g.0(x_1)) = x_1 544.15/242.31 POL(g.1(x_1)) = x_1 544.15/242.31 POL(g_flat.0(x_1)) = x_1 544.15/242.31 POL(up.0(x_1)) = x_1 544.15/242.31 544.15/242.31 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1323) 544.15/242.31 Obligation: 544.15/242.31 Q DP problem: 544.15/242.31 The TRS P consists of the following rules: 544.15/242.31 544.15/242.31 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.31 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.31 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.31 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.31 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.31 544.15/242.31 The TRS R consists of the following rules: 544.15/242.31 544.15/242.31 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.31 down.1(b.) -> up.0(g.1(b.)) 544.15/242.31 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.31 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.31 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.31 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.31 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.31 down.0(f.0(f.1(b.))) -> f_flat.0(down.0(f.1(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.31 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.31 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.31 down.0(f.0(f.0(f.1(b.)))) -> f_flat.0(down.0(f.0(f.1(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(b.))))) -> f_flat.0(down.0(f.0(f.0(f.1(b.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.1(b.)) -> g_flat.0(down.1(b.)) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.31 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.31 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.31 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.31 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.31 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.31 down.0(g.0(g.1(b.))) -> g_flat.0(down.0(g.1(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.31 down.0(g.0(g.0(g.1(b.)))) -> g_flat.0(down.0(g.0(g.1(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(b.))))) -> g_flat.0(down.0(g.0(g.0(g.1(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 down.0(a.) -> up.0(f.0(a.)) 544.15/242.31 544.15/242.31 The set Q consists of the following terms: 544.15/242.31 544.15/242.31 down.0(a.) 544.15/242.31 down.1(b.) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.0(a.)) 544.15/242.31 down.0(f.1(b.)) 544.15/242.31 down.0(f.0(g.0(x0))) 544.15/242.31 down.0(f.0(g.1(x0))) 544.15/242.31 down.0(f.0(c.)) 544.15/242.31 down.0(f.0(fresh_constant.)) 544.15/242.31 down.0(g.0(a.)) 544.15/242.31 down.0(g.0(f.0(x0))) 544.15/242.31 down.0(g.0(f.1(x0))) 544.15/242.31 down.0(g.1(b.)) 544.15/242.31 down.0(g.0(c.)) 544.15/242.31 down.0(g.0(fresh_constant.)) 544.15/242.31 down.0(f.0(f.0(a.))) 544.15/242.31 down.0(f.0(f.1(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(x0)))) 544.15/242.31 down.0(f.0(f.0(g.1(x0)))) 544.15/242.31 down.0(f.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(x0)))) 544.15/242.31 down.0(g.0(g.0(f.1(x0)))) 544.15/242.31 down.0(g.0(g.1(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.0(a.)))) 544.15/242.31 down.0(f.0(f.0(f.1(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.31 down.0(g.0(g.0(g.1(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(b.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 f_flat.0(up.0(x0)) 544.15/242.31 f_flat.0(up.1(x0)) 544.15/242.31 g_flat.0(up.0(x0)) 544.15/242.31 g_flat.0(up.1(x0)) 544.15/242.31 544.15/242.31 We have to consider all minimal (P,Q,R)-chains. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1324) DependencyGraphProof (EQUIVALENT) 544.15/242.31 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 9 less nodes. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1325) 544.15/242.31 Obligation: 544.15/242.31 Q DP problem: 544.15/242.31 The TRS P consists of the following rules: 544.15/242.31 544.15/242.31 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.31 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.31 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.31 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.31 544.15/242.31 The TRS R consists of the following rules: 544.15/242.31 544.15/242.31 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.31 down.1(b.) -> up.0(g.1(b.)) 544.15/242.31 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.31 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.31 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.31 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.31 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.31 down.0(f.0(f.1(b.))) -> f_flat.0(down.0(f.1(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.31 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.31 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.31 down.0(f.0(f.0(f.1(b.)))) -> f_flat.0(down.0(f.0(f.1(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(b.))))) -> f_flat.0(down.0(f.0(f.0(f.1(b.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.1(b.)) -> g_flat.0(down.1(b.)) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.31 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.31 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.31 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.31 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.31 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.31 down.0(g.0(g.1(b.))) -> g_flat.0(down.0(g.1(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.31 down.0(g.0(g.0(g.1(b.)))) -> g_flat.0(down.0(g.0(g.1(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(b.))))) -> g_flat.0(down.0(g.0(g.0(g.1(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 down.0(a.) -> up.0(f.0(a.)) 544.15/242.31 544.15/242.31 The set Q consists of the following terms: 544.15/242.31 544.15/242.31 down.0(a.) 544.15/242.31 down.1(b.) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.0(a.)) 544.15/242.31 down.0(f.1(b.)) 544.15/242.31 down.0(f.0(g.0(x0))) 544.15/242.31 down.0(f.0(g.1(x0))) 544.15/242.31 down.0(f.0(c.)) 544.15/242.31 down.0(f.0(fresh_constant.)) 544.15/242.31 down.0(g.0(a.)) 544.15/242.31 down.0(g.0(f.0(x0))) 544.15/242.31 down.0(g.0(f.1(x0))) 544.15/242.31 down.0(g.1(b.)) 544.15/242.31 down.0(g.0(c.)) 544.15/242.31 down.0(g.0(fresh_constant.)) 544.15/242.31 down.0(f.0(f.0(a.))) 544.15/242.31 down.0(f.0(f.1(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(x0)))) 544.15/242.31 down.0(f.0(f.0(g.1(x0)))) 544.15/242.31 down.0(f.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(x0)))) 544.15/242.31 down.0(g.0(g.0(f.1(x0)))) 544.15/242.31 down.0(g.0(g.1(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.0(a.)))) 544.15/242.31 down.0(f.0(f.0(f.1(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.31 down.0(g.0(g.0(g.1(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(b.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 f_flat.0(up.0(x0)) 544.15/242.31 f_flat.0(up.1(x0)) 544.15/242.31 g_flat.0(up.0(x0)) 544.15/242.31 g_flat.0(up.1(x0)) 544.15/242.31 544.15/242.31 We have to consider all minimal (P,Q,R)-chains. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1326) QDPOrderProof (EQUIVALENT) 544.15/242.31 We use the reduction pair processor [LPAR04,JAR06]. 544.15/242.31 544.15/242.31 544.15/242.31 The following pairs can be oriented strictly and are deleted. 544.15/242.31 544.15/242.31 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.31 The remaining pairs can at least be oriented weakly. 544.15/242.31 Used ordering: Polynomial interpretation [POLO]: 544.15/242.31 544.15/242.31 POL(TOP.0(x_1)) = x_1 544.15/242.31 POL(a.) = 0 544.15/242.31 POL(b.) = 0 544.15/242.31 POL(c.) = 0 544.15/242.31 POL(down.0(x_1)) = 0 544.15/242.31 POL(down.1(x_1)) = 0 544.15/242.31 POL(f.0(x_1)) = x_1 544.15/242.31 POL(f.1(x_1)) = 0 544.15/242.31 POL(f_flat.0(x_1)) = x_1 544.15/242.31 POL(fresh_constant.) = 0 544.15/242.31 POL(g.0(x_1)) = 0 544.15/242.31 POL(g.1(x_1)) = 1 544.15/242.31 POL(g_flat.0(x_1)) = 0 544.15/242.31 POL(up.0(x_1)) = x_1 544.15/242.31 544.15/242.31 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 544.15/242.31 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.31 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.31 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.31 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.31 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.31 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.31 down.0(g.0(g.1(b.))) -> g_flat.0(down.0(g.1(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.31 down.0(g.0(g.0(g.1(b.)))) -> g_flat.0(down.0(g.0(g.1(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(b.))))) -> g_flat.0(down.0(g.0(g.0(g.1(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.31 down.0(g.1(b.)) -> g_flat.0(down.1(b.)) 544.15/242.31 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.31 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.31 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.31 544.15/242.31 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1327) 544.15/242.31 Obligation: 544.15/242.31 Q DP problem: 544.15/242.31 The TRS P consists of the following rules: 544.15/242.31 544.15/242.31 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.31 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.31 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.31 544.15/242.31 The TRS R consists of the following rules: 544.15/242.31 544.15/242.31 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.31 down.1(b.) -> up.0(g.1(b.)) 544.15/242.31 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.31 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.31 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.31 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.31 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.31 down.0(f.0(f.1(b.))) -> f_flat.0(down.0(f.1(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.31 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.31 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.31 down.0(f.0(f.0(f.1(b.)))) -> f_flat.0(down.0(f.0(f.1(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(b.))))) -> f_flat.0(down.0(f.0(f.0(f.1(b.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.1(b.)) -> g_flat.0(down.1(b.)) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(g.0(a.)) -> g_flat.0(down.0(a.)) 544.15/242.31 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.31 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.31 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.31 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.31 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.31 down.0(g.0(g.1(b.))) -> g_flat.0(down.0(g.1(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.31 down.0(g.0(g.0(g.1(b.)))) -> g_flat.0(down.0(g.0(g.1(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(b.))))) -> g_flat.0(down.0(g.0(g.0(g.1(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 down.0(a.) -> up.0(f.0(a.)) 544.15/242.31 544.15/242.31 The set Q consists of the following terms: 544.15/242.31 544.15/242.31 down.0(a.) 544.15/242.31 down.1(b.) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.0(a.)) 544.15/242.31 down.0(f.1(b.)) 544.15/242.31 down.0(f.0(g.0(x0))) 544.15/242.31 down.0(f.0(g.1(x0))) 544.15/242.31 down.0(f.0(c.)) 544.15/242.31 down.0(f.0(fresh_constant.)) 544.15/242.31 down.0(g.0(a.)) 544.15/242.31 down.0(g.0(f.0(x0))) 544.15/242.31 down.0(g.0(f.1(x0))) 544.15/242.31 down.0(g.1(b.)) 544.15/242.31 down.0(g.0(c.)) 544.15/242.31 down.0(g.0(fresh_constant.)) 544.15/242.31 down.0(f.0(f.0(a.))) 544.15/242.31 down.0(f.0(f.1(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(x0)))) 544.15/242.31 down.0(f.0(f.0(g.1(x0)))) 544.15/242.31 down.0(f.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(x0)))) 544.15/242.31 down.0(g.0(g.0(f.1(x0)))) 544.15/242.31 down.0(g.0(g.1(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.0(a.)))) 544.15/242.31 down.0(f.0(f.0(f.1(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.31 down.0(g.0(g.0(g.1(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(b.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.1(b.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 f_flat.0(up.0(x0)) 544.15/242.31 f_flat.0(up.1(x0)) 544.15/242.31 g_flat.0(up.0(x0)) 544.15/242.31 g_flat.0(up.1(x0)) 544.15/242.31 544.15/242.31 We have to consider all minimal (P,Q,R)-chains. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1328) PisEmptyProof (SOUND) 544.15/242.31 The TRS P is empty. Hence, there is no (P,Q,R) chain. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1329) 544.15/242.31 TRUE 544.15/242.31 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1330) 544.15/242.31 Obligation: 544.15/242.31 Q DP problem: 544.15/242.31 The TRS P consists of the following rules: 544.15/242.31 544.15/242.31 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.31 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.31 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.31 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.31 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.31 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.31 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.31 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.31 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.31 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.31 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.31 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.31 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.31 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.31 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.31 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.31 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.31 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.31 544.15/242.31 The TRS R consists of the following rules: 544.15/242.31 544.15/242.31 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.31 down(b) -> up(g(b)) 544.15/242.31 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.31 down(f(a)) -> f_flat(down(a)) 544.15/242.31 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.31 down(f(c)) -> f_flat(down(c)) 544.15/242.31 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.31 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.31 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.31 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.31 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.31 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.31 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.31 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.31 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.31 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.31 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.31 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.31 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.31 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.31 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.31 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.31 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.31 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.31 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.31 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.31 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.31 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.31 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.31 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.31 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.31 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.31 down(g(b)) -> g_flat(down(b)) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.31 down(g(a)) -> g_flat(down(a)) 544.15/242.31 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.31 down(g(c)) -> g_flat(down(c)) 544.15/242.31 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.31 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.31 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.31 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.31 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.31 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.31 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.31 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.31 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.31 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.31 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.31 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.31 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.31 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.31 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.31 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.31 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.31 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.31 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.31 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.31 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.31 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.31 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.31 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.31 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.31 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.31 down(a) -> up(f(a)) 544.15/242.31 544.15/242.31 The set Q consists of the following terms: 544.15/242.31 544.15/242.31 down(a) 544.15/242.31 down(b) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.31 down(f(a)) 544.15/242.31 down(f(b)) 544.15/242.31 down(f(g(x0))) 544.15/242.31 down(f(c)) 544.15/242.31 down(f(fresh_constant)) 544.15/242.31 down(g(a)) 544.15/242.31 down(g(f(x0))) 544.15/242.31 down(g(b)) 544.15/242.31 down(g(c)) 544.15/242.31 down(g(fresh_constant)) 544.15/242.31 down(f(f(a))) 544.15/242.31 down(f(f(b))) 544.15/242.31 down(f(f(g(x0)))) 544.15/242.31 down(f(f(c))) 544.15/242.31 down(f(f(fresh_constant))) 544.15/242.31 down(g(g(a))) 544.15/242.31 down(g(g(f(x0)))) 544.15/242.31 down(g(g(b))) 544.15/242.31 down(g(g(c))) 544.15/242.31 down(g(g(fresh_constant))) 544.15/242.31 down(f(f(f(a)))) 544.15/242.31 down(f(f(f(b)))) 544.15/242.31 down(f(f(f(g(x0))))) 544.15/242.31 down(f(f(f(c)))) 544.15/242.31 down(f(f(f(fresh_constant)))) 544.15/242.31 down(g(g(g(a)))) 544.15/242.31 down(g(g(g(f(x0))))) 544.15/242.31 down(g(g(g(b)))) 544.15/242.31 down(g(g(g(c)))) 544.15/242.31 down(g(g(g(fresh_constant)))) 544.15/242.31 down(f(f(f(f(a))))) 544.15/242.31 down(f(f(f(f(b))))) 544.15/242.31 down(f(f(f(f(g(x0)))))) 544.15/242.31 down(f(f(f(f(c))))) 544.15/242.31 down(f(f(f(f(fresh_constant))))) 544.15/242.31 down(g(g(g(g(a))))) 544.15/242.31 down(g(g(g(g(f(x0)))))) 544.15/242.31 down(g(g(g(g(b))))) 544.15/242.31 down(g(g(g(g(c))))) 544.15/242.31 down(g(g(g(g(fresh_constant))))) 544.15/242.31 down(f(f(f(f(f(a)))))) 544.15/242.31 down(f(f(f(f(f(b)))))) 544.15/242.31 down(f(f(f(f(f(g(x0))))))) 544.15/242.31 down(f(f(f(f(f(c)))))) 544.15/242.31 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.31 down(g(g(g(g(g(a)))))) 544.15/242.31 down(g(g(g(g(g(f(x0))))))) 544.15/242.31 down(g(g(g(g(g(b)))))) 544.15/242.31 down(g(g(g(g(g(c)))))) 544.15/242.31 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.31 down(f(f(f(f(f(f(a))))))) 544.15/242.31 down(f(f(f(f(f(f(b))))))) 544.15/242.31 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.31 down(f(f(f(f(f(f(c))))))) 544.15/242.31 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.31 down(g(g(g(g(g(g(a))))))) 544.15/242.31 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.31 down(g(g(g(g(g(g(b))))))) 544.15/242.31 down(g(g(g(g(g(g(c))))))) 544.15/242.31 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.31 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.31 f_flat(up(x0)) 544.15/242.31 g_flat(up(x0)) 544.15/242.31 544.15/242.31 We have to consider all minimal (P,Q,R)-chains. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1331) SplitQDPProof (EQUIVALENT) 544.15/242.31 We show in the first subproof that some pairs and rules can be removed, afterwards, we continue with the remaining DP-Problem 544.15/242.31 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1332) 544.15/242.31 Complex Obligation (AND) 544.15/242.31 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1333) 544.15/242.31 Obligation: 544.15/242.31 Q DP problem: 544.15/242.31 The TRS P consists of the following rules: 544.15/242.31 544.15/242.31 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.31 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.31 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.31 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.31 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.31 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.31 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.31 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.31 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.31 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.31 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.31 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.31 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.31 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.31 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.31 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.31 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.31 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.31 544.15/242.31 The TRS R consists of the following rules: 544.15/242.31 544.15/242.31 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.31 down(b) -> up(g(b)) 544.15/242.31 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.31 down(f(a)) -> f_flat(down(a)) 544.15/242.31 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.31 down(f(c)) -> f_flat(down(c)) 544.15/242.31 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.31 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.31 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.31 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.31 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.31 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.31 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.31 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.31 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.31 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.31 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.31 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.31 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.31 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.31 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.31 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.31 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.31 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.31 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.31 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.31 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.31 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.31 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.31 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.31 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.31 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.31 down(g(b)) -> g_flat(down(b)) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.31 down(g(a)) -> g_flat(down(a)) 544.15/242.31 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.31 down(g(c)) -> g_flat(down(c)) 544.15/242.31 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.31 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.31 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.31 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.31 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.31 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.31 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.31 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.31 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.31 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.31 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.31 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.31 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.31 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.31 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.31 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.31 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.31 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.31 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.31 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.31 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.31 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.31 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.31 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.31 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.31 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.31 down(a) -> up(f(a)) 544.15/242.31 544.15/242.31 The set Q consists of the following terms: 544.15/242.31 544.15/242.31 down(a) 544.15/242.31 down(b) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.31 down(f(a)) 544.15/242.31 down(f(b)) 544.15/242.31 down(f(g(x0))) 544.15/242.31 down(f(c)) 544.15/242.31 down(f(fresh_constant)) 544.15/242.31 down(g(a)) 544.15/242.31 down(g(f(x0))) 544.15/242.31 down(g(b)) 544.15/242.31 down(g(c)) 544.15/242.31 down(g(fresh_constant)) 544.15/242.31 down(f(f(a))) 544.15/242.31 down(f(f(b))) 544.15/242.31 down(f(f(g(x0)))) 544.15/242.31 down(f(f(c))) 544.15/242.31 down(f(f(fresh_constant))) 544.15/242.31 down(g(g(a))) 544.15/242.31 down(g(g(f(x0)))) 544.15/242.31 down(g(g(b))) 544.15/242.31 down(g(g(c))) 544.15/242.31 down(g(g(fresh_constant))) 544.15/242.31 down(f(f(f(a)))) 544.15/242.31 down(f(f(f(b)))) 544.15/242.31 down(f(f(f(g(x0))))) 544.15/242.31 down(f(f(f(c)))) 544.15/242.31 down(f(f(f(fresh_constant)))) 544.15/242.31 down(g(g(g(a)))) 544.15/242.31 down(g(g(g(f(x0))))) 544.15/242.31 down(g(g(g(b)))) 544.15/242.31 down(g(g(g(c)))) 544.15/242.31 down(g(g(g(fresh_constant)))) 544.15/242.31 down(f(f(f(f(a))))) 544.15/242.31 down(f(f(f(f(b))))) 544.15/242.31 down(f(f(f(f(g(x0)))))) 544.15/242.31 down(f(f(f(f(c))))) 544.15/242.31 down(f(f(f(f(fresh_constant))))) 544.15/242.31 down(g(g(g(g(a))))) 544.15/242.31 down(g(g(g(g(f(x0)))))) 544.15/242.31 down(g(g(g(g(b))))) 544.15/242.31 down(g(g(g(g(c))))) 544.15/242.31 down(g(g(g(g(fresh_constant))))) 544.15/242.31 down(f(f(f(f(f(a)))))) 544.15/242.31 down(f(f(f(f(f(b)))))) 544.15/242.31 down(f(f(f(f(f(g(x0))))))) 544.15/242.31 down(f(f(f(f(f(c)))))) 544.15/242.31 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.31 down(g(g(g(g(g(a)))))) 544.15/242.31 down(g(g(g(g(g(f(x0))))))) 544.15/242.31 down(g(g(g(g(g(b)))))) 544.15/242.31 down(g(g(g(g(g(c)))))) 544.15/242.31 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.31 down(f(f(f(f(f(f(a))))))) 544.15/242.31 down(f(f(f(f(f(f(b))))))) 544.15/242.31 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.31 down(f(f(f(f(f(f(c))))))) 544.15/242.31 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.31 down(g(g(g(g(g(g(a))))))) 544.15/242.31 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.31 down(g(g(g(g(g(g(b))))))) 544.15/242.31 down(g(g(g(g(g(g(c))))))) 544.15/242.31 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.31 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.31 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.31 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.31 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.31 f_flat(up(x0)) 544.15/242.31 g_flat(up(x0)) 544.15/242.31 544.15/242.31 We have to consider all minimal (P,Q,R)-chains. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1334) SemLabProof (SOUND) 544.15/242.31 We found the following model for the rules of the TRSs R and P. 544.15/242.31 Interpretation over the domain with elements from 0 to 1. 544.15/242.31 a: 1 544.15/242.31 b: 0 544.15/242.31 c: 0 544.15/242.31 down: 0 544.15/242.31 f: 0 544.15/242.31 fresh_constant: 0 544.15/242.31 up: 0 544.15/242.31 f_flat: 0 544.15/242.31 TOP: 0 544.15/242.31 g_flat: 0 544.15/242.31 g: 0 544.15/242.31 By semantic labelling [SEMLAB] we obtain the following labelled QDP problem. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1335) 544.15/242.31 Obligation: 544.15/242.31 Q DP problem: 544.15/242.31 The TRS P consists of the following rules: 544.15/242.31 544.15/242.31 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.31 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.31 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.31 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.31 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.31 544.15/242.31 The TRS R consists of the following rules: 544.15/242.31 544.15/242.31 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.31 g_flat.0(up.1(x_1)) -> up.0(g.1(x_1)) 544.15/242.31 down.0(b.) -> up.0(g.0(b.)) 544.15/242.31 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.31 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(f.1(a.)) -> f_flat.0(down.1(a.)) 544.15/242.31 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.31 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.31 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.31 down.0(f.0(f.1(a.))) -> f_flat.0(down.0(f.1(a.))) 544.15/242.31 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.31 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.31 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.1(a.)))) -> f_flat.0(down.0(f.0(f.1(a.)))) 544.15/242.31 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(a.))))) -> f_flat.0(down.0(f.0(f.0(f.1(a.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(g.1(a.)) -> g_flat.0(down.1(a.)) 544.15/242.31 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.31 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.31 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.31 down.0(g.0(g.1(a.))) -> g_flat.0(down.0(g.1(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.31 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.31 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.0(g.1(a.)))) -> g_flat.0(down.0(g.0(g.1(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.31 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(a.))))) -> g_flat.0(down.0(g.0(g.0(g.1(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 down.1(a.) -> up.0(f.1(a.)) 544.15/242.31 544.15/242.31 The set Q consists of the following terms: 544.15/242.31 544.15/242.31 down.1(a.) 544.15/242.31 down.0(b.) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.1(a.)) 544.15/242.31 down.0(f.0(b.)) 544.15/242.31 down.0(f.0(g.0(x0))) 544.15/242.31 down.0(f.0(g.1(x0))) 544.15/242.31 down.0(f.0(c.)) 544.15/242.31 down.0(f.0(fresh_constant.)) 544.15/242.31 down.0(g.1(a.)) 544.15/242.31 down.0(g.0(f.0(x0))) 544.15/242.31 down.0(g.0(f.1(x0))) 544.15/242.31 down.0(g.0(b.)) 544.15/242.31 down.0(g.0(c.)) 544.15/242.31 down.0(g.0(fresh_constant.)) 544.15/242.31 down.0(f.0(f.1(a.))) 544.15/242.31 down.0(f.0(f.0(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(x0)))) 544.15/242.31 down.0(f.0(f.0(g.1(x0)))) 544.15/242.31 down.0(f.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) 544.15/242.31 down.0(g.0(g.1(a.))) 544.15/242.31 down.0(g.0(g.0(f.0(x0)))) 544.15/242.31 down.0(g.0(g.0(f.1(x0)))) 544.15/242.31 down.0(g.0(g.0(b.))) 544.15/242.31 down.0(g.0(g.0(c.))) 544.15/242.31 down.0(g.0(g.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.1(a.)))) 544.15/242.31 down.0(f.0(f.0(f.0(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(g.0(g.0(g.1(a.)))) 544.15/242.31 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.31 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.31 down.0(g.0(g.0(g.0(b.)))) 544.15/242.31 down.0(g.0(g.0(g.0(c.)))) 544.15/242.31 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(a.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.1(a.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.31 f_flat.0(up.0(x0)) 544.15/242.31 f_flat.0(up.1(x0)) 544.15/242.31 g_flat.0(up.0(x0)) 544.15/242.31 g_flat.0(up.1(x0)) 544.15/242.31 544.15/242.31 We have to consider all minimal (P,Q,R)-chains. 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1336) UsableRulesReductionPairsProof (EQUIVALENT) 544.15/242.31 By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well. 544.15/242.31 544.15/242.31 No dependency pairs are removed. 544.15/242.31 544.15/242.31 The following rules are removed from R: 544.15/242.31 544.15/242.31 g_flat.0(up.1(x_1)) -> up.0(g.1(x_1)) 544.15/242.31 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x))))))))))) -> up.0(c.) 544.15/242.31 Used ordering: POLO with Polynomial interpretation [POLO]: 544.15/242.31 544.15/242.31 POL(TOP.0(x_1)) = x_1 544.15/242.31 POL(a.) = 0 544.15/242.31 POL(b.) = 0 544.15/242.31 POL(c.) = 0 544.15/242.31 POL(down.0(x_1)) = x_1 544.15/242.31 POL(down.1(x_1)) = 1 + x_1 544.15/242.31 POL(f.0(x_1)) = x_1 544.15/242.31 POL(f.1(x_1)) = 1 + x_1 544.15/242.31 POL(f_flat.0(x_1)) = x_1 544.15/242.31 POL(fresh_constant.) = 0 544.15/242.31 POL(g.0(x_1)) = x_1 544.15/242.31 POL(g.1(x_1)) = 1 + x_1 544.15/242.31 POL(g_flat.0(x_1)) = x_1 544.15/242.31 POL(up.0(x_1)) = x_1 544.15/242.31 POL(up.1(x_1)) = 1 + x_1 544.15/242.31 544.15/242.31 544.15/242.31 ---------------------------------------- 544.15/242.31 544.15/242.31 (1337) 544.15/242.31 Obligation: 544.15/242.31 Q DP problem: 544.15/242.31 The TRS P consists of the following rules: 544.15/242.31 544.15/242.31 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.31 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.31 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.31 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.31 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.31 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.31 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.31 544.15/242.31 The TRS R consists of the following rules: 544.15/242.31 544.15/242.31 down.0(f.1(a.)) -> f_flat.0(down.1(a.)) 544.15/242.31 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.31 down.1(a.) -> up.0(f.1(a.)) 544.15/242.31 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.31 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.31 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.31 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.31 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.31 down.0(f.0(f.1(a.))) -> f_flat.0(down.0(f.1(a.))) 544.15/242.31 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.31 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.31 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.31 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.31 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.31 down.0(f.0(f.0(f.1(a.)))) -> f_flat.0(down.0(f.0(f.1(a.)))) 544.15/242.31 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.31 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.31 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.31 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.31 down.0(f.0(f.0(f.0(f.1(a.))))) -> f_flat.0(down.0(f.0(f.0(f.1(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.1(a.)) -> g_flat.0(down.1(a.)) 544.15/242.32 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.32 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.32 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.32 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.32 down.0(g.0(g.1(a.))) -> g_flat.0(down.0(g.1(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.32 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.32 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.0(g.1(a.)))) -> g_flat.0(down.0(g.0(g.1(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(a.))))) -> g_flat.0(down.0(g.0(g.0(g.1(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 down.0(b.) -> up.0(g.0(b.)) 544.15/242.32 544.15/242.32 The set Q consists of the following terms: 544.15/242.32 544.15/242.32 down.1(a.) 544.15/242.32 down.0(b.) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.1(a.)) 544.15/242.32 down.0(f.0(b.)) 544.15/242.32 down.0(f.0(g.0(x0))) 544.15/242.32 down.0(f.0(g.1(x0))) 544.15/242.32 down.0(f.0(c.)) 544.15/242.32 down.0(f.0(fresh_constant.)) 544.15/242.32 down.0(g.1(a.)) 544.15/242.32 down.0(g.0(f.0(x0))) 544.15/242.32 down.0(g.0(f.1(x0))) 544.15/242.32 down.0(g.0(b.)) 544.15/242.32 down.0(g.0(c.)) 544.15/242.32 down.0(g.0(fresh_constant.)) 544.15/242.32 down.0(f.0(f.1(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(x0)))) 544.15/242.32 down.0(f.0(f.0(g.1(x0)))) 544.15/242.32 down.0(f.0(f.0(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.1(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(x0)))) 544.15/242.32 down.0(g.0(g.0(f.1(x0)))) 544.15/242.32 down.0(g.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.0(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.1(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.32 down.0(f.0(f.0(f.0(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.1(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.0(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 f_flat.0(up.0(x0)) 544.15/242.32 f_flat.0(up.1(x0)) 544.15/242.32 g_flat.0(up.0(x0)) 544.15/242.32 g_flat.0(up.1(x0)) 544.15/242.32 544.15/242.32 We have to consider all minimal (P,Q,R)-chains. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1338) MRRProof (EQUIVALENT) 544.15/242.32 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 544.15/242.32 544.15/242.32 544.15/242.32 Strictly oriented rules of the TRS R: 544.15/242.32 544.15/242.32 down.0(g.1(a.)) -> g_flat.0(down.1(a.)) 544.15/242.32 544.15/242.32 Used ordering: Polynomial interpretation [POLO]: 544.15/242.32 544.15/242.32 POL(TOP.0(x_1)) = x_1 544.15/242.32 POL(a.) = 0 544.15/242.32 POL(b.) = 0 544.15/242.32 POL(c.) = 0 544.15/242.32 POL(down.0(x_1)) = 1 + x_1 544.15/242.32 POL(down.1(x_1)) = 1 + x_1 544.15/242.32 POL(f.0(x_1)) = x_1 544.15/242.32 POL(f.1(x_1)) = x_1 544.15/242.32 POL(f_flat.0(x_1)) = x_1 544.15/242.32 POL(fresh_constant.) = 0 544.15/242.32 POL(g.0(x_1)) = x_1 544.15/242.32 POL(g.1(x_1)) = 1 + x_1 544.15/242.32 POL(g_flat.0(x_1)) = x_1 544.15/242.32 POL(up.0(x_1)) = 1 + x_1 544.15/242.32 544.15/242.32 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1339) 544.15/242.32 Obligation: 544.15/242.32 Q DP problem: 544.15/242.32 The TRS P consists of the following rules: 544.15/242.32 544.15/242.32 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.32 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.32 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.32 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.32 544.15/242.32 The TRS R consists of the following rules: 544.15/242.32 544.15/242.32 down.0(f.1(a.)) -> f_flat.0(down.1(a.)) 544.15/242.32 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.32 down.1(a.) -> up.0(f.1(a.)) 544.15/242.32 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.32 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.32 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.32 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.32 down.0(f.0(f.1(a.))) -> f_flat.0(down.0(f.1(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.32 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.32 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.1(a.)))) -> f_flat.0(down.0(f.0(f.1(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.32 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(a.))))) -> f_flat.0(down.0(f.0(f.0(f.1(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.32 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.32 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.32 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.32 down.0(g.0(g.1(a.))) -> g_flat.0(down.0(g.1(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.32 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.32 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.0(g.1(a.)))) -> g_flat.0(down.0(g.0(g.1(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(a.))))) -> g_flat.0(down.0(g.0(g.0(g.1(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 down.0(b.) -> up.0(g.0(b.)) 544.15/242.32 544.15/242.32 The set Q consists of the following terms: 544.15/242.32 544.15/242.32 down.1(a.) 544.15/242.32 down.0(b.) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.1(a.)) 544.15/242.32 down.0(f.0(b.)) 544.15/242.32 down.0(f.0(g.0(x0))) 544.15/242.32 down.0(f.0(g.1(x0))) 544.15/242.32 down.0(f.0(c.)) 544.15/242.32 down.0(f.0(fresh_constant.)) 544.15/242.32 down.0(g.1(a.)) 544.15/242.32 down.0(g.0(f.0(x0))) 544.15/242.32 down.0(g.0(f.1(x0))) 544.15/242.32 down.0(g.0(b.)) 544.15/242.32 down.0(g.0(c.)) 544.15/242.32 down.0(g.0(fresh_constant.)) 544.15/242.32 down.0(f.0(f.1(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(x0)))) 544.15/242.32 down.0(f.0(f.0(g.1(x0)))) 544.15/242.32 down.0(f.0(f.0(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.1(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(x0)))) 544.15/242.32 down.0(g.0(g.0(f.1(x0)))) 544.15/242.32 down.0(g.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.0(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.1(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.32 down.0(f.0(f.0(f.0(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.1(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.0(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 f_flat.0(up.0(x0)) 544.15/242.32 f_flat.0(up.1(x0)) 544.15/242.32 g_flat.0(up.0(x0)) 544.15/242.32 g_flat.0(up.1(x0)) 544.15/242.32 544.15/242.32 We have to consider all minimal (P,Q,R)-chains. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1340) DependencyGraphProof (EQUIVALENT) 544.15/242.32 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 9 less nodes. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1341) 544.15/242.32 Obligation: 544.15/242.32 Q DP problem: 544.15/242.32 The TRS P consists of the following rules: 544.15/242.32 544.15/242.32 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.32 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.32 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.32 544.15/242.32 The TRS R consists of the following rules: 544.15/242.32 544.15/242.32 down.0(f.1(a.)) -> f_flat.0(down.1(a.)) 544.15/242.32 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.32 down.1(a.) -> up.0(f.1(a.)) 544.15/242.32 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.32 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.32 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.32 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.32 down.0(f.0(f.1(a.))) -> f_flat.0(down.0(f.1(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.32 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.32 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.1(a.)))) -> f_flat.0(down.0(f.0(f.1(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.32 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(a.))))) -> f_flat.0(down.0(f.0(f.0(f.1(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.32 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.32 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.32 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.32 down.0(g.0(g.1(a.))) -> g_flat.0(down.0(g.1(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.32 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.32 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.0(g.1(a.)))) -> g_flat.0(down.0(g.0(g.1(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(a.))))) -> g_flat.0(down.0(g.0(g.0(g.1(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 down.0(b.) -> up.0(g.0(b.)) 544.15/242.32 544.15/242.32 The set Q consists of the following terms: 544.15/242.32 544.15/242.32 down.1(a.) 544.15/242.32 down.0(b.) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.1(a.)) 544.15/242.32 down.0(f.0(b.)) 544.15/242.32 down.0(f.0(g.0(x0))) 544.15/242.32 down.0(f.0(g.1(x0))) 544.15/242.32 down.0(f.0(c.)) 544.15/242.32 down.0(f.0(fresh_constant.)) 544.15/242.32 down.0(g.1(a.)) 544.15/242.32 down.0(g.0(f.0(x0))) 544.15/242.32 down.0(g.0(f.1(x0))) 544.15/242.32 down.0(g.0(b.)) 544.15/242.32 down.0(g.0(c.)) 544.15/242.32 down.0(g.0(fresh_constant.)) 544.15/242.32 down.0(f.0(f.1(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(x0)))) 544.15/242.32 down.0(f.0(f.0(g.1(x0)))) 544.15/242.32 down.0(f.0(f.0(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.1(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(x0)))) 544.15/242.32 down.0(g.0(g.0(f.1(x0)))) 544.15/242.32 down.0(g.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.0(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.1(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.32 down.0(f.0(f.0(f.0(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.1(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.0(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 f_flat.0(up.0(x0)) 544.15/242.32 f_flat.0(up.1(x0)) 544.15/242.32 g_flat.0(up.0(x0)) 544.15/242.32 g_flat.0(up.1(x0)) 544.15/242.32 544.15/242.32 We have to consider all minimal (P,Q,R)-chains. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1342) QDPOrderProof (EQUIVALENT) 544.15/242.32 We use the reduction pair processor [LPAR04,JAR06]. 544.15/242.32 544.15/242.32 544.15/242.32 The following pairs can be oriented strictly and are deleted. 544.15/242.32 544.15/242.32 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.32 The remaining pairs can at least be oriented weakly. 544.15/242.32 Used ordering: Polynomial interpretation [POLO]: 544.15/242.32 544.15/242.32 POL(TOP.0(x_1)) = x_1 544.15/242.32 POL(a.) = 0 544.15/242.32 POL(b.) = 0 544.15/242.32 POL(c.) = 0 544.15/242.32 POL(down.0(x_1)) = 0 544.15/242.32 POL(down.1(x_1)) = x_1 544.15/242.32 POL(f.0(x_1)) = 0 544.15/242.32 POL(f.1(x_1)) = 1 544.15/242.32 POL(f_flat.0(x_1)) = 0 544.15/242.32 POL(fresh_constant.) = 0 544.15/242.32 POL(g.0(x_1)) = x_1 544.15/242.32 POL(g.1(x_1)) = 0 544.15/242.32 POL(g_flat.0(x_1)) = x_1 544.15/242.32 POL(up.0(x_1)) = x_1 544.15/242.32 544.15/242.32 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 544.15/242.32 544.15/242.32 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.32 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.32 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.32 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.32 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.32 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.32 down.0(f.0(f.1(a.))) -> f_flat.0(down.0(f.1(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.32 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.32 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.1(a.)))) -> f_flat.0(down.0(f.0(f.1(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.32 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(a.))))) -> f_flat.0(down.0(f.0(f.0(f.1(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.32 down.0(f.1(a.)) -> f_flat.0(down.1(a.)) 544.15/242.32 544.15/242.32 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1343) 544.15/242.32 Obligation: 544.15/242.32 Q DP problem: 544.15/242.32 The TRS P consists of the following rules: 544.15/242.32 544.15/242.32 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.32 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.32 544.15/242.32 The TRS R consists of the following rules: 544.15/242.32 544.15/242.32 down.0(f.1(a.)) -> f_flat.0(down.1(a.)) 544.15/242.32 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.32 down.1(a.) -> up.0(f.1(a.)) 544.15/242.32 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.32 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.32 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.32 down.0(f.0(c.)) -> f_flat.0(down.0(c.)) 544.15/242.32 down.0(f.0(f.1(a.))) -> f_flat.0(down.0(f.1(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.32 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.32 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.1(a.)))) -> f_flat.0(down.0(f.0(f.1(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.32 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(a.))))) -> f_flat.0(down.0(f.0(f.0(f.1(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.32 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.32 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.32 down.0(g.0(c.)) -> g_flat.0(down.0(c.)) 544.15/242.32 down.0(g.0(g.1(a.))) -> g_flat.0(down.0(g.1(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.32 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.32 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.0(g.1(a.)))) -> g_flat.0(down.0(g.0(g.1(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(a.))))) -> g_flat.0(down.0(g.0(g.0(g.1(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 down.0(b.) -> up.0(g.0(b.)) 544.15/242.32 544.15/242.32 The set Q consists of the following terms: 544.15/242.32 544.15/242.32 down.1(a.) 544.15/242.32 down.0(b.) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.1(a.)) 544.15/242.32 down.0(f.0(b.)) 544.15/242.32 down.0(f.0(g.0(x0))) 544.15/242.32 down.0(f.0(g.1(x0))) 544.15/242.32 down.0(f.0(c.)) 544.15/242.32 down.0(f.0(fresh_constant.)) 544.15/242.32 down.0(g.1(a.)) 544.15/242.32 down.0(g.0(f.0(x0))) 544.15/242.32 down.0(g.0(f.1(x0))) 544.15/242.32 down.0(g.0(b.)) 544.15/242.32 down.0(g.0(c.)) 544.15/242.32 down.0(g.0(fresh_constant.)) 544.15/242.32 down.0(f.0(f.1(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(x0)))) 544.15/242.32 down.0(f.0(f.0(g.1(x0)))) 544.15/242.32 down.0(f.0(f.0(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.1(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(x0)))) 544.15/242.32 down.0(g.0(g.0(f.1(x0)))) 544.15/242.32 down.0(g.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.0(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.1(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.32 down.0(f.0(f.0(f.0(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.1(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.0(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 f_flat.0(up.0(x0)) 544.15/242.32 f_flat.0(up.1(x0)) 544.15/242.32 g_flat.0(up.0(x0)) 544.15/242.32 g_flat.0(up.1(x0)) 544.15/242.32 544.15/242.32 We have to consider all minimal (P,Q,R)-chains. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1344) PisEmptyProof (SOUND) 544.15/242.32 The TRS P is empty. Hence, there is no (P,Q,R) chain. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1345) 544.15/242.32 TRUE 544.15/242.32 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1346) 544.15/242.32 Obligation: 544.15/242.32 Q DP problem: 544.15/242.32 The TRS P consists of the following rules: 544.15/242.32 544.15/242.32 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.32 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.32 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.32 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.32 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.32 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.32 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.32 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.32 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.32 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.32 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.32 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.32 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.32 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.32 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.32 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.32 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.32 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.32 544.15/242.32 The TRS R consists of the following rules: 544.15/242.32 544.15/242.32 down(f(a)) -> f_flat(down(a)) 544.15/242.32 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.32 down(a) -> up(f(a)) 544.15/242.32 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.32 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.32 down(f(c)) -> f_flat(down(c)) 544.15/242.32 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.32 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.32 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.32 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.32 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.32 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.32 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.32 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.32 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.32 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.32 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.32 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.32 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.32 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.32 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.32 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.32 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.32 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.32 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.32 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.32 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.32 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.32 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.32 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.32 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.32 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.32 down(g(b)) -> g_flat(down(b)) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.32 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.32 down(g(c)) -> g_flat(down(c)) 544.15/242.32 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.32 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.32 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.32 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.32 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.32 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.32 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.32 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.32 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.32 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.32 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.32 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.32 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.32 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.32 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.32 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.32 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.32 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.32 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.32 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.32 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.32 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.32 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.32 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.32 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.32 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.32 down(b) -> up(g(b)) 544.15/242.32 544.15/242.32 The set Q consists of the following terms: 544.15/242.32 544.15/242.32 down(a) 544.15/242.32 down(b) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.32 down(f(a)) 544.15/242.32 down(f(b)) 544.15/242.32 down(f(g(x0))) 544.15/242.32 down(f(c)) 544.15/242.32 down(f(fresh_constant)) 544.15/242.32 down(g(a)) 544.15/242.32 down(g(f(x0))) 544.15/242.32 down(g(b)) 544.15/242.32 down(g(c)) 544.15/242.32 down(g(fresh_constant)) 544.15/242.32 down(f(f(a))) 544.15/242.32 down(f(f(b))) 544.15/242.32 down(f(f(g(x0)))) 544.15/242.32 down(f(f(c))) 544.15/242.32 down(f(f(fresh_constant))) 544.15/242.32 down(g(g(a))) 544.15/242.32 down(g(g(f(x0)))) 544.15/242.32 down(g(g(b))) 544.15/242.32 down(g(g(c))) 544.15/242.32 down(g(g(fresh_constant))) 544.15/242.32 down(f(f(f(a)))) 544.15/242.32 down(f(f(f(b)))) 544.15/242.32 down(f(f(f(g(x0))))) 544.15/242.32 down(f(f(f(c)))) 544.15/242.32 down(f(f(f(fresh_constant)))) 544.15/242.32 down(g(g(g(a)))) 544.15/242.32 down(g(g(g(f(x0))))) 544.15/242.32 down(g(g(g(b)))) 544.15/242.32 down(g(g(g(c)))) 544.15/242.32 down(g(g(g(fresh_constant)))) 544.15/242.32 down(f(f(f(f(a))))) 544.15/242.32 down(f(f(f(f(b))))) 544.15/242.32 down(f(f(f(f(g(x0)))))) 544.15/242.32 down(f(f(f(f(c))))) 544.15/242.32 down(f(f(f(f(fresh_constant))))) 544.15/242.32 down(g(g(g(g(a))))) 544.15/242.32 down(g(g(g(g(f(x0)))))) 544.15/242.32 down(g(g(g(g(b))))) 544.15/242.32 down(g(g(g(g(c))))) 544.15/242.32 down(g(g(g(g(fresh_constant))))) 544.15/242.32 down(f(f(f(f(f(a)))))) 544.15/242.32 down(f(f(f(f(f(b)))))) 544.15/242.32 down(f(f(f(f(f(g(x0))))))) 544.15/242.32 down(f(f(f(f(f(c)))))) 544.15/242.32 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.32 down(g(g(g(g(g(a)))))) 544.15/242.32 down(g(g(g(g(g(f(x0))))))) 544.15/242.32 down(g(g(g(g(g(b)))))) 544.15/242.32 down(g(g(g(g(g(c)))))) 544.15/242.32 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.32 down(f(f(f(f(f(f(a))))))) 544.15/242.32 down(f(f(f(f(f(f(b))))))) 544.15/242.32 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.32 down(f(f(f(f(f(f(c))))))) 544.15/242.32 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.32 down(g(g(g(g(g(g(a))))))) 544.15/242.32 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.32 down(g(g(g(g(g(g(b))))))) 544.15/242.32 down(g(g(g(g(g(g(c))))))) 544.15/242.32 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.32 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.32 f_flat(up(x0)) 544.15/242.32 g_flat(up(x0)) 544.15/242.32 544.15/242.32 We have to consider all minimal (P,Q,R)-chains. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1347) SplitQDPProof (EQUIVALENT) 544.15/242.32 We show in the first subproof that some pairs and rules can be removed, afterwards, we continue with the remaining DP-Problem 544.15/242.32 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1348) 544.15/242.32 Complex Obligation (AND) 544.15/242.32 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1349) 544.15/242.32 Obligation: 544.15/242.32 Q DP problem: 544.15/242.32 The TRS P consists of the following rules: 544.15/242.32 544.15/242.32 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.32 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.32 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.32 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.32 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.32 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.32 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.32 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.32 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.32 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.32 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.32 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.32 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.32 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.32 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.32 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.32 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.32 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.32 544.15/242.32 The TRS R consists of the following rules: 544.15/242.32 544.15/242.32 down(f(a)) -> f_flat(down(a)) 544.15/242.32 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.32 down(a) -> up(f(a)) 544.15/242.32 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.32 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.32 down(f(c)) -> f_flat(down(c)) 544.15/242.32 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.32 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.32 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.32 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.32 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.32 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.32 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.32 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.32 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.32 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.32 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.32 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.32 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.32 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.32 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.32 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.32 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.32 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.32 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.32 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.32 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.32 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.32 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.32 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.32 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.32 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.32 down(g(b)) -> g_flat(down(b)) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.32 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.32 down(g(c)) -> g_flat(down(c)) 544.15/242.32 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.32 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.32 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.32 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.32 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.32 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.32 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.32 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.32 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.32 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.32 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.32 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.32 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.32 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.32 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.32 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.32 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.32 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.32 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.32 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.32 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.32 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.32 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.32 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.32 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.32 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.32 down(b) -> up(g(b)) 544.15/242.32 544.15/242.32 The set Q consists of the following terms: 544.15/242.32 544.15/242.32 down(a) 544.15/242.32 down(b) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.32 down(f(a)) 544.15/242.32 down(f(b)) 544.15/242.32 down(f(g(x0))) 544.15/242.32 down(f(c)) 544.15/242.32 down(f(fresh_constant)) 544.15/242.32 down(g(a)) 544.15/242.32 down(g(f(x0))) 544.15/242.32 down(g(b)) 544.15/242.32 down(g(c)) 544.15/242.32 down(g(fresh_constant)) 544.15/242.32 down(f(f(a))) 544.15/242.32 down(f(f(b))) 544.15/242.32 down(f(f(g(x0)))) 544.15/242.32 down(f(f(c))) 544.15/242.32 down(f(f(fresh_constant))) 544.15/242.32 down(g(g(a))) 544.15/242.32 down(g(g(f(x0)))) 544.15/242.32 down(g(g(b))) 544.15/242.32 down(g(g(c))) 544.15/242.32 down(g(g(fresh_constant))) 544.15/242.32 down(f(f(f(a)))) 544.15/242.32 down(f(f(f(b)))) 544.15/242.32 down(f(f(f(g(x0))))) 544.15/242.32 down(f(f(f(c)))) 544.15/242.32 down(f(f(f(fresh_constant)))) 544.15/242.32 down(g(g(g(a)))) 544.15/242.32 down(g(g(g(f(x0))))) 544.15/242.32 down(g(g(g(b)))) 544.15/242.32 down(g(g(g(c)))) 544.15/242.32 down(g(g(g(fresh_constant)))) 544.15/242.32 down(f(f(f(f(a))))) 544.15/242.32 down(f(f(f(f(b))))) 544.15/242.32 down(f(f(f(f(g(x0)))))) 544.15/242.32 down(f(f(f(f(c))))) 544.15/242.32 down(f(f(f(f(fresh_constant))))) 544.15/242.32 down(g(g(g(g(a))))) 544.15/242.32 down(g(g(g(g(f(x0)))))) 544.15/242.32 down(g(g(g(g(b))))) 544.15/242.32 down(g(g(g(g(c))))) 544.15/242.32 down(g(g(g(g(fresh_constant))))) 544.15/242.32 down(f(f(f(f(f(a)))))) 544.15/242.32 down(f(f(f(f(f(b)))))) 544.15/242.32 down(f(f(f(f(f(g(x0))))))) 544.15/242.32 down(f(f(f(f(f(c)))))) 544.15/242.32 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.32 down(g(g(g(g(g(a)))))) 544.15/242.32 down(g(g(g(g(g(f(x0))))))) 544.15/242.32 down(g(g(g(g(g(b)))))) 544.15/242.32 down(g(g(g(g(g(c)))))) 544.15/242.32 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.32 down(f(f(f(f(f(f(a))))))) 544.15/242.32 down(f(f(f(f(f(f(b))))))) 544.15/242.32 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.32 down(f(f(f(f(f(f(c))))))) 544.15/242.32 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.32 down(g(g(g(g(g(g(a))))))) 544.15/242.32 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.32 down(g(g(g(g(g(g(b))))))) 544.15/242.32 down(g(g(g(g(g(g(c))))))) 544.15/242.32 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.32 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.32 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.32 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.32 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.32 f_flat(up(x0)) 544.15/242.32 g_flat(up(x0)) 544.15/242.32 544.15/242.32 We have to consider all minimal (P,Q,R)-chains. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1350) SemLabProof (SOUND) 544.15/242.32 We found the following model for the rules of the TRSs R and P. 544.15/242.32 Interpretation over the domain with elements from 0 to 1. 544.15/242.32 a: 0 544.15/242.32 b: 0 544.15/242.32 c: 1 544.15/242.32 down: 0 544.15/242.32 f: 0 544.15/242.32 fresh_constant: 0 544.15/242.32 up: 0 544.15/242.32 f_flat: 0 544.15/242.32 TOP: 0 544.15/242.32 g_flat: 0 544.15/242.32 g: 0 544.15/242.32 By semantic labelling [SEMLAB] we obtain the following labelled QDP problem. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1351) 544.15/242.32 Obligation: 544.15/242.32 Q DP problem: 544.15/242.32 The TRS P consists of the following rules: 544.15/242.32 544.15/242.32 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.32 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.32 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.32 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.32 544.15/242.32 The TRS R consists of the following rules: 544.15/242.32 544.15/242.32 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.32 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.32 g_flat.0(up.1(x_1)) -> up.0(g.1(x_1)) 544.15/242.32 down.0(a.) -> up.0(f.0(a.)) 544.15/242.32 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.32 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.1(c.) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.1(c.) 544.15/242.32 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.32 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.32 down.0(f.1(c.)) -> f_flat.0(down.1(c.)) 544.15/242.32 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.32 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.32 down.0(f.0(f.1(c.))) -> f_flat.0(down.0(f.1(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.32 down.0(f.0(f.0(f.1(c.)))) -> f_flat.0(down.0(f.0(f.1(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(c.))))) -> f_flat.0(down.0(f.0(f.0(f.1(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.1(c.) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x))))))))))) -> up.1(c.) 544.15/242.32 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.32 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.32 down.0(g.1(c.)) -> g_flat.0(down.1(c.)) 544.15/242.32 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.32 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.32 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.1(c.))) -> g_flat.0(down.0(g.1(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.1(c.)))) -> g_flat.0(down.0(g.0(g.1(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(c.))))) -> g_flat.0(down.0(g.0(g.0(g.1(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 down.0(b.) -> up.0(g.0(b.)) 544.15/242.32 544.15/242.32 The set Q consists of the following terms: 544.15/242.32 544.15/242.32 down.0(a.) 544.15/242.32 down.0(b.) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.0(a.)) 544.15/242.32 down.0(f.0(b.)) 544.15/242.32 down.0(f.0(g.0(x0))) 544.15/242.32 down.0(f.0(g.1(x0))) 544.15/242.32 down.0(f.1(c.)) 544.15/242.32 down.0(f.0(fresh_constant.)) 544.15/242.32 down.0(g.0(a.)) 544.15/242.32 down.0(g.0(f.0(x0))) 544.15/242.32 down.0(g.0(f.1(x0))) 544.15/242.32 down.0(g.0(b.)) 544.15/242.32 down.0(g.1(c.)) 544.15/242.32 down.0(g.0(fresh_constant.)) 544.15/242.32 down.0(f.0(f.0(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(x0)))) 544.15/242.32 down.0(f.0(f.0(g.1(x0)))) 544.15/242.32 down.0(f.0(f.1(c.))) 544.15/242.32 down.0(f.0(f.0(fresh_constant.))) 544.15/242.32 down.0(g.0(g.0(a.))) 544.15/242.32 down.0(g.0(g.0(f.0(x0)))) 544.15/242.32 down.0(g.0(g.0(f.1(x0)))) 544.15/242.32 down.0(g.0(g.0(b.))) 544.15/242.32 down.0(g.0(g.1(c.))) 544.15/242.32 down.0(g.0(g.0(fresh_constant.))) 544.15/242.32 down.0(f.0(f.0(f.0(a.)))) 544.15/242.32 down.0(f.0(f.0(f.0(b.)))) 544.15/242.32 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.32 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.32 down.0(f.0(f.0(f.1(c.)))) 544.15/242.32 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.32 down.0(g.0(g.0(g.0(a.)))) 544.15/242.32 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.32 down.0(g.0(g.0(g.0(b.)))) 544.15/242.32 down.0(g.0(g.0(g.1(c.)))) 544.15/242.32 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.1(c.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.1(c.))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.1(c.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.1(c.)))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))))) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))))) 544.15/242.32 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.32 f_flat.0(up.0(x0)) 544.15/242.32 f_flat.0(up.1(x0)) 544.15/242.32 g_flat.0(up.0(x0)) 544.15/242.32 g_flat.0(up.1(x0)) 544.15/242.32 544.15/242.32 We have to consider all minimal (P,Q,R)-chains. 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1352) MRRProof (EQUIVALENT) 544.15/242.32 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 544.15/242.32 544.15/242.32 544.15/242.32 Strictly oriented rules of the TRS R: 544.15/242.32 544.15/242.32 down.0(f.1(c.)) -> f_flat.0(down.1(c.)) 544.15/242.32 down.0(g.1(c.)) -> g_flat.0(down.1(c.)) 544.15/242.32 544.15/242.32 Used ordering: Polynomial interpretation [POLO]: 544.15/242.32 544.15/242.32 POL(TOP.0(x_1)) = x_1 544.15/242.32 POL(a.) = 0 544.15/242.32 POL(b.) = 0 544.15/242.32 POL(c.) = 0 544.15/242.32 POL(down.0(x_1)) = 1 + x_1 544.15/242.32 POL(down.1(x_1)) = x_1 544.15/242.32 POL(f.0(x_1)) = x_1 544.15/242.32 POL(f.1(x_1)) = x_1 544.15/242.32 POL(f_flat.0(x_1)) = x_1 544.15/242.32 POL(fresh_constant.) = 0 544.15/242.32 POL(g.0(x_1)) = x_1 544.15/242.32 POL(g.1(x_1)) = x_1 544.15/242.32 POL(g_flat.0(x_1)) = x_1 544.15/242.32 POL(up.0(x_1)) = 1 + x_1 544.15/242.32 POL(up.1(x_1)) = 1 + x_1 544.15/242.32 544.15/242.32 544.15/242.32 ---------------------------------------- 544.15/242.32 544.15/242.32 (1353) 544.15/242.32 Obligation: 544.15/242.32 Q DP problem: 544.15/242.32 The TRS P consists of the following rules: 544.15/242.32 544.15/242.32 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.32 TOP.0(up.0(f.0(g.1(x0)))) -> TOP.0(f_flat.0(down.0(g.1(x0)))) 544.15/242.32 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.32 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.1(x0))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.32 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.1(x0)))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.32 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.32 544.15/242.32 The TRS R consists of the following rules: 544.15/242.32 544.15/242.32 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.32 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.32 g_flat.0(up.1(x_1)) -> up.0(g.1(x_1)) 544.15/242.32 down.0(a.) -> up.0(f.0(a.)) 544.15/242.32 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.32 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.1(c.) 544.15/242.32 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.1(c.) 544.15/242.32 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.32 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.32 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.32 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.32 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.33 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.33 down.0(f.0(f.1(c.))) -> f_flat.0(down.0(f.1(c.))) 544.15/242.33 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.33 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.33 down.0(f.0(f.0(f.1(c.)))) -> f_flat.0(down.0(f.0(f.1(c.)))) 544.15/242.33 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(c.))))) -> f_flat.0(down.0(f.0(f.0(f.1(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.1(c.) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x))))))))))) -> up.1(c.) 544.15/242.33 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.33 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.33 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.33 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.33 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.1(c.))) -> g_flat.0(down.0(g.1(c.))) 544.15/242.33 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.1(c.)))) -> g_flat.0(down.0(g.0(g.1(c.)))) 544.15/242.33 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.1(c.))))) -> g_flat.0(down.0(g.0(g.0(g.1(c.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.1(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(c.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(c.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.33 down.0(b.) -> up.0(g.0(b.)) 544.15/242.33 544.15/242.33 The set Q consists of the following terms: 544.15/242.33 544.15/242.33 down.0(a.) 544.15/242.33 down.0(b.) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(a.)) 544.15/242.33 down.0(f.0(b.)) 544.15/242.33 down.0(f.0(g.0(x0))) 544.15/242.33 down.0(f.0(g.1(x0))) 544.15/242.33 down.0(f.1(c.)) 544.15/242.33 down.0(f.0(fresh_constant.)) 544.15/242.33 down.0(g.0(a.)) 544.15/242.33 down.0(g.0(f.0(x0))) 544.15/242.33 down.0(g.0(f.1(x0))) 544.15/242.33 down.0(g.0(b.)) 544.15/242.33 down.0(g.1(c.)) 544.15/242.33 down.0(g.0(fresh_constant.)) 544.15/242.33 down.0(f.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(x0)))) 544.15/242.33 down.0(f.0(f.0(g.1(x0)))) 544.15/242.33 down.0(f.0(f.1(c.))) 544.15/242.33 down.0(f.0(f.0(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(x0)))) 544.15/242.33 down.0(g.0(g.0(f.1(x0)))) 544.15/242.33 down.0(g.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.1(c.))) 544.15/242.33 down.0(g.0(g.0(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.33 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.33 down.0(f.0(f.0(f.1(c.)))) 544.15/242.33 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.1(c.)))) 544.15/242.33 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.1(c.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.1(c.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.33 f_flat.0(up.0(x0)) 544.15/242.33 f_flat.0(up.1(x0)) 544.15/242.33 g_flat.0(up.0(x0)) 544.15/242.33 g_flat.0(up.1(x0)) 544.15/242.33 544.15/242.33 We have to consider all minimal (P,Q,R)-chains. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1354) DependencyGraphProof (EQUIVALENT) 544.15/242.33 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 18 less nodes. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1355) 544.15/242.33 Obligation: 544.15/242.33 Q DP problem: 544.15/242.33 The TRS P consists of the following rules: 544.15/242.33 544.15/242.33 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.33 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.33 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.33 544.15/242.33 The TRS R consists of the following rules: 544.15/242.33 544.15/242.33 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.33 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.33 g_flat.0(up.1(x_1)) -> up.0(g.1(x_1)) 544.15/242.33 down.0(a.) -> up.0(f.0(a.)) 544.15/242.33 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.33 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.1(c.) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.1(c.) 544.15/242.33 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.33 down.0(f.0(g.1(y4))) -> f_flat.0(down.0(g.1(y4))) 544.15/242.33 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.33 down.0(f.0(f.0(g.1(y10)))) -> f_flat.0(down.0(f.0(g.1(y10)))) 544.15/242.33 down.0(f.0(f.1(c.))) -> f_flat.0(down.0(f.1(c.))) 544.15/242.33 down.0(f.0(f.0(fresh_constant.))) -> f_flat.0(down.0(f.0(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.33 down.0(f.0(f.0(f.0(g.1(y16))))) -> f_flat.0(down.0(f.0(f.0(g.1(y16))))) 544.15/242.33 down.0(f.0(f.0(f.1(c.)))) -> f_flat.0(down.0(f.0(f.1(c.)))) 544.15/242.33 down.0(f.0(f.0(f.0(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.0(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.1(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(c.))))) -> f_flat.0(down.0(f.0(f.0(f.1(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.1(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.1(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.1(c.) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x))))))))))) -> up.1(c.) 544.15/242.33 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.33 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.33 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.33 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.33 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.1(c.))) -> g_flat.0(down.0(g.1(c.))) 544.15/242.33 down.0(g.0(g.0(fresh_constant.))) -> g_flat.0(down.0(g.0(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.1(c.)))) -> g_flat.0(down.0(g.0(g.1(c.)))) 544.15/242.33 down.0(g.0(g.0(g.0(fresh_constant.)))) -> g_flat.0(down.0(g.0(g.0(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.1(c.))))) -> g_flat.0(down.0(g.0(g.0(g.1(c.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) -> g_flat.0(down.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.1(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.1(c.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.1(c.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.33 down.0(b.) -> up.0(g.0(b.)) 544.15/242.33 544.15/242.33 The set Q consists of the following terms: 544.15/242.33 544.15/242.33 down.0(a.) 544.15/242.33 down.0(b.) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(a.)) 544.15/242.33 down.0(f.0(b.)) 544.15/242.33 down.0(f.0(g.0(x0))) 544.15/242.33 down.0(f.0(g.1(x0))) 544.15/242.33 down.0(f.1(c.)) 544.15/242.33 down.0(f.0(fresh_constant.)) 544.15/242.33 down.0(g.0(a.)) 544.15/242.33 down.0(g.0(f.0(x0))) 544.15/242.33 down.0(g.0(f.1(x0))) 544.15/242.33 down.0(g.0(b.)) 544.15/242.33 down.0(g.1(c.)) 544.15/242.33 down.0(g.0(fresh_constant.)) 544.15/242.33 down.0(f.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(x0)))) 544.15/242.33 down.0(f.0(f.0(g.1(x0)))) 544.15/242.33 down.0(f.0(f.1(c.))) 544.15/242.33 down.0(f.0(f.0(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(x0)))) 544.15/242.33 down.0(g.0(g.0(f.1(x0)))) 544.15/242.33 down.0(g.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.1(c.))) 544.15/242.33 down.0(g.0(g.0(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.33 down.0(f.0(f.0(f.0(g.1(x0))))) 544.15/242.33 down.0(f.0(f.0(f.1(c.)))) 544.15/242.33 down.0(f.0(f.0(f.0(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.1(c.)))) 544.15/242.33 down.0(g.0(g.0(g.0(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.1(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.1(c.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.1(c.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.1(c.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(fresh_constant.)))))))))) 544.15/242.33 f_flat.0(up.0(x0)) 544.15/242.33 f_flat.0(up.1(x0)) 544.15/242.33 g_flat.0(up.0(x0)) 544.15/242.33 g_flat.0(up.1(x0)) 544.15/242.33 544.15/242.33 We have to consider all minimal (P,Q,R)-chains. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1356) PisEmptyProof (SOUND) 544.15/242.33 The TRS P is empty. Hence, there is no (P,Q,R) chain. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1357) 544.15/242.33 TRUE 544.15/242.33 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1358) 544.15/242.33 Obligation: 544.15/242.33 Q DP problem: 544.15/242.33 The TRS P consists of the following rules: 544.15/242.33 544.15/242.33 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.33 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.33 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.33 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.33 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.33 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.33 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.33 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.33 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.33 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.33 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.33 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.33 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.33 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.33 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.33 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.33 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.33 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.33 544.15/242.33 The TRS R consists of the following rules: 544.15/242.33 544.15/242.33 down(f(a)) -> f_flat(down(a)) 544.15/242.33 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.33 down(a) -> up(f(a)) 544.15/242.33 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.33 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.33 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.33 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.33 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.33 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.33 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.33 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.33 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.33 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.33 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.33 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.33 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.33 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.33 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.33 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.33 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.33 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.33 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.33 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.33 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.33 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.33 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.33 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.33 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.33 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.33 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.33 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.33 down(g(b)) -> g_flat(down(b)) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.33 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.33 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.33 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.33 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.33 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.33 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.33 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.33 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.33 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.33 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.33 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.33 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.33 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.33 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.33 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.33 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.33 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.33 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.33 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.33 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.33 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.33 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.33 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.33 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.33 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.33 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.33 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.33 down(b) -> up(g(b)) 544.15/242.33 544.15/242.33 The set Q consists of the following terms: 544.15/242.33 544.15/242.33 down(a) 544.15/242.33 down(b) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.33 down(f(a)) 544.15/242.33 down(f(b)) 544.15/242.33 down(f(g(x0))) 544.15/242.33 down(f(c)) 544.15/242.33 down(f(fresh_constant)) 544.15/242.33 down(g(a)) 544.15/242.33 down(g(f(x0))) 544.15/242.33 down(g(b)) 544.15/242.33 down(g(c)) 544.15/242.33 down(g(fresh_constant)) 544.15/242.33 down(f(f(a))) 544.15/242.33 down(f(f(b))) 544.15/242.33 down(f(f(g(x0)))) 544.15/242.33 down(f(f(c))) 544.15/242.33 down(f(f(fresh_constant))) 544.15/242.33 down(g(g(a))) 544.15/242.33 down(g(g(f(x0)))) 544.15/242.33 down(g(g(b))) 544.15/242.33 down(g(g(c))) 544.15/242.33 down(g(g(fresh_constant))) 544.15/242.33 down(f(f(f(a)))) 544.15/242.33 down(f(f(f(b)))) 544.15/242.33 down(f(f(f(g(x0))))) 544.15/242.33 down(f(f(f(c)))) 544.15/242.33 down(f(f(f(fresh_constant)))) 544.15/242.33 down(g(g(g(a)))) 544.15/242.33 down(g(g(g(f(x0))))) 544.15/242.33 down(g(g(g(b)))) 544.15/242.33 down(g(g(g(c)))) 544.15/242.33 down(g(g(g(fresh_constant)))) 544.15/242.33 down(f(f(f(f(a))))) 544.15/242.33 down(f(f(f(f(b))))) 544.15/242.33 down(f(f(f(f(g(x0)))))) 544.15/242.33 down(f(f(f(f(c))))) 544.15/242.33 down(f(f(f(f(fresh_constant))))) 544.15/242.33 down(g(g(g(g(a))))) 544.15/242.33 down(g(g(g(g(f(x0)))))) 544.15/242.33 down(g(g(g(g(b))))) 544.15/242.33 down(g(g(g(g(c))))) 544.15/242.33 down(g(g(g(g(fresh_constant))))) 544.15/242.33 down(f(f(f(f(f(a)))))) 544.15/242.33 down(f(f(f(f(f(b)))))) 544.15/242.33 down(f(f(f(f(f(g(x0))))))) 544.15/242.33 down(f(f(f(f(f(c)))))) 544.15/242.33 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.33 down(g(g(g(g(g(a)))))) 544.15/242.33 down(g(g(g(g(g(f(x0))))))) 544.15/242.33 down(g(g(g(g(g(b)))))) 544.15/242.33 down(g(g(g(g(g(c)))))) 544.15/242.33 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.33 down(f(f(f(f(f(f(a))))))) 544.15/242.33 down(f(f(f(f(f(f(b))))))) 544.15/242.33 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.33 down(f(f(f(f(f(f(c))))))) 544.15/242.33 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.33 down(g(g(g(g(g(g(a))))))) 544.15/242.33 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.33 down(g(g(g(g(g(g(b))))))) 544.15/242.33 down(g(g(g(g(g(g(c))))))) 544.15/242.33 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.33 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.33 f_flat(up(x0)) 544.15/242.33 g_flat(up(x0)) 544.15/242.33 544.15/242.33 We have to consider all minimal (P,Q,R)-chains. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1359) SplitQDPProof (EQUIVALENT) 544.15/242.33 We show in the first subproof that some pairs and rules can be removed, afterwards, we continue with the remaining DP-Problem 544.15/242.33 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1360) 544.15/242.33 Complex Obligation (AND) 544.15/242.33 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1361) 544.15/242.33 Obligation: 544.15/242.33 Q DP problem: 544.15/242.33 The TRS P consists of the following rules: 544.15/242.33 544.15/242.33 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.33 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.33 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.33 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.33 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.33 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.33 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.33 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.33 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.33 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.33 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.33 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.33 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.33 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.33 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.33 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.33 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.33 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.33 544.15/242.33 The TRS R consists of the following rules: 544.15/242.33 544.15/242.33 down(f(a)) -> f_flat(down(a)) 544.15/242.33 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.33 down(a) -> up(f(a)) 544.15/242.33 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.33 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.33 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.33 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.33 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.33 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.33 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.33 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.33 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.33 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.33 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.33 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.33 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.33 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.33 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.33 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.33 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.33 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.33 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.33 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.33 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.33 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.33 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.33 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.33 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.33 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.33 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.33 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.33 down(g(b)) -> g_flat(down(b)) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.33 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.33 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.33 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.33 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.33 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.33 down(g(g(fresh_constant))) -> g_flat(down(g(fresh_constant))) 544.15/242.33 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.33 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.33 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.33 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.33 down(g(g(g(fresh_constant)))) -> g_flat(down(g(g(fresh_constant)))) 544.15/242.33 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.33 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.33 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.33 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.33 down(g(g(g(g(fresh_constant))))) -> g_flat(down(g(g(g(fresh_constant))))) 544.15/242.33 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.33 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.33 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.33 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.33 down(g(g(g(g(g(fresh_constant)))))) -> g_flat(down(g(g(g(g(fresh_constant)))))) 544.15/242.33 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.33 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.33 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.33 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.33 down(g(g(g(g(g(g(fresh_constant))))))) -> g_flat(down(g(g(g(g(g(fresh_constant))))))) 544.15/242.33 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) -> g_flat(down(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) -> g_flat(down(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.33 down(b) -> up(g(b)) 544.15/242.33 544.15/242.33 The set Q consists of the following terms: 544.15/242.33 544.15/242.33 down(a) 544.15/242.33 down(b) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.33 down(f(a)) 544.15/242.33 down(f(b)) 544.15/242.33 down(f(g(x0))) 544.15/242.33 down(f(c)) 544.15/242.33 down(f(fresh_constant)) 544.15/242.33 down(g(a)) 544.15/242.33 down(g(f(x0))) 544.15/242.33 down(g(b)) 544.15/242.33 down(g(c)) 544.15/242.33 down(g(fresh_constant)) 544.15/242.33 down(f(f(a))) 544.15/242.33 down(f(f(b))) 544.15/242.33 down(f(f(g(x0)))) 544.15/242.33 down(f(f(c))) 544.15/242.33 down(f(f(fresh_constant))) 544.15/242.33 down(g(g(a))) 544.15/242.33 down(g(g(f(x0)))) 544.15/242.33 down(g(g(b))) 544.15/242.33 down(g(g(c))) 544.15/242.33 down(g(g(fresh_constant))) 544.15/242.33 down(f(f(f(a)))) 544.15/242.33 down(f(f(f(b)))) 544.15/242.33 down(f(f(f(g(x0))))) 544.15/242.33 down(f(f(f(c)))) 544.15/242.33 down(f(f(f(fresh_constant)))) 544.15/242.33 down(g(g(g(a)))) 544.15/242.33 down(g(g(g(f(x0))))) 544.15/242.33 down(g(g(g(b)))) 544.15/242.33 down(g(g(g(c)))) 544.15/242.33 down(g(g(g(fresh_constant)))) 544.15/242.33 down(f(f(f(f(a))))) 544.15/242.33 down(f(f(f(f(b))))) 544.15/242.33 down(f(f(f(f(g(x0)))))) 544.15/242.33 down(f(f(f(f(c))))) 544.15/242.33 down(f(f(f(f(fresh_constant))))) 544.15/242.33 down(g(g(g(g(a))))) 544.15/242.33 down(g(g(g(g(f(x0)))))) 544.15/242.33 down(g(g(g(g(b))))) 544.15/242.33 down(g(g(g(g(c))))) 544.15/242.33 down(g(g(g(g(fresh_constant))))) 544.15/242.33 down(f(f(f(f(f(a)))))) 544.15/242.33 down(f(f(f(f(f(b)))))) 544.15/242.33 down(f(f(f(f(f(g(x0))))))) 544.15/242.33 down(f(f(f(f(f(c)))))) 544.15/242.33 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.33 down(g(g(g(g(g(a)))))) 544.15/242.33 down(g(g(g(g(g(f(x0))))))) 544.15/242.33 down(g(g(g(g(g(b)))))) 544.15/242.33 down(g(g(g(g(g(c)))))) 544.15/242.33 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.33 down(f(f(f(f(f(f(a))))))) 544.15/242.33 down(f(f(f(f(f(f(b))))))) 544.15/242.33 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.33 down(f(f(f(f(f(f(c))))))) 544.15/242.33 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.33 down(g(g(g(g(g(g(a))))))) 544.15/242.33 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.33 down(g(g(g(g(g(g(b))))))) 544.15/242.33 down(g(g(g(g(g(g(c))))))) 544.15/242.33 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.33 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.33 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.33 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.33 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.33 f_flat(up(x0)) 544.15/242.33 g_flat(up(x0)) 544.15/242.33 544.15/242.33 We have to consider all minimal (P,Q,R)-chains. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1362) SemLabProof (SOUND) 544.15/242.33 We found the following model for the rules of the TRSs R and P. 544.15/242.33 Interpretation over the domain with elements from 0 to 1. 544.15/242.33 a: 0 544.15/242.33 b: 0 544.15/242.33 c: 0 544.15/242.33 down: 0 544.15/242.33 f: 0 544.15/242.33 fresh_constant: 1 544.15/242.33 up: 0 544.15/242.33 f_flat: 0 544.15/242.33 TOP: 0 544.15/242.33 g_flat: 0 544.15/242.33 g: x0 544.15/242.33 By semantic labelling [SEMLAB] we obtain the following labelled QDP problem. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1363) 544.15/242.33 Obligation: 544.15/242.33 Q DP problem: 544.15/242.33 The TRS P consists of the following rules: 544.15/242.33 544.15/242.33 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.33 TOP.0(up.0(f.1(g.1(x0)))) -> TOP.0(f_flat.0(down.1(g.1(x0)))) 544.15/242.33 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.33 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.33 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.1(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.1(g.1(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.1(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0)))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.1(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0)))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0)))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0)))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.33 544.15/242.33 The TRS R consists of the following rules: 544.15/242.33 544.15/242.33 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.33 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.33 g_flat.0(up.1(x_1)) -> up.1(g.1(x_1)) 544.15/242.33 down.0(a.) -> up.0(f.0(a.)) 544.15/242.33 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.33 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.33 down.0(f.1(g.1(y4))) -> f_flat.0(down.1(g.1(y4))) 544.15/242.33 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.33 down.0(f.0(f.1(g.1(y10)))) -> f_flat.0(down.0(f.1(g.1(y10)))) 544.15/242.33 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.33 down.0(f.0(f.1(fresh_constant.))) -> f_flat.0(down.0(f.1(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.33 down.0(f.0(f.0(f.1(g.1(y16))))) -> f_flat.0(down.0(f.0(f.1(g.1(y16))))) 544.15/242.33 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.33 down.0(f.0(f.0(f.1(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.1(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.1(g.1(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(g.1(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.33 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.33 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.33 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.33 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.33 down.1(g.1(g.1(fresh_constant.))) -> g_flat.0(down.1(g.1(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.33 down.1(g.1(g.1(g.1(fresh_constant.)))) -> g_flat.0(down.1(g.1(g.1(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(fresh_constant.))))) -> g_flat.0(down.1(g.1(g.1(g.1(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) 544.15/242.33 down.0(b.) -> up.0(g.0(b.)) 544.15/242.33 544.15/242.33 The set Q consists of the following terms: 544.15/242.33 544.15/242.33 down.0(a.) 544.15/242.33 down.0(b.) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(a.)) 544.15/242.33 down.0(f.0(b.)) 544.15/242.33 down.0(f.0(g.0(x0))) 544.15/242.33 down.0(f.1(g.1(x0))) 544.15/242.33 down.0(f.0(c.)) 544.15/242.33 down.0(f.1(fresh_constant.)) 544.15/242.33 down.0(g.0(a.)) 544.15/242.33 down.0(g.0(f.0(x0))) 544.15/242.33 down.0(g.0(f.1(x0))) 544.15/242.33 down.0(g.0(b.)) 544.15/242.33 down.0(g.0(c.)) 544.15/242.33 down.1(g.1(fresh_constant.)) 544.15/242.33 down.0(f.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(x0)))) 544.15/242.33 down.0(f.0(f.1(g.1(x0)))) 544.15/242.33 down.0(f.0(f.0(c.))) 544.15/242.33 down.0(f.0(f.1(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(x0)))) 544.15/242.33 down.0(g.0(g.0(f.1(x0)))) 544.15/242.33 down.0(g.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.0(c.))) 544.15/242.33 down.1(g.1(g.1(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.33 down.0(f.0(f.0(f.1(g.1(x0))))) 544.15/242.33 down.0(f.0(f.0(f.0(c.)))) 544.15/242.33 down.0(f.0(f.0(f.1(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.0(c.)))) 544.15/242.33 down.1(g.1(g.1(g.1(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(g.1(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) 544.15/242.33 f_flat.0(up.0(x0)) 544.15/242.33 f_flat.0(up.1(x0)) 544.15/242.33 g_flat.0(up.0(x0)) 544.15/242.33 g_flat.0(up.1(x0)) 544.15/242.33 544.15/242.33 We have to consider all minimal (P,Q,R)-chains. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1364) MRRProof (EQUIVALENT) 544.15/242.33 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 544.15/242.33 544.15/242.33 Strictly oriented dependency pairs: 544.15/242.33 544.15/242.33 TOP.0(up.0(f.1(g.1(x0)))) -> TOP.0(f_flat.0(down.1(g.1(x0)))) 544.15/242.33 TOP.0(up.0(f.0(f.1(g.1(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.1(g.1(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.1(g.1(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0)))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.1(g.1(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0)))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0)))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0))))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.1(g.1(x0)))))))))))) 544.15/242.33 544.15/242.33 Strictly oriented rules of the TRS R: 544.15/242.33 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(f.1(g.1(y4))) -> f_flat.0(down.1(g.1(y4))) 544.15/242.33 544.15/242.33 Used ordering: Polynomial interpretation [POLO]: 544.15/242.33 544.15/242.33 POL(TOP.0(x_1)) = x_1 544.15/242.33 POL(a.) = 0 544.15/242.33 POL(b.) = 0 544.15/242.33 POL(c.) = 0 544.15/242.33 POL(down.0(x_1)) = x_1 544.15/242.33 POL(down.1(x_1)) = x_1 544.15/242.33 POL(f.0(x_1)) = x_1 544.15/242.33 POL(f.1(x_1)) = 1 + x_1 544.15/242.33 POL(f_flat.0(x_1)) = x_1 544.15/242.33 POL(fresh_constant.) = 0 544.15/242.33 POL(g.0(x_1)) = x_1 544.15/242.33 POL(g.1(x_1)) = x_1 544.15/242.33 POL(g_flat.0(x_1)) = x_1 544.15/242.33 POL(up.0(x_1)) = x_1 544.15/242.33 POL(up.1(x_1)) = 1 + x_1 544.15/242.33 544.15/242.33 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1365) 544.15/242.33 Obligation: 544.15/242.33 Q DP problem: 544.15/242.33 The TRS P consists of the following rules: 544.15/242.33 544.15/242.33 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.33 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.33 TOP.0(up.0(g.0(f.1(x0)))) -> TOP.0(g_flat.0(down.0(f.1(x0)))) 544.15/242.33 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(f.1(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.1(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(f.1(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(f.1(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0))))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.1(x0)))))))))))) 544.15/242.33 544.15/242.33 The TRS R consists of the following rules: 544.15/242.33 544.15/242.33 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.33 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.33 g_flat.0(up.1(x_1)) -> up.1(g.1(x_1)) 544.15/242.33 down.0(a.) -> up.0(f.0(a.)) 544.15/242.33 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.33 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.33 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.33 down.0(f.0(f.1(g.1(y10)))) -> f_flat.0(down.0(f.1(g.1(y10)))) 544.15/242.33 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.33 down.0(f.0(f.1(fresh_constant.))) -> f_flat.0(down.0(f.1(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.33 down.0(f.0(f.0(f.1(g.1(y16))))) -> f_flat.0(down.0(f.0(f.1(g.1(y16))))) 544.15/242.33 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.33 down.0(f.0(f.0(f.1(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.1(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.1(g.1(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(g.1(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.33 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.33 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.33 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.33 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.33 down.1(g.1(g.1(fresh_constant.))) -> g_flat.0(down.1(g.1(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.33 down.1(g.1(g.1(g.1(fresh_constant.)))) -> g_flat.0(down.1(g.1(g.1(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(fresh_constant.))))) -> g_flat.0(down.1(g.1(g.1(g.1(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) 544.15/242.33 down.0(b.) -> up.0(g.0(b.)) 544.15/242.33 544.15/242.33 The set Q consists of the following terms: 544.15/242.33 544.15/242.33 down.0(a.) 544.15/242.33 down.0(b.) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(a.)) 544.15/242.33 down.0(f.0(b.)) 544.15/242.33 down.0(f.0(g.0(x0))) 544.15/242.33 down.0(f.1(g.1(x0))) 544.15/242.33 down.0(f.0(c.)) 544.15/242.33 down.0(f.1(fresh_constant.)) 544.15/242.33 down.0(g.0(a.)) 544.15/242.33 down.0(g.0(f.0(x0))) 544.15/242.33 down.0(g.0(f.1(x0))) 544.15/242.33 down.0(g.0(b.)) 544.15/242.33 down.0(g.0(c.)) 544.15/242.33 down.1(g.1(fresh_constant.)) 544.15/242.33 down.0(f.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(x0)))) 544.15/242.33 down.0(f.0(f.1(g.1(x0)))) 544.15/242.33 down.0(f.0(f.0(c.))) 544.15/242.33 down.0(f.0(f.1(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(x0)))) 544.15/242.33 down.0(g.0(g.0(f.1(x0)))) 544.15/242.33 down.0(g.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.0(c.))) 544.15/242.33 down.1(g.1(g.1(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.33 down.0(f.0(f.0(f.1(g.1(x0))))) 544.15/242.33 down.0(f.0(f.0(f.0(c.)))) 544.15/242.33 down.0(f.0(f.0(f.1(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.0(c.)))) 544.15/242.33 down.1(g.1(g.1(g.1(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(g.1(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) 544.15/242.33 f_flat.0(up.0(x0)) 544.15/242.33 f_flat.0(up.1(x0)) 544.15/242.33 g_flat.0(up.0(x0)) 544.15/242.33 g_flat.0(up.1(x0)) 544.15/242.33 544.15/242.33 We have to consider all minimal (P,Q,R)-chains. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1366) DependencyGraphProof (EQUIVALENT) 544.15/242.33 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 9 less nodes. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1367) 544.15/242.33 Obligation: 544.15/242.33 Q DP problem: 544.15/242.33 The TRS P consists of the following rules: 544.15/242.33 544.15/242.33 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.33 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.33 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.33 544.15/242.33 The TRS R consists of the following rules: 544.15/242.33 544.15/242.33 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.33 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.33 g_flat.0(up.1(x_1)) -> up.1(g.1(x_1)) 544.15/242.33 down.0(a.) -> up.0(f.0(a.)) 544.15/242.33 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.33 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.33 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.33 down.0(f.0(f.1(g.1(y10)))) -> f_flat.0(down.0(f.1(g.1(y10)))) 544.15/242.33 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.33 down.0(f.0(f.1(fresh_constant.))) -> f_flat.0(down.0(f.1(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.33 down.0(f.0(f.0(f.1(g.1(y16))))) -> f_flat.0(down.0(f.0(f.1(g.1(y16))))) 544.15/242.33 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.33 down.0(f.0(f.0(f.1(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.1(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.1(g.1(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(g.1(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.33 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.33 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.33 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.33 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.33 down.1(g.1(g.1(fresh_constant.))) -> g_flat.0(down.1(g.1(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.33 down.1(g.1(g.1(g.1(fresh_constant.)))) -> g_flat.0(down.1(g.1(g.1(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(fresh_constant.))))) -> g_flat.0(down.1(g.1(g.1(g.1(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) 544.15/242.33 down.0(b.) -> up.0(g.0(b.)) 544.15/242.33 544.15/242.33 The set Q consists of the following terms: 544.15/242.33 544.15/242.33 down.0(a.) 544.15/242.33 down.0(b.) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(a.)) 544.15/242.33 down.0(f.0(b.)) 544.15/242.33 down.0(f.0(g.0(x0))) 544.15/242.33 down.0(f.1(g.1(x0))) 544.15/242.33 down.0(f.0(c.)) 544.15/242.33 down.0(f.1(fresh_constant.)) 544.15/242.33 down.0(g.0(a.)) 544.15/242.33 down.0(g.0(f.0(x0))) 544.15/242.33 down.0(g.0(f.1(x0))) 544.15/242.33 down.0(g.0(b.)) 544.15/242.33 down.0(g.0(c.)) 544.15/242.33 down.1(g.1(fresh_constant.)) 544.15/242.33 down.0(f.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(x0)))) 544.15/242.33 down.0(f.0(f.1(g.1(x0)))) 544.15/242.33 down.0(f.0(f.0(c.))) 544.15/242.33 down.0(f.0(f.1(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(x0)))) 544.15/242.33 down.0(g.0(g.0(f.1(x0)))) 544.15/242.33 down.0(g.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.0(c.))) 544.15/242.33 down.1(g.1(g.1(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.33 down.0(f.0(f.0(f.1(g.1(x0))))) 544.15/242.33 down.0(f.0(f.0(f.0(c.)))) 544.15/242.33 down.0(f.0(f.0(f.1(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.0(c.)))) 544.15/242.33 down.1(g.1(g.1(g.1(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(g.1(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) 544.15/242.33 f_flat.0(up.0(x0)) 544.15/242.33 f_flat.0(up.1(x0)) 544.15/242.33 g_flat.0(up.0(x0)) 544.15/242.33 g_flat.0(up.1(x0)) 544.15/242.33 544.15/242.33 We have to consider all minimal (P,Q,R)-chains. 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1368) UsableRulesReductionPairsProof (EQUIVALENT) 544.15/242.33 By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well. 544.15/242.33 544.15/242.33 No dependency pairs are removed. 544.15/242.33 544.15/242.33 The following rules are removed from R: 544.15/242.33 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(x))))))))))) -> up.0(c.) 544.15/242.33 down.1(g.1(g.1(fresh_constant.))) -> g_flat.0(down.1(g.1(fresh_constant.))) 544.15/242.33 down.1(g.1(g.1(g.1(fresh_constant.)))) -> g_flat.0(down.1(g.1(g.1(fresh_constant.)))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(fresh_constant.))))) -> g_flat.0(down.1(g.1(g.1(g.1(fresh_constant.))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) -> g_flat.0(down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) 544.15/242.33 Used ordering: POLO with Polynomial interpretation [POLO]: 544.15/242.33 544.15/242.33 POL(TOP.0(x_1)) = x_1 544.15/242.33 POL(a.) = 0 544.15/242.33 POL(b.) = 0 544.15/242.33 POL(c.) = 0 544.15/242.33 POL(down.0(x_1)) = 1 + x_1 544.15/242.33 POL(f.0(x_1)) = x_1 544.15/242.33 POL(f.1(x_1)) = x_1 544.15/242.33 POL(f_flat.0(x_1)) = x_1 544.15/242.33 POL(fresh_constant.) = 0 544.15/242.33 POL(g.0(x_1)) = x_1 544.15/242.33 POL(g.1(x_1)) = x_1 544.15/242.33 POL(g_flat.0(x_1)) = x_1 544.15/242.33 POL(up.0(x_1)) = 1 + x_1 544.15/242.33 POL(up.1(x_1)) = 1 + x_1 544.15/242.33 544.15/242.33 544.15/242.33 ---------------------------------------- 544.15/242.33 544.15/242.33 (1369) 544.15/242.33 Obligation: 544.15/242.33 Q DP problem: 544.15/242.33 The TRS P consists of the following rules: 544.15/242.33 544.15/242.33 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.33 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.33 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.33 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.33 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.33 544.15/242.33 The TRS R consists of the following rules: 544.15/242.33 544.15/242.33 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.33 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.33 down.0(f.0(f.1(g.1(y10)))) -> f_flat.0(down.0(f.1(g.1(y10)))) 544.15/242.33 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.33 down.0(f.0(f.1(fresh_constant.))) -> f_flat.0(down.0(f.1(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.33 down.0(f.0(f.0(f.1(g.1(y16))))) -> f_flat.0(down.0(f.0(f.1(g.1(y16))))) 544.15/242.33 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.33 down.0(f.0(f.0(f.1(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.1(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.1(g.1(y22)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(g.1(y28))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.33 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.33 g_flat.0(up.1(x_1)) -> up.1(g.1(x_1)) 544.15/242.33 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.33 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.33 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.33 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.33 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.33 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.33 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.33 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.33 down.0(b.) -> up.0(g.0(b.)) 544.15/242.33 down.0(a.) -> up.0(f.0(a.)) 544.15/242.33 544.15/242.33 The set Q consists of the following terms: 544.15/242.33 544.15/242.33 down.0(a.) 544.15/242.33 down.0(b.) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.33 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(x0))))))))))) 544.15/242.33 down.0(f.0(a.)) 544.15/242.33 down.0(f.0(b.)) 544.15/242.33 down.0(f.0(g.0(x0))) 544.15/242.33 down.0(f.1(g.1(x0))) 544.15/242.33 down.0(f.0(c.)) 544.15/242.33 down.0(f.1(fresh_constant.)) 544.15/242.33 down.0(g.0(a.)) 544.15/242.33 down.0(g.0(f.0(x0))) 544.15/242.33 down.0(g.0(f.1(x0))) 544.15/242.33 down.0(g.0(b.)) 544.15/242.33 down.0(g.0(c.)) 544.15/242.33 down.1(g.1(fresh_constant.)) 544.15/242.33 down.0(f.0(f.0(a.))) 544.15/242.33 down.0(f.0(f.0(b.))) 544.15/242.33 down.0(f.0(f.0(g.0(x0)))) 544.15/242.33 down.0(f.0(f.1(g.1(x0)))) 544.15/242.33 down.0(f.0(f.0(c.))) 544.15/242.33 down.0(f.0(f.1(fresh_constant.))) 544.15/242.33 down.0(g.0(g.0(a.))) 544.15/242.33 down.0(g.0(g.0(f.0(x0)))) 544.15/242.33 down.0(g.0(g.0(f.1(x0)))) 544.15/242.33 down.0(g.0(g.0(b.))) 544.15/242.33 down.0(g.0(g.0(c.))) 544.15/242.33 down.1(g.1(g.1(fresh_constant.))) 544.15/242.33 down.0(f.0(f.0(f.0(a.)))) 544.15/242.33 down.0(f.0(f.0(f.0(b.)))) 544.15/242.33 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.33 down.0(f.0(f.0(f.1(g.1(x0))))) 544.15/242.33 down.0(f.0(f.0(f.0(c.)))) 544.15/242.33 down.0(f.0(f.0(f.1(fresh_constant.)))) 544.15/242.33 down.0(g.0(g.0(g.0(a.)))) 544.15/242.33 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.33 down.0(g.0(g.0(g.0(b.)))) 544.15/242.33 down.0(g.0(g.0(g.0(c.)))) 544.15/242.33 down.1(g.1(g.1(g.1(fresh_constant.)))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(g.1(x0)))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.33 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.33 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(fresh_constant.))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) 544.15/242.34 f_flat.0(up.0(x0)) 544.15/242.34 f_flat.0(up.1(x0)) 544.15/242.34 g_flat.0(up.0(x0)) 544.15/242.34 g_flat.0(up.1(x0)) 544.15/242.34 544.15/242.34 We have to consider all minimal (P,Q,R)-chains. 544.15/242.34 ---------------------------------------- 544.15/242.34 544.15/242.34 (1370) MRRProof (EQUIVALENT) 544.15/242.34 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 544.15/242.34 544.15/242.34 544.15/242.34 Strictly oriented rules of the TRS R: 544.15/242.34 544.15/242.34 f_flat.0(up.1(x_1)) -> up.0(f.1(x_1)) 544.15/242.34 544.15/242.34 Used ordering: Polynomial interpretation [POLO]: 544.15/242.34 544.15/242.34 POL(TOP.0(x_1)) = x_1 544.15/242.34 POL(a.) = 0 544.15/242.34 POL(b.) = 0 544.15/242.34 POL(c.) = 0 544.15/242.34 POL(down.0(x_1)) = x_1 544.15/242.34 POL(f.0(x_1)) = x_1 544.15/242.34 POL(f.1(x_1)) = x_1 544.15/242.34 POL(f_flat.0(x_1)) = x_1 544.15/242.34 POL(fresh_constant.) = 0 544.15/242.34 POL(g.0(x_1)) = x_1 544.15/242.34 POL(g.1(x_1)) = x_1 544.15/242.34 POL(g_flat.0(x_1)) = x_1 544.15/242.34 POL(up.0(x_1)) = x_1 544.15/242.34 POL(up.1(x_1)) = 1 + x_1 544.15/242.34 544.15/242.34 544.15/242.34 ---------------------------------------- 544.15/242.34 544.15/242.34 (1371) 544.15/242.34 Obligation: 544.15/242.34 Q DP problem: 544.15/242.34 The TRS P consists of the following rules: 544.15/242.34 544.15/242.34 TOP.0(up.0(f.0(g.0(x0)))) -> TOP.0(f_flat.0(down.0(g.0(x0)))) 544.15/242.34 TOP.0(up.0(g.0(f.0(x0)))) -> TOP.0(g_flat.0(down.0(f.0(x0)))) 544.15/242.34 TOP.0(up.0(g.0(g.0(f.0(x0))))) -> TOP.0(g_flat.0(g_flat.0(down.0(f.0(x0))))) 544.15/242.34 TOP.0(up.0(f.0(f.0(g.0(x0))))) -> TOP.0(f_flat.0(f_flat.0(down.0(g.0(x0))))) 544.15/242.34 TOP.0(up.0(f.0(f.0(f.0(g.0(x0)))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))) 544.15/242.34 TOP.0(up.0(g.0(g.0(g.0(f.0(x0)))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))) 544.15/242.34 TOP.0(up.0(f.0(f.0(f.0(f.0(g.0(x0))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))) 544.15/242.34 TOP.0(up.0(g.0(g.0(g.0(g.0(f.0(x0))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))) 544.15/242.34 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))) 544.15/242.34 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))) 544.15/242.34 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))) 544.15/242.34 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))) 544.15/242.34 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))) 544.15/242.34 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))) 544.15/242.34 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0))))))))))) 544.15/242.34 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0))))))))))) 544.15/242.34 TOP.0(up.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))))) -> TOP.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(f_flat.0(down.0(g.0(x0)))))))))))) 544.15/242.34 TOP.0(up.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))))) -> TOP.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(g_flat.0(down.0(f.0(x0)))))))))))) 544.15/242.34 544.15/242.34 The TRS R consists of the following rules: 544.15/242.34 544.15/242.34 down.0(f.0(a.)) -> f_flat.0(down.0(a.)) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x))))))))))) -> up.0(c.) 544.15/242.34 down.0(f.0(g.0(y4))) -> f_flat.0(down.0(g.0(y4))) 544.15/242.34 down.0(f.0(f.0(a.))) -> f_flat.0(down.0(f.0(a.))) 544.15/242.34 down.0(f.0(f.0(b.))) -> f_flat.0(down.0(f.0(b.))) 544.15/242.34 down.0(f.0(f.0(g.0(y10)))) -> f_flat.0(down.0(f.0(g.0(y10)))) 544.15/242.34 down.0(f.0(f.1(g.1(y10)))) -> f_flat.0(down.0(f.1(g.1(y10)))) 544.15/242.34 down.0(f.0(f.0(c.))) -> f_flat.0(down.0(f.0(c.))) 544.15/242.34 down.0(f.0(f.1(fresh_constant.))) -> f_flat.0(down.0(f.1(fresh_constant.))) 544.15/242.34 down.0(f.0(f.0(f.0(a.)))) -> f_flat.0(down.0(f.0(f.0(a.)))) 544.15/242.34 down.0(f.0(f.0(f.0(b.)))) -> f_flat.0(down.0(f.0(f.0(b.)))) 544.15/242.34 down.0(f.0(f.0(f.0(g.0(y16))))) -> f_flat.0(down.0(f.0(f.0(g.0(y16))))) 544.15/242.34 down.0(f.0(f.0(f.1(g.1(y16))))) -> f_flat.0(down.0(f.0(f.1(g.1(y16))))) 544.15/242.34 down.0(f.0(f.0(f.0(c.)))) -> f_flat.0(down.0(f.0(f.0(c.)))) 544.15/242.34 down.0(f.0(f.0(f.1(fresh_constant.)))) -> f_flat.0(down.0(f.0(f.1(fresh_constant.)))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(a.))))) -> f_flat.0(down.0(f.0(f.0(f.0(a.))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(b.))))) -> f_flat.0(down.0(f.0(f.0(f.0(b.))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(g.0(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.0(g.0(y22)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.1(g.1(y22)))))) -> f_flat.0(down.0(f.0(f.0(f.1(g.1(y22)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(c.))))) -> f_flat.0(down.0(f.0(f.0(f.0(c.))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) -> f_flat.0(down.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(g.0(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(g.0(y28))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.1(g.1(y28))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(g.1(y28))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(g.0(y34)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(g.1(y34)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y40))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y40))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y46)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y46)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(y52))))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(y52))))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) -> f_flat.0(down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.34 g_flat.0(up.0(x_1)) -> up.0(g.0(x_1)) 544.15/242.34 g_flat.0(up.1(x_1)) -> up.1(g.1(x_1)) 544.15/242.34 f_flat.0(up.0(x_1)) -> up.0(f.0(x_1)) 544.15/242.34 down.0(g.0(b.)) -> g_flat.0(down.0(b.)) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x))))))))))) -> up.0(c.) 544.15/242.34 down.0(g.0(f.0(y6))) -> g_flat.0(down.0(f.0(y6))) 544.15/242.34 down.0(g.0(f.1(y6))) -> g_flat.0(down.0(f.1(y6))) 544.15/242.34 down.0(g.0(g.0(a.))) -> g_flat.0(down.0(g.0(a.))) 544.15/242.34 down.0(g.0(g.0(f.0(y12)))) -> g_flat.0(down.0(g.0(f.0(y12)))) 544.15/242.34 down.0(g.0(g.0(f.1(y12)))) -> g_flat.0(down.0(g.0(f.1(y12)))) 544.15/242.34 down.0(g.0(g.0(b.))) -> g_flat.0(down.0(g.0(b.))) 544.15/242.34 down.0(g.0(g.0(c.))) -> g_flat.0(down.0(g.0(c.))) 544.15/242.34 down.0(g.0(g.0(g.0(a.)))) -> g_flat.0(down.0(g.0(g.0(a.)))) 544.15/242.34 down.0(g.0(g.0(g.0(f.0(y18))))) -> g_flat.0(down.0(g.0(g.0(f.0(y18))))) 544.15/242.34 down.0(g.0(g.0(g.0(f.1(y18))))) -> g_flat.0(down.0(g.0(g.0(f.1(y18))))) 544.15/242.34 down.0(g.0(g.0(g.0(b.)))) -> g_flat.0(down.0(g.0(g.0(b.)))) 544.15/242.34 down.0(g.0(g.0(g.0(c.)))) -> g_flat.0(down.0(g.0(g.0(c.)))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(a.))))) -> g_flat.0(down.0(g.0(g.0(g.0(a.))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(f.0(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.0(y24)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(f.1(y24)))))) -> g_flat.0(down.0(g.0(g.0(g.0(f.1(y24)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(b.))))) -> g_flat.0(down.0(g.0(g.0(g.0(b.))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(c.))))) -> g_flat.0(down.0(g.0(g.0(g.0(c.))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(f.0(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.0(y30))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(f.1(y30))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(f.1(y30))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.0(y36)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(f.1(y36)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y42))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y42))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y48)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y48)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(y54))))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(y54))))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) -> g_flat.0(down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.34 down.0(b.) -> up.0(g.0(b.)) 544.15/242.34 down.0(a.) -> up.0(f.0(a.)) 544.15/242.34 544.15/242.34 The set Q consists of the following terms: 544.15/242.34 544.15/242.34 down.0(a.) 544.15/242.34 down.0(b.) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(x0))))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(x0))))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(x0))))))))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(x0))))))))))) 544.15/242.34 down.0(f.0(a.)) 544.15/242.34 down.0(f.0(b.)) 544.15/242.34 down.0(f.0(g.0(x0))) 544.15/242.34 down.0(f.1(g.1(x0))) 544.15/242.34 down.0(f.0(c.)) 544.15/242.34 down.0(f.1(fresh_constant.)) 544.15/242.34 down.0(g.0(a.)) 544.15/242.34 down.0(g.0(f.0(x0))) 544.15/242.34 down.0(g.0(f.1(x0))) 544.15/242.34 down.0(g.0(b.)) 544.15/242.34 down.0(g.0(c.)) 544.15/242.34 down.1(g.1(fresh_constant.)) 544.15/242.34 down.0(f.0(f.0(a.))) 544.15/242.34 down.0(f.0(f.0(b.))) 544.15/242.34 down.0(f.0(f.0(g.0(x0)))) 544.15/242.34 down.0(f.0(f.1(g.1(x0)))) 544.15/242.34 down.0(f.0(f.0(c.))) 544.15/242.34 down.0(f.0(f.1(fresh_constant.))) 544.15/242.34 down.0(g.0(g.0(a.))) 544.15/242.34 down.0(g.0(g.0(f.0(x0)))) 544.15/242.34 down.0(g.0(g.0(f.1(x0)))) 544.15/242.34 down.0(g.0(g.0(b.))) 544.15/242.34 down.0(g.0(g.0(c.))) 544.15/242.34 down.1(g.1(g.1(fresh_constant.))) 544.15/242.34 down.0(f.0(f.0(f.0(a.)))) 544.15/242.34 down.0(f.0(f.0(f.0(b.)))) 544.15/242.34 down.0(f.0(f.0(f.0(g.0(x0))))) 544.15/242.34 down.0(f.0(f.0(f.1(g.1(x0))))) 544.15/242.34 down.0(f.0(f.0(f.0(c.)))) 544.15/242.34 down.0(f.0(f.0(f.1(fresh_constant.)))) 544.15/242.34 down.0(g.0(g.0(g.0(a.)))) 544.15/242.34 down.0(g.0(g.0(g.0(f.0(x0))))) 544.15/242.34 down.0(g.0(g.0(g.0(f.1(x0))))) 544.15/242.34 down.0(g.0(g.0(g.0(b.)))) 544.15/242.34 down.0(g.0(g.0(g.0(c.)))) 544.15/242.34 down.1(g.1(g.1(g.1(fresh_constant.)))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(a.))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(b.))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(g.0(x0)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.1(g.1(x0)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(c.))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.1(fresh_constant.))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(a.))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(f.0(x0)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(f.1(x0)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(b.))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(c.))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(fresh_constant.))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(a.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(b.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(c.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(a.)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(b.)))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(c.)))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.))))))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(a.)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(b.)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(g.0(x0))))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(g.1(x0))))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(c.)))))))))) 544.15/242.34 down.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.0(f.1(fresh_constant.)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(a.)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.0(x0))))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(f.1(x0))))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(b.)))))))))) 544.15/242.34 down.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(g.0(c.)))))))))) 544.15/242.34 down.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(g.1(fresh_constant.)))))))))) 544.15/242.34 f_flat.0(up.0(x0)) 544.15/242.34 f_flat.0(up.1(x0)) 544.15/242.34 g_flat.0(up.0(x0)) 544.15/242.34 g_flat.0(up.1(x0)) 544.15/242.34 544.15/242.34 We have to consider all minimal (P,Q,R)-chains. 544.15/242.34 ---------------------------------------- 544.15/242.34 544.15/242.34 (1372) PisEmptyProof (SOUND) 544.15/242.34 The TRS P is empty. Hence, there is no (P,Q,R) chain. 544.15/242.34 ---------------------------------------- 544.15/242.34 544.15/242.34 (1373) 544.15/242.34 TRUE 544.15/242.34 544.15/242.34 ---------------------------------------- 544.15/242.34 544.15/242.34 (1374) 544.15/242.34 Obligation: 544.15/242.34 Q DP problem: 544.15/242.34 The TRS P consists of the following rules: 544.15/242.34 544.15/242.34 TOP(up(f(g(x0)))) -> TOP(f_flat(down(g(x0)))) 544.15/242.34 TOP(up(g(f(x0)))) -> TOP(g_flat(down(f(x0)))) 544.15/242.34 TOP(up(g(g(f(x0))))) -> TOP(g_flat(g_flat(down(f(x0))))) 544.15/242.34 TOP(up(f(f(g(x0))))) -> TOP(f_flat(f_flat(down(g(x0))))) 544.15/242.34 TOP(up(f(f(f(g(x0)))))) -> TOP(f_flat(f_flat(f_flat(down(g(x0)))))) 544.15/242.34 TOP(up(g(g(g(f(x0)))))) -> TOP(g_flat(g_flat(g_flat(down(f(x0)))))) 544.15/242.34 TOP(up(f(f(f(f(g(x0))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))) 544.15/242.34 TOP(up(g(g(g(g(f(x0))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))) 544.15/242.34 TOP(up(f(f(f(f(f(g(x0)))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))) 544.15/242.34 TOP(up(g(g(g(g(g(f(x0)))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))) 544.15/242.34 TOP(up(f(f(f(f(f(f(g(x0))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))) 544.15/242.34 TOP(up(g(g(g(g(g(g(f(x0))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))) 544.15/242.34 TOP(up(f(f(f(f(f(f(f(g(x0)))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))) 544.15/242.34 TOP(up(g(g(g(g(g(g(g(f(x0)))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))) 544.15/242.34 TOP(up(f(f(f(f(f(f(f(f(g(x0))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0))))))))))) 544.15/242.34 TOP(up(g(g(g(g(g(g(g(g(f(x0))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0))))))))))) 544.15/242.34 TOP(up(f(f(f(f(f(f(f(f(f(g(x0)))))))))))) -> TOP(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(f_flat(down(g(x0)))))))))))) 544.15/242.34 TOP(up(g(g(g(g(g(g(g(g(g(f(x0)))))))))))) -> TOP(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(g_flat(down(f(x0)))))))))))) 544.15/242.34 544.15/242.34 The TRS R consists of the following rules: 544.15/242.34 544.15/242.34 down(f(a)) -> f_flat(down(a)) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(f(x))))))))))) -> up(c) 544.15/242.34 down(f(g(y4))) -> f_flat(down(g(y4))) 544.15/242.34 down(f(f(a))) -> f_flat(down(f(a))) 544.15/242.34 down(f(f(b))) -> f_flat(down(f(b))) 544.15/242.34 down(f(f(g(y10)))) -> f_flat(down(f(g(y10)))) 544.15/242.34 down(f(f(c))) -> f_flat(down(f(c))) 544.15/242.34 down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant))) 544.15/242.34 down(f(f(f(a)))) -> f_flat(down(f(f(a)))) 544.15/242.34 down(f(f(f(b)))) -> f_flat(down(f(f(b)))) 544.15/242.34 down(f(f(f(g(y16))))) -> f_flat(down(f(f(g(y16))))) 544.15/242.34 down(f(f(f(c)))) -> f_flat(down(f(f(c)))) 544.15/242.34 down(f(f(f(fresh_constant)))) -> f_flat(down(f(f(fresh_constant)))) 544.15/242.34 down(f(f(f(f(a))))) -> f_flat(down(f(f(f(a))))) 544.15/242.34 down(f(f(f(f(b))))) -> f_flat(down(f(f(f(b))))) 544.15/242.34 down(f(f(f(f(g(y22)))))) -> f_flat(down(f(f(f(g(y22)))))) 544.15/242.34 down(f(f(f(f(c))))) -> f_flat(down(f(f(f(c))))) 544.15/242.34 down(f(f(f(f(fresh_constant))))) -> f_flat(down(f(f(f(fresh_constant))))) 544.15/242.34 down(f(f(f(f(f(a)))))) -> f_flat(down(f(f(f(f(a)))))) 544.15/242.34 down(f(f(f(f(f(b)))))) -> f_flat(down(f(f(f(f(b)))))) 544.15/242.34 down(f(f(f(f(f(g(y28))))))) -> f_flat(down(f(f(f(f(g(y28))))))) 544.15/242.34 down(f(f(f(f(f(c)))))) -> f_flat(down(f(f(f(f(c)))))) 544.15/242.34 down(f(f(f(f(f(fresh_constant)))))) -> f_flat(down(f(f(f(f(fresh_constant)))))) 544.15/242.34 down(f(f(f(f(f(f(a))))))) -> f_flat(down(f(f(f(f(f(a))))))) 544.15/242.34 down(f(f(f(f(f(f(b))))))) -> f_flat(down(f(f(f(f(f(b))))))) 544.15/242.34 down(f(f(f(f(f(f(g(y34)))))))) -> f_flat(down(f(f(f(f(f(g(y34)))))))) 544.15/242.34 down(f(f(f(f(f(f(c))))))) -> f_flat(down(f(f(f(f(f(c))))))) 544.15/242.34 down(f(f(f(f(f(f(fresh_constant))))))) -> f_flat(down(f(f(f(f(f(fresh_constant))))))) 544.15/242.34 down(f(f(f(f(f(f(f(a)))))))) -> f_flat(down(f(f(f(f(f(f(a)))))))) 544.15/242.34 down(f(f(f(f(f(f(f(b)))))))) -> f_flat(down(f(f(f(f(f(f(b)))))))) 544.15/242.34 down(f(f(f(f(f(f(f(g(y40))))))))) -> f_flat(down(f(f(f(f(f(f(g(y40))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(c)))))))) -> f_flat(down(f(f(f(f(f(f(c)))))))) 544.15/242.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) -> f_flat(down(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(a))))))))) -> f_flat(down(f(f(f(f(f(f(f(a))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(b))))))))) -> f_flat(down(f(f(f(f(f(f(f(b))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(g(y46)))))))))) -> f_flat(down(f(f(f(f(f(f(f(g(y46)))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(c))))))))) -> f_flat(down(f(f(f(f(f(f(f(c))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) -> f_flat(down(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(g(y52))))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(g(y52))))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) -> f_flat(down(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.34 g_flat(up(x_1)) -> up(g(x_1)) 544.15/242.34 f_flat(up(x_1)) -> up(f(x_1)) 544.15/242.34 down(g(b)) -> g_flat(down(b)) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(g(x))))))))))) -> up(c) 544.15/242.34 down(g(f(y6))) -> g_flat(down(f(y6))) 544.15/242.34 down(g(g(a))) -> g_flat(down(g(a))) 544.15/242.34 down(g(g(f(y12)))) -> g_flat(down(g(f(y12)))) 544.15/242.34 down(g(g(b))) -> g_flat(down(g(b))) 544.15/242.34 down(g(g(c))) -> g_flat(down(g(c))) 544.15/242.34 down(g(g(g(a)))) -> g_flat(down(g(g(a)))) 544.15/242.34 down(g(g(g(f(y18))))) -> g_flat(down(g(g(f(y18))))) 544.15/242.34 down(g(g(g(b)))) -> g_flat(down(g(g(b)))) 544.15/242.34 down(g(g(g(c)))) -> g_flat(down(g(g(c)))) 544.15/242.34 down(g(g(g(g(a))))) -> g_flat(down(g(g(g(a))))) 544.15/242.34 down(g(g(g(g(f(y24)))))) -> g_flat(down(g(g(g(f(y24)))))) 544.15/242.34 down(g(g(g(g(b))))) -> g_flat(down(g(g(g(b))))) 544.15/242.34 down(g(g(g(g(c))))) -> g_flat(down(g(g(g(c))))) 544.15/242.34 down(g(g(g(g(g(a)))))) -> g_flat(down(g(g(g(g(a)))))) 544.15/242.34 down(g(g(g(g(g(f(y30))))))) -> g_flat(down(g(g(g(g(f(y30))))))) 544.15/242.34 down(g(g(g(g(g(b)))))) -> g_flat(down(g(g(g(g(b)))))) 544.15/242.34 down(g(g(g(g(g(c)))))) -> g_flat(down(g(g(g(g(c)))))) 544.15/242.34 down(g(g(g(g(g(g(a))))))) -> g_flat(down(g(g(g(g(g(a))))))) 544.15/242.34 down(g(g(g(g(g(g(f(y36)))))))) -> g_flat(down(g(g(g(g(g(f(y36)))))))) 544.15/242.34 down(g(g(g(g(g(g(b))))))) -> g_flat(down(g(g(g(g(g(b))))))) 544.15/242.34 down(g(g(g(g(g(g(c))))))) -> g_flat(down(g(g(g(g(g(c))))))) 544.15/242.34 down(g(g(g(g(g(g(g(a)))))))) -> g_flat(down(g(g(g(g(g(g(a)))))))) 544.15/242.34 down(g(g(g(g(g(g(g(f(y42))))))))) -> g_flat(down(g(g(g(g(g(g(f(y42))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(b)))))))) -> g_flat(down(g(g(g(g(g(g(b)))))))) 544.15/242.34 down(g(g(g(g(g(g(g(c)))))))) -> g_flat(down(g(g(g(g(g(g(c)))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(a))))))))) -> g_flat(down(g(g(g(g(g(g(g(a))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(f(y48)))))))))) -> g_flat(down(g(g(g(g(g(g(g(f(y48)))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(b))))))))) -> g_flat(down(g(g(g(g(g(g(g(b))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(c))))))))) -> g_flat(down(g(g(g(g(g(g(g(c))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(f(y54))))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(f(y54))))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) -> g_flat(down(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.34 down(b) -> up(g(b)) 544.15/242.34 down(a) -> up(f(a)) 544.15/242.34 544.15/242.34 The set Q consists of the following terms: 544.15/242.34 544.15/242.34 down(a) 544.15/242.34 down(b) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(f(x0))))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(g(x0))))))))))) 544.15/242.34 down(f(a)) 544.15/242.34 down(f(b)) 544.15/242.34 down(f(g(x0))) 544.15/242.34 down(f(c)) 544.15/242.34 down(f(fresh_constant)) 544.15/242.34 down(g(a)) 544.15/242.34 down(g(f(x0))) 544.15/242.34 down(g(b)) 544.15/242.34 down(g(c)) 544.15/242.34 down(g(fresh_constant)) 544.15/242.34 down(f(f(a))) 544.15/242.34 down(f(f(b))) 544.15/242.34 down(f(f(g(x0)))) 544.15/242.34 down(f(f(c))) 544.15/242.34 down(f(f(fresh_constant))) 544.15/242.34 down(g(g(a))) 544.15/242.34 down(g(g(f(x0)))) 544.15/242.34 down(g(g(b))) 544.15/242.34 down(g(g(c))) 544.15/242.34 down(g(g(fresh_constant))) 544.15/242.34 down(f(f(f(a)))) 544.15/242.34 down(f(f(f(b)))) 544.15/242.34 down(f(f(f(g(x0))))) 544.15/242.34 down(f(f(f(c)))) 544.15/242.34 down(f(f(f(fresh_constant)))) 544.15/242.34 down(g(g(g(a)))) 544.15/242.34 down(g(g(g(f(x0))))) 544.15/242.34 down(g(g(g(b)))) 544.15/242.34 down(g(g(g(c)))) 544.15/242.34 down(g(g(g(fresh_constant)))) 544.15/242.34 down(f(f(f(f(a))))) 544.15/242.34 down(f(f(f(f(b))))) 544.15/242.34 down(f(f(f(f(g(x0)))))) 544.15/242.34 down(f(f(f(f(c))))) 544.15/242.34 down(f(f(f(f(fresh_constant))))) 544.15/242.34 down(g(g(g(g(a))))) 544.15/242.34 down(g(g(g(g(f(x0)))))) 544.15/242.34 down(g(g(g(g(b))))) 544.15/242.34 down(g(g(g(g(c))))) 544.15/242.34 down(g(g(g(g(fresh_constant))))) 544.15/242.34 down(f(f(f(f(f(a)))))) 544.15/242.34 down(f(f(f(f(f(b)))))) 544.15/242.34 down(f(f(f(f(f(g(x0))))))) 544.15/242.34 down(f(f(f(f(f(c)))))) 544.15/242.34 down(f(f(f(f(f(fresh_constant)))))) 544.15/242.34 down(g(g(g(g(g(a)))))) 544.15/242.34 down(g(g(g(g(g(f(x0))))))) 544.15/242.34 down(g(g(g(g(g(b)))))) 544.15/242.34 down(g(g(g(g(g(c)))))) 544.15/242.34 down(g(g(g(g(g(fresh_constant)))))) 544.15/242.34 down(f(f(f(f(f(f(a))))))) 544.15/242.34 down(f(f(f(f(f(f(b))))))) 544.15/242.34 down(f(f(f(f(f(f(g(x0)))))))) 544.15/242.34 down(f(f(f(f(f(f(c))))))) 544.15/242.34 down(f(f(f(f(f(f(fresh_constant))))))) 544.15/242.34 down(g(g(g(g(g(g(a))))))) 544.15/242.34 down(g(g(g(g(g(g(f(x0)))))))) 544.15/242.34 down(g(g(g(g(g(g(b))))))) 544.15/242.34 down(g(g(g(g(g(g(c))))))) 544.15/242.34 down(g(g(g(g(g(g(fresh_constant))))))) 544.15/242.34 down(f(f(f(f(f(f(f(a)))))))) 544.15/242.34 down(f(f(f(f(f(f(f(b)))))))) 544.15/242.34 down(f(f(f(f(f(f(f(g(x0))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(c)))))))) 544.15/242.34 down(f(f(f(f(f(f(f(fresh_constant)))))))) 544.15/242.34 down(g(g(g(g(g(g(g(a)))))))) 544.15/242.34 down(g(g(g(g(g(g(g(f(x0))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(b)))))))) 544.15/242.34 down(g(g(g(g(g(g(g(c)))))))) 544.15/242.34 down(g(g(g(g(g(g(g(fresh_constant)))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(a))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(b))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(g(x0)))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(c))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(fresh_constant))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(a))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(f(x0)))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(b))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(c))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(fresh_constant))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(a)))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(b)))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(g(x0))))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(c)))))))))) 544.15/242.34 down(f(f(f(f(f(f(f(f(f(fresh_constant)))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(a)))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(f(x0))))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(b)))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(c)))))))))) 544.15/242.34 down(g(g(g(g(g(g(g(g(g(fresh_constant)))))))))) 544.15/242.34 f_flat(up(x0)) 544.15/242.34 g_flat(up(x0)) 544.15/242.34 544.15/242.34 We have to consider all minimal (P,Q,R)-chains. 544.66/242.81 EOF